Measures of Disease Frequency: Incidence and Prevalence

Incidence and prevalence are two important measures of disease frequency. Incidence measures the speed at which new cases of a disease are emerging, while prevalence measures the burden of disease within a population. Cumulative incidence and incidence rate are two types of incidence measures, while point prevalence and period prevalence are two types of prevalence measures.

Cumulative incidence is the average risk of getting a disease over a certain period of time, while incidence rate is a measure of the speed at which new cases are emerging. Prevalence is a proportion and is a measure of the burden of disease within a population. Point prevalence measures the number of cases in a defined population at a specific point in time, while period prevalence measures the number of identified cases during a specified period of time.

It is important to note that prevalence is equal to incidence multiplied by the duration of the condition. In chronic diseases, the prevalence is much greater than the incidence. The incidence rate is stated in units of person-time, while cumulative incidence is always a proportion. When describing cumulative incidence, it is necessary to give the follow-up period over which the risk is estimated. In acute diseases, the prevalence and incidence may be similar, while for conditions such as the common cold, the incidence may be greater than the prevalence.

Incidence is a useful measure to study disease etiology and risk factors, while prevalence is useful for health resource planning. Understanding these measures of disease frequency is important for public health professionals and researchers in order to effectively monitor and address the burden of disease within populations.

A cost benefit analysis is a method of evaluating whether the benefits of an intervention outweigh its costs, using monetary units as the common measurement. Typically, this type of analysis is employed by funding bodies to make decisions about financing, such as whether to allocate resources for a new delivery suite of electroconvulsive therapy suite.

Measures of Disease Frequency: Incidence and Prevalence

Incidence and prevalence are two important measures of disease frequency. Incidence measures the speed at which new cases of a disease are emerging, while prevalence measures the burden of disease within a population. Cumulative incidence and incidence rate are two types of incidence measures, while point prevalence and period prevalence are two types of prevalence measures.

Cumulative incidence is the average risk of getting a disease over a certain period of time, while incidence rate is a measure of the speed at which new cases are emerging. Prevalence is a proportion and is a measure of the burden of disease within a population. Point prevalence measures the number of cases in a defined population at a specific point in time, while period prevalence measures the number of identified cases during a specified period of time.

It is important to note that prevalence is equal to incidence multiplied by the duration of the condition. In chronic diseases, the prevalence is much greater than the incidence. The incidence rate is stated in units of person-time, while cumulative incidence is always a proportion. When describing cumulative incidence, it is necessary to give the follow-up period over which the risk is estimated. In acute diseases, the prevalence and incidence may be similar, while for conditions such as the common cold, the incidence may be greater than the prevalence.

Incidence is a useful measure to study disease etiology and risk factors, while prevalence is useful for health resource planning. Understanding these measures of disease frequency is important for public health professionals and researchers in order to effectively monitor and address the burden of disease within populations.

The mean, mode, and median are all measures of central tendency.

Measures of dispersion are used to indicate the variation of spread of a data set, often in conjunction with a measure of central tendency such as the mean of median. The range, which is the difference between the largest and smallest value, is the simplest measure of dispersion. The interquartile range, which is the difference between the 3rd and 1st quartiles, is another useful measure. Quartiles divide a data set into quarters, and the interquartile range can provide additional information about the spread of the data. However, to get a more representative idea of spread, measures such as the variance and standard deviation are needed. The variance gives an indication of how much the items in the data set vary from the mean, while the standard deviation reflects the distribution of individual scores around their mean. The standard deviation is expressed in the same units as the data set and can be used to indicate how confident we are that data points lie within a particular range. The standard error of the mean is an inferential statistic used to estimate the population mean and is a measure of the spread expected for the mean of the observations. Confidence intervals are often presented alongside sample results such as the mean value, indicating a range that is likely to contain the true value.

Clinical tests are used to determine the presence of absence of a disease of condition. To interpret test results, it is important to have a working knowledge of statistics used to describe them. Two by two tables are commonly used to calculate test statistics such as sensitivity and specificity. Sensitivity refers to the proportion of people with a condition that the test correctly identifies, while specificity refers to the proportion of people without a condition that the test correctly identifies. Accuracy tells us how closely a test measures to its true value, while predictive values help us understand the likelihood of having a disease based on a positive of negative test result. Likelihood ratios combine sensitivity and specificity into a single figure that can refine our estimation of the probability of a disease being present. Pre and post-test odds and probabilities can also be calculated to better understand the likelihood of having a disease before and after a test is carried out. Fagan’s nomogram is a useful tool for calculating post-test probabilities.

Validity in statistics refers to how accurately something measures what it claims to measure. There are two main types of validity: internal and external. Internal validity refers to the confidence we have in the cause and effect relationship in a study, while external validity refers to the degree to which the conclusions of a study can be applied to other people, places, and times. There are various threats to both internal and external validity, such as sampling, measurement instrument obtrusiveness, and reactive effects of setting. Additionally, there are several subtypes of validity, including face validity, content validity, criterion validity, and construct validity. Each subtype has its own specific focus and methods for testing validity.

Choosing the right statistical test can be challenging, but understanding the basic principles can help. Different tests have different assumptions, and using the wrong one can lead to inaccurate results. To identify the appropriate test, a flow chart can be used based on three main factors: the type of dependent variable, the type of data, and whether the groups/samples are independent of dependent. It is important to know which tests are parametric and non-parametric, as well as their alternatives. For example, the chi-squared test is used to assess differences in categorical variables and is non-parametric, while Pearson’s correlation coefficient measures linear correlation between two variables and is parametric. T-tests are used to compare means between two groups, and ANOVA is used to compare means between more than two groups. Non-parametric equivalents to ANOVA include the Kruskal-Wallis analysis of ranks, the Median test, Friedman’s two-way analysis of variance, and Cochran Q test. Understanding these tests and their assumptions can help researchers choose the appropriate statistical test for their data.

Case-studies and case-series can have an experimental nature due to the potential involvement of interventions of treatments.

Types of Primary Research Studies and Their Advantages and Disadvantages

Primary research studies can be categorized into six types based on the research question they aim to address. The best type of study for each question type is listed in the table below. There are two main types of study design: experimental and observational. Experimental studies involve an intervention, while observational studies do not. The advantages and disadvantages of each study type are summarized in the table below.

Type of Question Best Type of Study

Therapy Randomized controlled trial (RCT), cohort, case control, case series
Diagnosis Cohort studies with comparison to gold standard test
Prognosis Cohort studies, case control, case series
Etiology/Harm RCT, cohort studies, case control, case series
Prevention RCT, cohort studies, case control, case series
Cost Economic analysis

Study Type Advantages Disadvantages

Randomized Controlled Trial – Unbiased distribution of confounders – Blinding more likely – Randomization facilitates statistical analysis – Expensive – Time-consuming – Volunteer bias – Ethically problematic at times
Cohort Study – Ethically safe – Subjects can be matched – Can establish timing and directionality of events – Eligibility criteria and outcome assessments can be standardized – Administratively easier and cheaper than RCT – Controls may be difficult to identify – Exposure may be linked to a hidden confounder – Blinding is difficult – Randomization not present – For rare disease, large sample sizes of long follow-up necessary
Case-Control Study – Quick and cheap – Only feasible method for very rare disorders of those with long lag between exposure and outcome – Fewer subjects needed than cross-sectional studies – Reliance on recall of records to determine exposure status – Confounders – Selection of control groups is difficult – Potential bias: recall, selection
Cross-Sectional Survey – Cheap and simple – Ethically safe – Establishes association at most, not causality – Recall bias susceptibility – Confounders may be unequally distributed – Neyman bias – Group sizes may be unequal
Ecological Study – Cheap and simple – Ethically safe – Ecological fallacy (when relationships which exist for groups are assumed to also be true for individuals)

In conclusion, the choice of study type depends on the research question being addressed. Each study type has its own advantages and disadvantages, and researchers should carefully consider these when designing their studies.

Measures of dispersion are used to indicate the variation of spread of a data set, often in conjunction with a measure of central tendency such as the mean of median. The range, which is the difference between the largest and smallest value, is the simplest measure of dispersion. The interquartile range, which is the difference between the 3rd and 1st quartiles, is another useful measure. Quartiles divide a data set into quarters, and the interquartile range can provide additional information about the spread of the data. However, to get a more representative idea of spread, measures such as the variance and standard deviation are needed. The variance gives an indication of how much the items in the data set vary from the mean, while the standard deviation reflects the distribution of individual scores around their mean. The standard deviation is expressed in the same units as the data set and can be used to indicate how confident we are that data points lie within a particular range. The standard error of the mean is an inferential statistic used to estimate the population mean and is a measure of the spread expected for the mean of the observations. Confidence intervals are often presented alongside sample results such as the mean value, indicating a range that is likely to contain the true value.

To calculate the event rates for the medication and control groups, we divide the number of events by the total number of subjects in each group. For the medication group, the event rate is 0.2 (30/150), and for the control group, it is 0.4 (80/200).

We can also calculate the absolute risk reduction (ARR) by subtracting the event rate in the medication group from the event rate in the control group: ARR = CER – EER = 0.4 – 0.2 = 0.2.

Finally, we can use the ARR to calculate the number needed to treat (NNT), which represents the number of patients who need to be treated with the medication to prevent one additional event compared to the control group. NNT = 1/ARR = 1/0.2 = 5.

The most crucial factor in Hill’s criteria for causation is temporality, of the temporal relationship between exposure and outcome. It is imperative that the exposure to a potential causal factor, such as factor ‘A’, always occurs before the onset of the disease. This criterion is the only absolute requirement for causation. The other criteria include the strength of the relationship, dose-response relationship, consistency, plausibility, consideration of alternative explanations, experimental evidence, specificity, and coherence.

Neyman bias arises when a research study is examining a condition that is marked by either undetected cases of cases that result in early deaths, leading to the exclusion of such cases from the analysis.

Types of Bias in Statistics

Bias is a systematic error that can lead to incorrect conclusions. Confounding factors are variables that are associated with both the outcome and the exposure but have no causative role. Confounding can be addressed in the design and analysis stage of a study. The main method of controlling confounding in the analysis phase is stratification analysis. The main methods used in the design stage are matching, randomization, and restriction of participants.

There are two main types of bias: selection bias and information bias. Selection bias occurs when the selected sample is not a representative sample of the reference population. Disease spectrum bias, self-selection bias, participation bias, incidence-prevalence bias, exclusion bias, publication of dissemination bias, citation bias, and Berkson’s bias are all subtypes of selection bias. Information bias occurs when gathered information about exposure, outcome, of both is not correct and there was an error in measurement. Detection bias, recall bias, lead time bias, interviewer/observer bias, verification and work-up bias, Hawthorne effect, and ecological fallacy are all subtypes of information bias.

Levels and Grades of Evidence in Evidence-Based Medicine

To evaluate the quality of evidence on a subject of question, levels of grades are used. The traditional hierarchy approach places systematic reviews of randomized control trials at the top and case-series/report at the bottom. However, this approach is overly simplistic as certain research questions cannot be answered using RCTs. To address this, the Oxford Centre for Evidence-Based Medicine introduced their 2011 Levels of Evidence system, which separates the type of study questions and gives a hierarchy for each.

The grading approach to be aware of is the GRADE system, which classifies the quality of evidence as high, moderate, low, of very low. The process begins by formulating a study question and identifying specific outcomes. Outcomes are then graded as critical of important. The evidence is then gathered and criteria are used to grade the evidence, with the type of evidence being a significant factor. Evidence can be promoted of downgraded based on certain criteria, such as limitations to study quality, inconsistency, uncertainty about directness, imprecise of sparse data, and reporting bias. The GRADE system allows for the promotion of observational studies to high-quality evidence under the right circumstances.

Levels and Grades of Evidence in Evidence-Based Medicine

To evaluate the quality of evidence on a subject of question, levels of grades are used. The traditional hierarchy approach places systematic reviews of randomized control trials at the top and case-series/report at the bottom. However, this approach is overly simplistic as certain research questions cannot be answered using RCTs. To address this, the Oxford Centre for Evidence-Based Medicine introduced their 2011 Levels of Evidence system, which separates the type of study questions and gives a hierarchy for each.

The grading approach to be aware of is the GRADE system, which classifies the quality of evidence as high, moderate, low, of very low. The process begins by formulating a study question and identifying specific outcomes. Outcomes are then graded as critical of important. The evidence is then gathered and criteria are used to grade the evidence, with the type of evidence being a significant factor. Evidence can be promoted of downgraded based on certain criteria, such as limitations to study quality, inconsistency, uncertainty about directness, imprecise of sparse data, and reporting bias. The GRADE system allows for the promotion of observational studies to high-quality evidence under the right circumstances.

When comparing new diagnostic tests with gold standard tests, work-up bias can be a concern. Clinicians may be hesitant to order the gold standard test unless the new test yields a positive result, as the gold standard test may involve invasive procedures like tissue biopsy. This can significantly skew the study’s findings and affect metrics such as sensitivity and specificity. While it may not always be possible to eliminate work-up bias, researchers must account for it in their analysis.

Types of Bias in Statistics

Bias is a systematic error that can lead to incorrect conclusions. Confounding factors are variables that are associated with both the outcome and the exposure but have no causative role. Confounding can be addressed in the design and analysis stage of a study. The main method of controlling confounding in the analysis phase is stratification analysis. The main methods used in the design stage are matching, randomization, and restriction of participants.

There are two main types of bias: selection bias and information bias. Selection bias occurs when the selected sample is not a representative sample of the reference population. Disease spectrum bias, self-selection bias, participation bias, incidence-prevalence bias, exclusion bias, publication of dissemination bias, citation bias, and Berkson’s bias are all subtypes of selection bias. Information bias occurs when gathered information about exposure, outcome, of both is not correct and there was an error in measurement. Detection bias, recall bias, lead time bias, interviewer/observer bias, verification and work-up bias, Hawthorne effect, and ecological fallacy are all subtypes of information bias.

Scales of Measurement in Statistics

In the 1940s, Stanley Smith Stevens introduced four scales of measurement to categorize data variables. Knowing the scale of measurement for a variable is crucial in selecting the appropriate statistical analysis. The four scales of measurement are ratio, interval, ordinal, and nominal.

Ratio scales are similar to interval scales, but they have true zero points. Examples of ratio scales include weight, time, and length. Interval scales measure the difference between two values, and one unit on the scale represents the same magnitude on the trait of characteristic being measured across the whole range of the scale. The Fahrenheit scale for temperature is an example of an interval scale.

Ordinal scales categorize observed values into set categories that can be ordered, but the intervals between each value are uncertain. Examples of ordinal scales include social class, education level, and income level. Nominal scales categorize observed values into set categories that have no particular order of hierarchy. Examples of nominal scales include genotype, blood type, and political party.

Data can also be categorized as quantitative of qualitative. Quantitative variables take on numeric values and can be further classified into discrete and continuous types. Qualitative variables do not take on numerical values and are usually names. Some qualitative variables have an inherent order in their categories and are described as ordinal. Qualitative variables are also called categorical of nominal variables. When a qualitative variable has only two categories, it is called a binary variable.

The specificity of the GHQ test is 91%, meaning that 91% of individuals who do not have depression are correctly identified as such by the general practitioner using the test.

The acronym ICER stands for incremental cost-effectiveness ratio.

Methods of Economic Evaluation

There are four main methods of economic evaluation: cost-effectiveness analysis (CEA), cost-benefit analysis (CBA), cost-utility analysis (CUA), and cost-minimisation analysis (CMA). While all four methods capture costs, they differ in how they assess health effects.

Cost-effectiveness analysis (CEA) compares interventions by relating costs to a single clinical measure of effectiveness, such as symptom reduction of improvement in activities of daily living. The cost-effectiveness ratio is calculated as total cost divided by units of effectiveness. CEA is typically used when CBA cannot be performed due to the inability to monetise benefits.

Cost-benefit analysis (CBA) measures all costs and benefits of an intervention in monetary terms to establish which alternative has the greatest net benefit. CBA requires that all consequences of an intervention, such as life-years saved, treatment side-effects, symptom relief, disability, pain, and discomfort, are allocated a monetary value. CBA is rarely used in mental health service evaluation due to the difficulty in converting benefits from mental health programmes into monetary values.

Cost-utility analysis (CUA) is a special form of CEA in which health benefits/outcomes are measured in broader, more generic ways, enabling comparisons between treatments for different diseases and conditions. Multidimensional health outcomes are measured by a single preference- of utility-based index such as the Quality-Adjusted-Life-Years (QALY). QALYs are a composite measure of gains in life expectancy and health-related quality of life. CUA allows for comparisons across treatments for different conditions.

Cost-minimisation analysis (CMA) is an economic evaluation in which the consequences of competing interventions are the same, and only inputs, i.e. costs, are taken into consideration. The aim is to decide the least costly way of achieving the same outcome.

Costs in Economic Evaluation Studies

There are three main types of costs in economic evaluation studies: direct, indirect, and intangible. Direct costs are associated directly with the healthcare intervention, such as staff time, medical supplies, cost of travel for the patient, childcare costs for the patient, and costs falling on other social sectors such as domestic help from social services. Indirect costs are incurred by the reduced productivity of the patient, such as time off work, reduced work productivity, and time spent caring for the patient by relatives. Intangible costs are difficult to measure, such as pain of suffering on the part of the patient.

The t-test is appropriate for analyzing data that meets parametric assumptions, while other tests are more suitable for non-parametric data.

Choosing the right statistical test can be challenging, but understanding the basic principles can help. Different tests have different assumptions, and using the wrong one can lead to inaccurate results. To identify the appropriate test, a flow chart can be used based on three main factors: the type of dependent variable, the type of data, and whether the groups/samples are independent of dependent. It is important to know which tests are parametric and non-parametric, as well as their alternatives. For example, the chi-squared test is used to assess differences in categorical variables and is non-parametric, while Pearson’s correlation coefficient measures linear correlation between two variables and is parametric. T-tests are used to compare means between two groups, and ANOVA is used to compare means between more than two groups. Non-parametric equivalents to ANOVA include the Kruskal-Wallis analysis of ranks, the Median test, Friedman’s two-way analysis of variance, and Cochran Q test. Understanding these tests and their assumptions can help researchers choose the appropriate statistical test for their data.

Likert scales are a type of ordinal scale used in surveys to measure attitudes of opinions. Respondents are presented with a series of statements of questions and asked to rate their level of agreement of frequency of occurrence on a scale of options. For instance, a Likert scale question might ask how often someone prays, with response options ranging from never to daily. While the responses are ordered in terms of frequency, the intervals between each option are not necessarily equal of quantifiable. Therefore, Likert scales are considered ordinal rather than interval scales.

Scales of Measurement in Statistics

In the 1940s, Stanley Smith Stevens introduced four scales of measurement to categorize data variables. Knowing the scale of measurement for a variable is crucial in selecting the appropriate statistical analysis. The four scales of measurement are ratio, interval, ordinal, and nominal.

Ratio scales are similar to interval scales, but they have true zero points. Examples of ratio scales include weight, time, and length. Interval scales measure the difference between two values, and one unit on the scale represents the same magnitude on the trait of characteristic being measured across the whole range of the scale. The Fahrenheit scale for temperature is an example of an interval scale.

Ordinal scales categorize observed values into set categories that can be ordered, but the intervals between each value are uncertain. Examples of ordinal scales include social class, education level, and income level. Nominal scales categorize observed values into set categories that have no particular order of hierarchy. Examples of nominal scales include genotype, blood type, and political party.

Data can also be categorized as quantitative of qualitative. Quantitative variables take on numeric values and can be further classified into discrete and continuous types. Qualitative variables do not take on numerical values and are usually names. Some qualitative variables have an inherent order in their categories and are described as ordinal. Qualitative variables are also called categorical of nominal variables. When a qualitative variable has only two categories, it is called a binary variable.

Wilson and Junger Criteria for Screening

1. The condition should be an important public health problem.
2. There should be an acceptable treatment for patients with recognised disease.
3. Facilities for diagnosis and treatment should be available.
4. There should be a recognised latent of early symptomatic stage.
5. The natural history of the condition, including its development from latent to declared disease should be adequately understood.
6. There should be a suitable test of examination.
7. The test of examination should be acceptable to the population.
8. There should be agreed policy on whom to treat.
9. The cost of case-finding (including diagnosis and subsequent treatment of patients) should be economically balanced in relation to the possible expenditure as a whole.
10. Case-finding should be a continuous process and not a ‘once and for all’ project.

The Wilson and Junger criteria provide a framework for evaluating the suitability of a screening program for a particular condition. The criteria emphasize the importance of the condition as a public health problem, the availability of effective treatment, and the feasibility of diagnosis and treatment. Additionally, the criteria highlight the importance of understanding the natural history of the condition and the need for a suitable test of examination that is acceptable to the population. The criteria also stress the importance of having agreed policies on whom to treat and ensuring that the cost of case-finding is economically balanced. Finally, the criteria emphasize that case-finding should be a continuous process rather than a one-time project. By considering these criteria, public health officials can determine whether a screening program is appropriate for a particular condition and ensure that resources are used effectively.

The prevalence of the disease is 20% as there are currently 200 cases out of a total population of 1000.

As the sample size (n) increases, the standard error of the mean (SEM) decreases. This is because the SEM is inversely proportional to the square root of the sample size (n). As n gets larger, the denominator of the SEM equation gets larger, causing the overall value of the SEM to decrease. This means that larger sample sizes provide more accurate estimates of the population mean, as the calculated sample mean is expected to be closer to the true population mean.

Measures of dispersion are used to indicate the variation of spread of a data set, often in conjunction with a measure of central tendency such as the mean of median. The range, which is the difference between the largest and smallest value, is the simplest measure of dispersion. The interquartile range, which is the difference between the 3rd and 1st quartiles, is another useful measure. Quartiles divide a data set into quarters, and the interquartile range can provide additional information about the spread of the data. However, to get a more representative idea of spread, measures such as the variance and standard deviation are needed. The variance gives an indication of how much the items in the data set vary from the mean, while the standard deviation reflects the distribution of individual scores around their mean. The standard deviation is expressed in the same units as the data set and can be used to indicate how confident we are that data points lie within a particular range. The standard error of the mean is an inferential statistic used to estimate the population mean and is a measure of the spread expected for the mean of the observations. Confidence intervals are often presented alongside sample results such as the mean value, indicating a range that is likely to contain the true value.

Accuracy and reproducibility together make up precision.

Clinical tests are used to determine the presence of absence of a disease of condition. To interpret test results, it is important to have a working knowledge of statistics used to describe them. Two by two tables are commonly used to calculate test statistics such as sensitivity and specificity. Sensitivity refers to the proportion of people with a condition that the test correctly identifies, while specificity refers to the proportion of people without a condition that the test correctly identifies. Accuracy tells us how closely a test measures to its true value, while predictive values help us understand the likelihood of having a disease based on a positive of negative test result. Likelihood ratios combine sensitivity and specificity into a single figure that can refine our estimation of the probability of a disease being present. Pre and post-test odds and probabilities can also be calculated to better understand the likelihood of having a disease before and after a test is carried out. Fagan’s nomogram is a useful tool for calculating post-test probabilities.

The characteristics of precision, sensitivity, accuracy, and specificity are not influenced by the prevalence of the condition and remain stable. However, the positive predictive value is affected by the prevalence of the condition, particularly in cases where the prevalence is low. This is because a decrease in the prevalence of the condition leads to a decrease in the number of true positives, which in turn reduces the numerator of the PPV equation, resulting in a lower PPV. The formula for PPV is TP/(TP+FP).

Clinical tests are used to determine the presence of absence of a disease of condition. To interpret test results, it is important to have a working knowledge of statistics used to describe them. Two by two tables are commonly used to calculate test statistics such as sensitivity and specificity. Sensitivity refers to the proportion of people with a condition that the test correctly identifies, while specificity refers to the proportion of people without a condition that the test correctly identifies. Accuracy tells us how closely a test measures to its true value, while predictive values help us understand the likelihood of having a disease based on a positive of negative test result. Likelihood ratios combine sensitivity and specificity into a single figure that can refine our estimation of the probability of a disease being present. Pre and post-test odds and probabilities can also be calculated to better understand the likelihood of having a disease before and after a test is carried out. Fagan’s nomogram is a useful tool for calculating post-test probabilities.

Evidence-based medicine involves four basic steps: developing a focused clinical question, searching for the best evidence, critically appraising the evidence, and applying the evidence and evaluating the outcome. When developing a question, it is important to understand the difference between background and foreground questions. Background questions are general questions about conditions, illnesses, syndromes, and pathophysiology, while foreground questions are more often about issues of care. The PICO system is often used to define the components of a foreground question: patient group of interest, intervention of interest, comparison, and primary outcome.

When searching for evidence, it is important to have a basic understanding of the types of evidence and sources of information. Scientific literature is divided into two basic categories: primary (empirical research) and secondary (interpretation and analysis of primary sources). Unfiltered sources are large databases of articles that have not been pre-screened for quality, while filtered resources summarize and appraise evidence from several studies.

There are several databases and search engines that can be used to search for evidence, including Medline and PubMed, Embase, the Cochrane Library, PsycINFO, CINAHL, and OpenGrey. Boolean logic can be used to combine search terms in PubMed, and phrase searching and truncation can also be used. Medical Subject Headings (MeSH) are used by indexers to describe articles for MEDLINE records, and the MeSH Database is like a thesaurus that enables exploration of this vocabulary.

The median value is equivalent to Q2 (the second quartile).

Measures of dispersion are used to indicate the variation of spread of a data set, often in conjunction with a measure of central tendency such as the mean of median. The range, which is the difference between the largest and smallest value, is the simplest measure of dispersion. The interquartile range, which is the difference between the 3rd and 1st quartiles, is another useful measure. Quartiles divide a data set into quarters, and the interquartile range can provide additional information about the spread of the data. However, to get a more representative idea of spread, measures such as the variance and standard deviation are needed. The variance gives an indication of how much the items in the data set vary from the mean, while the standard deviation reflects the distribution of individual scores around their mean. The standard deviation is expressed in the same units as the data set and can be used to indicate how confident we are that data points lie within a particular range. The standard error of the mean is an inferential statistic used to estimate the population mean and is a measure of the spread expected for the mean of the observations. Confidence intervals are often presented alongside sample results such as the mean value, indicating a range that is likely to contain the true value.

An RCT is not feasible in this situation, but a cohort study would be more reliable than a case-control study in generating evidence.

Types of Primary Research Studies and Their Advantages and Disadvantages

Primary research studies can be categorized into six types based on the research question they aim to address. The best type of study for each question type is listed in the table below. There are two main types of study design: experimental and observational. Experimental studies involve an intervention, while observational studies do not. The advantages and disadvantages of each study type are summarized in the table below.

Type of Question Best Type of Study

Therapy Randomized controlled trial (RCT), cohort, case control, case series
Diagnosis Cohort studies with comparison to gold standard test
Prognosis Cohort studies, case control, case series
Etiology/Harm RCT, cohort studies, case control, case series
Prevention RCT, cohort studies, case control, case series
Cost Economic analysis

Study Type Advantages Disadvantages

Randomized Controlled Trial – Unbiased distribution of confounders – Blinding more likely – Randomization facilitates statistical analysis – Expensive – Time-consuming – Volunteer bias – Ethically problematic at times
Cohort Study – Ethically safe – Subjects can be matched – Can establish timing and directionality of events – Eligibility criteria and outcome assessments can be standardized – Administratively easier and cheaper than RCT – Controls may be difficult to identify – Exposure may be linked to a hidden confounder – Blinding is difficult – Randomization not present – For rare disease, large sample sizes of long follow-up necessary
Case-Control Study – Quick and cheap – Only feasible method for very rare disorders of those with long lag between exposure and outcome – Fewer subjects needed than cross-sectional studies – Reliance on recall of records to determine exposure status – Confounders – Selection of control groups is difficult – Potential bias: recall, selection
Cross-Sectional Survey – Cheap and simple – Ethically safe – Establishes association at most, not causality – Recall bias susceptibility – Confounders may be unequally distributed – Neyman bias – Group sizes may be unequal
Ecological Study – Cheap and simple – Ethically safe – Ecological fallacy (when relationships which exist for groups are assumed to also be true for individuals)

In conclusion, the choice of study type depends on the research question being addressed. Each study type has its own advantages and disadvantages, and researchers should carefully consider these when designing their studies.

Types of Statistics: Descriptive and Inferential

Statistics can be divided into two categories: descriptive and inferential. Descriptive statistics are used to describe and summarize data without making any generalizations beyond the data at hand. On the other hand, inferential statistics are used to make inferences about a population based on sample data.

Descriptive statistics are useful for identifying patterns and trends in data. Common measures used to describe a data set include measures of central tendency (such as the mean, median, and mode) and measures of variability of dispersion (such as the standard deviation of variance).

Inferential statistics, on the other hand, are used to make predictions of draw conclusions about a population based on sample data. These statistics are also used to determine the probability that observed differences between groups are reliable and not due to chance.

Overall, both descriptive and inferential statistics play important roles in analyzing and interpreting data. Descriptive statistics help us understand the characteristics of a data set, while inferential statistics allow us to make predictions and draw conclusions about larger populations.

Box and whisker plots are a useful tool for displaying information about the range, median, and quartiles of a data set. The whiskers only contain values within 1.5 times the interquartile range (IQR), and any values outside of this range are considered outliers and displayed as dots. The IQR is the difference between the 3rd and 1st quartiles, which divide the data set into quarters. Quartiles can also be used to determine the percentage of observations that fall below a certain value. However, quartiles and ranges have limitations because they do not take into account every score in a data set. To get a more representative idea of spread, measures such as variance and standard deviation are needed. Box plots can also provide information about the shape of a data set, such as whether it is skewed or symmetric. Notched boxes on the plot represent the confidence intervals of the median values.

The appropriate statistical test to analyze the research question of the difference between two related groups with a dependent variable of change in BP (ratio) and parametric data is a paired t-test.

Choosing the right statistical test can be challenging, but understanding the basic principles can help. Different tests have different assumptions, and using the wrong one can lead to inaccurate results. To identify the appropriate test, a flow chart can be used based on three main factors: the type of dependent variable, the type of data, and whether the groups/samples are independent of dependent. It is important to know which tests are parametric and non-parametric, as well as their alternatives. For example, the chi-squared test is used to assess differences in categorical variables and is non-parametric, while Pearson’s correlation coefficient measures linear correlation between two variables and is parametric. T-tests are used to compare means between two groups, and ANOVA is used to compare means between more than two groups. Non-parametric equivalents to ANOVA include the Kruskal-Wallis analysis of ranks, the Median test, Friedman’s two-way analysis of variance, and Cochran Q test. Understanding these tests and their assumptions can help researchers choose the appropriate statistical test for their data.

Hypothesis testing involves the possibility of two types of errors: type I and type II errors. A type I error occurs when the null hypothesis is wrongly rejected of the alternative hypothesis is wrongly accepted. This error is also referred to as an alpha error, error of the first kind, of a false positive. On the other hand, a type II error occurs when the null hypothesis is wrongly accepted. This error is also known as the beta error, error of the second kind, of the false negative.

Understanding Hypothesis Testing in Statistics

In statistics, it is not feasible to investigate hypotheses on entire populations. Therefore, researchers take samples and use them to make estimates about the population they are drawn from. However, this leads to uncertainty as there is no guarantee that the sample taken will be truly representative of the population, resulting in potential errors. Statistical hypothesis testing is the process used to determine if claims from samples to populations can be made and with what certainty.

The null hypothesis (Ho) is the claim that there is no real difference between two groups, while the alternative hypothesis (H1 of Ha) suggests that any difference is due to some non-random chance. The alternative hypothesis can be one-tailed of two-tailed, depending on whether it seeks to establish a difference of a change in one direction.

Two types of errors may occur when testing the null hypothesis: Type I and Type II errors. Type I error occurs when the null hypothesis is rejected when it is true, while Type II error occurs when the null hypothesis is accepted when it is false. The power of a study is the probability of correctly rejecting the null hypothesis when it is false, and it can be increased by increasing the sample size.

P-values provide information on statistical significance and help researchers decide if study results have occurred due to chance. The p-value is the probability of obtaining a result that is as large of larger when in reality there is no difference between two groups. The cutoff for the p-value is called the significance level (alpha level), typically set at 0.05. If the p-value is less than the cutoff, the null hypothesis is rejected, and if it is greater or equal to the cut off, the null hypothesis is not rejected. However, the p-value does not indicate clinical significance, which may be too small to be meaningful.

Measures of Central Tendency

Measures of central tendency are used in descriptive statistics to summarize the middle of typical value of a data set. There are three common measures of central tendency: the mean, median, and mode.

The median is the middle value in a data set that has been arranged in numerical order. It is not affected by outliers and is used for ordinal data. The mode is the most frequent value in a data set and is used for categorical data. The mean is calculated by adding all the values in a data set and dividing by the number of values. It is sensitive to outliers and is used for interval and ratio data.

The appropriate measure of central tendency depends on the measurement scale of the data. For nominal and categorical data, the mode is used. For ordinal data, the median of mode is used. For interval data with a normal distribution, the mean is preferable, but the median of mode can also be used. For interval data with skewed distribution, the median is used. For ratio data, the mean is preferable, but the median of mode can also be used for skewed data.

In addition to measures of central tendency, the range is also used to describe the spread of a data set. It is calculated by subtracting the smallest value from the largest value.

Cost effectiveness analysis (CEA) is an economic evaluation method that compares the costs and outcomes of different courses of action. The outcomes of the interventions must be measurable using a single variable, such as life years gained, making it useful for comparing preventative treatments for fatal conditions.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

Clinical tests are used to determine the presence of absence of a disease of condition. To interpret test results, it is important to have a working knowledge of statistics used to describe them. Two by two tables are commonly used to calculate test statistics such as sensitivity and specificity. Sensitivity refers to the proportion of people with a condition that the test correctly identifies, while specificity refers to the proportion of people without a condition that the test correctly identifies. Accuracy tells us how closely a test measures to its true value, while predictive values help us understand the likelihood of having a disease based on a positive of negative test result. Likelihood ratios combine sensitivity and specificity into a single figure that can refine our estimation of the probability of a disease being present. Pre and post-test odds and probabilities can also be calculated to better understand the likelihood of having a disease before and after a test is carried out. Fagan’s nomogram is a useful tool for calculating post-test probabilities.

The prevalence refers to the percentage of individuals in a population who currently have a particular condition, while the incidence is the frequency at which new cases of the condition arise within a specific timeframe.

Clinical tests are used to determine the presence of absence of a disease of condition. To interpret test results, it is important to have a working knowledge of statistics used to describe them. Two by two tables are commonly used to calculate test statistics such as sensitivity and specificity. Sensitivity refers to the proportion of people with a condition that the test correctly identifies, while specificity refers to the proportion of people without a condition that the test correctly identifies. Accuracy tells us how closely a test measures to its true value, while predictive values help us understand the likelihood of having a disease based on a positive of negative test result. Likelihood ratios combine sensitivity and specificity into a single figure that can refine our estimation of the probability of a disease being present. Pre and post-test odds and probabilities can also be calculated to better understand the likelihood of having a disease before and after a test is carried out. Fagan’s nomogram is a useful tool for calculating post-test probabilities.

Disease Rates and Their Interpretation

Disease rates are a measure of the occurrence of a disease in a population. They are used to establish causation, monitor interventions, and measure the impact of exposure on disease rates. The attributable risk is the difference in the rate of disease between the exposed and unexposed groups. It tells us what proportion of deaths in the exposed group were due to the exposure. The relative risk is the risk of an event relative to exposure. It is calculated by dividing the rate of disease in the exposed group by the rate of disease in the unexposed group. A relative risk of 1 means there is no difference between the two groups. A relative risk of <1 means that the event is less likely to occur in the exposed group, while a relative risk of >1 means that the event is more likely to occur in the exposed group. The population attributable risk is the reduction in incidence that would be observed if the population were entirely unexposed. It can be calculated by multiplying the attributable risk by the prevalence of exposure in the population. The attributable proportion is the proportion of the disease that would be eliminated in a population if its disease rate were reduced to that of the unexposed group.

Measures of Disease Frequency: Incidence and Prevalence

Incidence and prevalence are two important measures of disease frequency. Incidence measures the speed at which new cases of a disease are emerging, while prevalence measures the burden of disease within a population. Cumulative incidence and incidence rate are two types of incidence measures, while point prevalence and period prevalence are two types of prevalence measures.

Cumulative incidence is the average risk of getting a disease over a certain period of time, while incidence rate is a measure of the speed at which new cases are emerging. Prevalence is a proportion and is a measure of the burden of disease within a population. Point prevalence measures the number of cases in a defined population at a specific point in time, while period prevalence measures the number of identified cases during a specified period of time.

It is important to note that prevalence is equal to incidence multiplied by the duration of the condition. In chronic diseases, the prevalence is much greater than the incidence. The incidence rate is stated in units of person-time, while cumulative incidence is always a proportion. When describing cumulative incidence, it is necessary to give the follow-up period over which the risk is estimated. In acute diseases, the prevalence and incidence may be similar, while for conditions such as the common cold, the incidence may be greater than the prevalence.

Incidence is a useful measure to study disease etiology and risk factors, while prevalence is useful for health resource planning. Understanding these measures of disease frequency is important for public health professionals and researchers in order to effectively monitor and address the burden of disease within populations.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

Validity in statistics refers to how accurately something measures what it claims to measure. There are two main types of validity: internal and external. Internal validity refers to the confidence we have in the cause and effect relationship in a study, while external validity refers to the degree to which the conclusions of a study can be applied to other people, places, and times. There are various threats to both internal and external validity, such as sampling, measurement instrument obtrusiveness, and reactive effects of setting. Additionally, there are several subtypes of validity, including face validity, content validity, criterion validity, and construct validity. Each subtype has its own specific focus and methods for testing validity.

NLM’s hierarchical vocabulary, known as MeSH (Medical Subject Heading), is utilized for the purpose of indexing articles in PubMed.

Evidence-based medicine involves four basic steps: developing a focused clinical question, searching for the best evidence, critically appraising the evidence, and applying the evidence and evaluating the outcome. When developing a question, it is important to understand the difference between background and foreground questions. Background questions are general questions about conditions, illnesses, syndromes, and pathophysiology, while foreground questions are more often about issues of care. The PICO system is often used to define the components of a foreground question: patient group of interest, intervention of interest, comparison, and primary outcome.

When searching for evidence, it is important to have a basic understanding of the types of evidence and sources of information. Scientific literature is divided into two basic categories: primary (empirical research) and secondary (interpretation and analysis of primary sources). Unfiltered sources are large databases of articles that have not been pre-screened for quality, while filtered resources summarize and appraise evidence from several studies.

There are several databases and search engines that can be used to search for evidence, including Medline and PubMed, Embase, the Cochrane Library, PsycINFO, CINAHL, and OpenGrey. Boolean logic can be used to combine search terms in PubMed, and phrase searching and truncation can also be used. Medical Subject Headings (MeSH) are used by indexers to describe articles for MEDLINE records, and the MeSH Database is like a thesaurus that enables exploration of this vocabulary.

Stevens suggested that scales can be categorized into one of four types based on measurements.

Scales of Measurement in Statistics

In the 1940s, Stanley Smith Stevens introduced four scales of measurement to categorize data variables. Knowing the scale of measurement for a variable is crucial in selecting the appropriate statistical analysis. The four scales of measurement are ratio, interval, ordinal, and nominal.

Ratio scales are similar to interval scales, but they have true zero points. Examples of ratio scales include weight, time, and length. Interval scales measure the difference between two values, and one unit on the scale represents the same magnitude on the trait of characteristic being measured across the whole range of the scale. The Fahrenheit scale for temperature is an example of an interval scale.

Ordinal scales categorize observed values into set categories that can be ordered, but the intervals between each value are uncertain. Examples of ordinal scales include social class, education level, and income level. Nominal scales categorize observed values into set categories that have no particular order of hierarchy. Examples of nominal scales include genotype, blood type, and political party.

Data can also be categorized as quantitative of qualitative. Quantitative variables take on numeric values and can be further classified into discrete and continuous types. Qualitative variables do not take on numerical values and are usually names. Some qualitative variables have an inherent order in their categories and are described as ordinal. Qualitative variables are also called categorical of nominal variables. When a qualitative variable has only two categories, it is called a binary variable.

Measures of Disease Frequency: Incidence and Prevalence

Incidence and prevalence are two important measures of disease frequency. Incidence measures the speed at which new cases of a disease are emerging, while prevalence measures the burden of disease within a population. Cumulative incidence and incidence rate are two types of incidence measures, while point prevalence and period prevalence are two types of prevalence measures.

Cumulative incidence is the average risk of getting a disease over a certain period of time, while incidence rate is a measure of the speed at which new cases are emerging. Prevalence is a proportion and is a measure of the burden of disease within a population. Point prevalence measures the number of cases in a defined population at a specific point in time, while period prevalence measures the number of identified cases during a specified period of time.

It is important to note that prevalence is equal to incidence multiplied by the duration of the condition. In chronic diseases, the prevalence is much greater than the incidence. The incidence rate is stated in units of person-time, while cumulative incidence is always a proportion. When describing cumulative incidence, it is necessary to give the follow-up period over which the risk is estimated. In acute diseases, the prevalence and incidence may be similar, while for conditions such as the common cold, the incidence may be greater than the prevalence.

Incidence is a useful measure to study disease etiology and risk factors, while prevalence is useful for health resource planning. Understanding these measures of disease frequency is important for public health professionals and researchers in order to effectively monitor and address the burden of disease within populations.

Validity in statistics refers to how accurately something measures what it claims to measure. There are two main types of validity: internal and external. Internal validity refers to the confidence we have in the cause and effect relationship in a study, while external validity refers to the degree to which the conclusions of a study can be applied to other people, places, and times. There are various threats to both internal and external validity, such as sampling, measurement instrument obtrusiveness, and reactive effects of setting. Additionally, there are several subtypes of validity, including face validity, content validity, criterion validity, and construct validity. Each subtype has its own specific focus and methods for testing validity.

Measures of Central Tendency

Measures of central tendency are used in descriptive statistics to summarize the middle of typical value of a data set. There are three common measures of central tendency: the mean, median, and mode.

The median is the middle value in a data set that has been arranged in numerical order. It is not affected by outliers and is used for ordinal data. The mode is the most frequent value in a data set and is used for categorical data. The mean is calculated by adding all the values in a data set and dividing by the number of values. It is sensitive to outliers and is used for interval and ratio data.

The appropriate measure of central tendency depends on the measurement scale of the data. For nominal and categorical data, the mode is used. For ordinal data, the median of mode is used. For interval data with a normal distribution, the mean is preferable, but the median of mode can also be used. For interval data with skewed distribution, the median is used. For ratio data, the mean is preferable, but the median of mode can also be used for skewed data.

In addition to measures of central tendency, the range is also used to describe the spread of a data set. It is calculated by subtracting the smallest value from the largest value.

Methods of Economic Evaluation

There are four main methods of economic evaluation: cost-effectiveness analysis (CEA), cost-benefit analysis (CBA), cost-utility analysis (CUA), and cost-minimisation analysis (CMA). While all four methods capture costs, they differ in how they assess health effects.

Cost-effectiveness analysis (CEA) compares interventions by relating costs to a single clinical measure of effectiveness, such as symptom reduction of improvement in activities of daily living. The cost-effectiveness ratio is calculated as total cost divided by units of effectiveness. CEA is typically used when CBA cannot be performed due to the inability to monetise benefits.

Cost-benefit analysis (CBA) measures all costs and benefits of an intervention in monetary terms to establish which alternative has the greatest net benefit. CBA requires that all consequences of an intervention, such as life-years saved, treatment side-effects, symptom relief, disability, pain, and discomfort, are allocated a monetary value. CBA is rarely used in mental health service evaluation due to the difficulty in converting benefits from mental health programmes into monetary values.

Cost-utility analysis (CUA) is a special form of CEA in which health benefits/outcomes are measured in broader, more generic ways, enabling comparisons between treatments for different diseases and conditions. Multidimensional health outcomes are measured by a single preference- of utility-based index such as the Quality-Adjusted-Life-Years (QALY). QALYs are a composite measure of gains in life expectancy and health-related quality of life. CUA allows for comparisons across treatments for different conditions.

Cost-minimisation analysis (CMA) is an economic evaluation in which the consequences of competing interventions are the same, and only inputs, i.e. costs, are taken into consideration. The aim is to decide the least costly way of achieving the same outcome.

Costs in Economic Evaluation Studies

There are three main types of costs in economic evaluation studies: direct, indirect, and intangible. Direct costs are associated directly with the healthcare intervention, such as staff time, medical supplies, cost of travel for the patient, childcare costs for the patient, and costs falling on other social sectors such as domestic help from social services. Indirect costs are incurred by the reduced productivity of the patient, such as time off work, reduced work productivity, and time spent caring for the patient by relatives. Intangible costs are difficult to measure, such as pain of suffering on the part of the patient.

Intention to Treat Analysis in Randomized Controlled Trials

Intention to treat analysis is a statistical method used in randomized controlled trials to analyze all patients who were randomly assigned to a treatment group, regardless of whether they completed of received the treatment. This approach is used to avoid the potential biases that may arise from patients dropping out of switching between treatment groups. By analyzing all patients according to their original treatment assignment, intention to treat analysis provides a more accurate representation of the true treatment effects. This method is widely used in clinical trials to ensure that the results are reliable and unbiased.

Scales of Measurement in Statistics

In the 1940s, Stanley Smith Stevens introduced four scales of measurement to categorize data variables. Knowing the scale of measurement for a variable is crucial in selecting the appropriate statistical analysis. The four scales of measurement are ratio, interval, ordinal, and nominal.

Ratio scales are similar to interval scales, but they have true zero points. Examples of ratio scales include weight, time, and length. Interval scales measure the difference between two values, and one unit on the scale represents the same magnitude on the trait of characteristic being measured across the whole range of the scale. The Fahrenheit scale for temperature is an example of an interval scale.

Ordinal scales categorize observed values into set categories that can be ordered, but the intervals between each value are uncertain. Examples of ordinal scales include social class, education level, and income level. Nominal scales categorize observed values into set categories that have no particular order of hierarchy. Examples of nominal scales include genotype, blood type, and political party.

Data can also be categorized as quantitative of qualitative. Quantitative variables take on numeric values and can be further classified into discrete and continuous types. Qualitative variables do not take on numerical values and are usually names. Some qualitative variables have an inherent order in their categories and are described as ordinal. Qualitative variables are also called categorical of nominal variables. When a qualitative variable has only two categories, it is called a binary variable.

Sampling Methods in Statistics

When collecting data from a population, it is often impractical and unnecessary to gather information from every single member. Instead, taking a sample is preferred. However, it is crucial that the sample accurately represents the population from which it is drawn. There are two main types of sampling methods: probability (random) sampling and non-probability (non-random) sampling.

Non-probability sampling methods, also known as judgement samples, are based on human choice rather than random selection. These samples are convenient and cheaper than probability sampling methods. Examples of non-probability sampling methods include voluntary sampling, convenience sampling, snowball sampling, and quota sampling.

Probability sampling methods give a more representative sample of the population than non-probability sampling. In each probability sampling technique, each population element has a known (non-zero) chance of being selected for the sample. Examples of probability sampling methods include simple random sampling, systematic sampling, cluster sampling, stratified sampling, and multistage sampling.

Simple random sampling is a sample in which every member of the population has an equal chance of being chosen. Systematic sampling involves selecting every kth member of the population. Cluster sampling involves dividing a population into separate groups (called clusters) and selecting a random sample of clusters. Stratified sampling involves dividing a population into groups (strata) and taking a random sample from each strata. Multistage sampling is a more complex method that involves several stages and combines two of more sampling methods.

Overall, probability sampling methods give a more representative sample of the population, but non-probability sampling methods are often more convenient and cheaper. It is important to choose the appropriate sampling method based on the research question and available resources.

The prevalence of a condition has an impact on both the PPV and NPV. When the prevalence decreases, the PPV also decreases while the NPV increases.

Clinical tests are used to determine the presence of absence of a disease of condition. To interpret test results, it is important to have a working knowledge of statistics used to describe them. Two by two tables are commonly used to calculate test statistics such as sensitivity and specificity. Sensitivity refers to the proportion of people with a condition that the test correctly identifies, while specificity refers to the proportion of people without a condition that the test correctly identifies. Accuracy tells us how closely a test measures to its true value, while predictive values help us understand the likelihood of having a disease based on a positive of negative test result. Likelihood ratios combine sensitivity and specificity into a single figure that can refine our estimation of the probability of a disease being present. Pre and post-test odds and probabilities can also be calculated to better understand the likelihood of having a disease before and after a test is carried out. Fagan’s nomogram is a useful tool for calculating post-test probabilities.

The use of relative risk is applicable in cohort, cross-sectional, and randomized control trials, but not in case-control studies. In situations where there are no events in the control group, neither the risk ratio nor the odds ratio can be computed. It is important to note that the odds ratio tends to overestimate effects and is always more extreme than the relative risk, moving away from the null value of 1.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

The study is a prospective cohort study that observes the effect of BMI as an exposure on the group over time, without manipulating any risk factors of interventions.

Types of Primary Research Studies and Their Advantages and Disadvantages

Primary research studies can be categorized into six types based on the research question they aim to address. The best type of study for each question type is listed in the table below. There are two main types of study design: experimental and observational. Experimental studies involve an intervention, while observational studies do not. The advantages and disadvantages of each study type are summarized in the table below.

Type of Question Best Type of Study

Therapy Randomized controlled trial (RCT), cohort, case control, case series
Diagnosis Cohort studies with comparison to gold standard test
Prognosis Cohort studies, case control, case series
Etiology/Harm RCT, cohort studies, case control, case series
Prevention RCT, cohort studies, case control, case series
Cost Economic analysis

Study Type Advantages Disadvantages

Randomized Controlled Trial – Unbiased distribution of confounders – Blinding more likely – Randomization facilitates statistical analysis – Expensive – Time-consuming – Volunteer bias – Ethically problematic at times
Cohort Study – Ethically safe – Subjects can be matched – Can establish timing and directionality of events – Eligibility criteria and outcome assessments can be standardized – Administratively easier and cheaper than RCT – Controls may be difficult to identify – Exposure may be linked to a hidden confounder – Blinding is difficult – Randomization not present – For rare disease, large sample sizes of long follow-up necessary
Case-Control Study – Quick and cheap – Only feasible method for very rare disorders of those with long lag between exposure and outcome – Fewer subjects needed than cross-sectional studies – Reliance on recall of records to determine exposure status – Confounders – Selection of control groups is difficult – Potential bias: recall, selection
Cross-Sectional Survey – Cheap and simple – Ethically safe – Establishes association at most, not causality – Recall bias susceptibility – Confounders may be unequally distributed – Neyman bias – Group sizes may be unequal
Ecological Study – Cheap and simple – Ethically safe – Ecological fallacy (when relationships which exist for groups are assumed to also be true for individuals)

In conclusion, the choice of study type depends on the research question being addressed. Each study type has its own advantages and disadvantages, and researchers should carefully consider these when designing their studies.

It is important to distinguish between the direction of the correlation (the slope of the line) and its strength (the spread of the data). To emphasize this difference, the correct answer to this question is a negative value.

Stats: Correlation and Regression

Correlation and regression are related but not interchangeable terms. Correlation is used to test for association between variables, while regression is used to predict values of dependent variables from independent variables. Correlation can be linear, non-linear, of non-existent, and can be strong, moderate, of weak. The strength of a linear relationship is measured by the correlation coefficient, which can be positive of negative and ranges from very weak to very strong. However, the interpretation of a correlation coefficient depends on the context and purposes. Correlation can suggest association but cannot prove of disprove causation. Linear regression, on the other hand, can be used to predict how much one variable changes when a second variable is changed. Scatter graphs are used in correlation and regression analyses to visually determine if variables are associated and to detect outliers. When constructing a scatter graph, the dependent variable is typically placed on the vertical axis and the independent variable on the horizontal axis.

Qualitative research is a method of inquiry that seeks to understand the meaning and experience dimensions of human lives and social worlds. There are different approaches to qualitative research, such as ethnography, phenomenology, and grounded theory, each with its own purpose, role of the researcher, stages of research, and method of data analysis. The most common methods used in healthcare research are interviews and focus groups. Sampling techniques include convenience sampling, purposive sampling, quota sampling, snowball sampling, and case study sampling. Sample size can be determined by data saturation, which occurs when new categories, themes, of explanations stop emerging from the data. Validity can be assessed through triangulation, respondent validation, bracketing, and reflexivity. Analytical approaches include content analysis and constant comparison.

Cost minimisation analysis is employed to compare net costs when the observed effects of health care interventions are similar. To conduct this analysis, it is necessary to have clinical evidence that demonstrates the differences in health effects between alternatives are negligible of insignificant. This approach is commonly used by institutions like the National Institute for Health and Care Excellence (NICE).

Stats Association and Causation

When two variables are found to be more commonly present together, they are said to be associated. However, this association can be of three types: spurious, indirect, of direct. Spurious association is one that has arisen by chance and is not real, while indirect association is due to the presence of another factor, known as a confounding variable. Direct association, on the other hand, is a true association not linked by a third variable.

Once an association has been established, the next question is whether it is causal. To determine causation, the Bradford Hill Causal Criteria are used. These criteria include strength, temporality, specificity, coherence, and consistency. The stronger the association, the more likely it is to be truly causal. Temporality refers to whether the exposure precedes the outcome. Specificity asks whether the suspected cause is associated with a specific outcome of disease. Coherence refers to whether the association fits with other biological knowledge. Finally, consistency asks whether the same association is found in many studies.

Qualitative research is a method of inquiry that seeks to understand the meaning and experience dimensions of human lives and social worlds. There are different approaches to qualitative research, such as ethnography, phenomenology, and grounded theory, each with its own purpose, role of the researcher, stages of research, and method of data analysis. The most common methods used in healthcare research are interviews and focus groups. Sampling techniques include convenience sampling, purposive sampling, quota sampling, snowball sampling, and case study sampling. Sample size can be determined by data saturation, which occurs when new categories, themes, of explanations stop emerging from the data. Validity can be assessed through triangulation, respondent validation, bracketing, and reflexivity. Analytical approaches include content analysis and constant comparison.

The effectiveness of a healthcare intervention, usually a medication, is measured by the number needed to treat (NNT). This represents the average number of patients who must receive treatment to prevent one additional negative outcome. An NNT of 1 would indicate that all treated patients improved while none of the control patients did, which is the ideal scenario. The NNT can be calculated by taking the inverse of the absolute risk reduction. A higher NNT indicates a less effective treatment, with the range of NNT being from 1 to infinity.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

– Treating 1000 patients with a new statin for five years prevented 50 MIs.
– The number needed to treat (NNT) to prevent one MI is 20 (1000/50).
– NNT provides information on treatment efficacy beyond statistical significance.
– Based on these data, treating as few as 20 patients over five years may prevent an infarct.
– Cost economic data can be calculated by factoring in drug costs and costs of treating and rehabilitating a patient with an MI.

The two sample unpaired t test is utilized to examine whether the null hypothesis that the two populations related to the two random samples are equivalent is true of not. When dealing with continuous data that is believed to conform to the normal distribution, a t test is suitable, making it appropriate for comparing weight loss between two groups. In contrast, a paired t test is used when the data is dependent, meaning there is a direct correlation between the values in the two samples. This could include the same subject being measured before and after a process change of at different times.

It is important to note that confidence intervals are derived from standard errors, not standard deviation, despite the common misconception. It is crucial to avoid mixing up these two terms.

Measures of dispersion are used to indicate the variation of spread of a data set, often in conjunction with a measure of central tendency such as the mean of median. The range, which is the difference between the largest and smallest value, is the simplest measure of dispersion. The interquartile range, which is the difference between the 3rd and 1st quartiles, is another useful measure. Quartiles divide a data set into quarters, and the interquartile range can provide additional information about the spread of the data. However, to get a more representative idea of spread, measures such as the variance and standard deviation are needed. The variance gives an indication of how much the items in the data set vary from the mean, while the standard deviation reflects the distribution of individual scores around their mean. The standard deviation is expressed in the same units as the data set and can be used to indicate how confident we are that data points lie within a particular range. The standard error of the mean is an inferential statistic used to estimate the population mean and is a measure of the spread expected for the mean of the observations. Confidence intervals are often presented alongside sample results such as the mean value, indicating a range that is likely to contain the true value.

As an AI language model, I do not have personal opinions of beliefs. However, I can provide information and guidance on the standards of reporting for different types of research studies. The guidelines mentioned above are essential for ensuring that research studies are reported accurately and transparently, which is crucial for the scientific community to evaluate and replicate the findings. It is important for researchers to be familiar with these standards and follow them when reporting their studies to ensure the quality and integrity of their research.

The threshold score that results in the lowest misclassification rate, achieved by minimizing both false positive and false negative rates, is known as the optimal threshold. Based on the findings of the previous study, the ideal cut off for identifying caseness on the MDQ is five, making it the optimal threshold.

The median represents the middle value in a set of data. For example, if there were 7 results (A, B, C, D, E, F, F), the median would be D. However, if the question asks for the most common result, the mode would be used. In this example, the mode would be F. The mean would not be appropriate in this case because adding all the values and dividing by the number of values would not provide a meaningful result.

Measures of Central Tendency

Measures of central tendency are used in descriptive statistics to summarize the middle of typical value of a data set. There are three common measures of central tendency: the mean, median, and mode.

The median is the middle value in a data set that has been arranged in numerical order. It is not affected by outliers and is used for ordinal data. The mode is the most frequent value in a data set and is used for categorical data. The mean is calculated by adding all the values in a data set and dividing by the number of values. It is sensitive to outliers and is used for interval and ratio data.

The appropriate measure of central tendency depends on the measurement scale of the data. For nominal and categorical data, the mode is used. For ordinal data, the median of mode is used. For interval data with a normal distribution, the mean is preferable, but the median of mode can also be used. For interval data with skewed distribution, the median is used. For ratio data, the mean is preferable, but the median of mode can also be used for skewed data.

In addition to measures of central tendency, the range is also used to describe the spread of a data set. It is calculated by subtracting the smallest value from the largest value.

Types of Bias in Statistics

Bias is a systematic error that can lead to incorrect conclusions. Confounding factors are variables that are associated with both the outcome and the exposure but have no causative role. Confounding can be addressed in the design and analysis stage of a study. The main method of controlling confounding in the analysis phase is stratification analysis. The main methods used in the design stage are matching, randomization, and restriction of participants.

There are two main types of bias: selection bias and information bias. Selection bias occurs when the selected sample is not a representative sample of the reference population. Disease spectrum bias, self-selection bias, participation bias, incidence-prevalence bias, exclusion bias, publication of dissemination bias, citation bias, and Berkson’s bias are all subtypes of selection bias. Information bias occurs when gathered information about exposure, outcome, of both is not correct and there was an error in measurement. Detection bias, recall bias, lead time bias, interviewer/observer bias, verification and work-up bias, Hawthorne effect, and ecological fallacy are all subtypes of information bias.

The aim of the STARD initiative is to enhance the precision and comprehensiveness of reporting diagnostic accuracy studies, enabling readers to evaluate the study’s potential for bias (internal validity) and generalizability (external validity). The STARD statement comprises a checklist of 25 items and suggests utilizing a flow diagram that outlines the study’s design and patient flow.

As an AI language model, I do not have personal opinions of beliefs. However, I can provide information and guidance on the standards of reporting for different types of research studies. The guidelines mentioned above are essential for ensuring that research studies are reported accurately and transparently, which is crucial for the scientific community to evaluate and replicate the findings. It is important for researchers to be familiar with these standards and follow them when reporting their studies to ensure the quality and integrity of their research.

Evidence-based medicine involves four basic steps: developing a focused clinical question, searching for the best evidence, critically appraising the evidence, and applying the evidence and evaluating the outcome. When developing a question, it is important to understand the difference between background and foreground questions. Background questions are general questions about conditions, illnesses, syndromes, and pathophysiology, while foreground questions are more often about issues of care. The PICO system is often used to define the components of a foreground question: patient group of interest, intervention of interest, comparison, and primary outcome.

When searching for evidence, it is important to have a basic understanding of the types of evidence and sources of information. Scientific literature is divided into two basic categories: primary (empirical research) and secondary (interpretation and analysis of primary sources). Unfiltered sources are large databases of articles that have not been pre-screened for quality, while filtered resources summarize and appraise evidence from several studies.

There are several databases and search engines that can be used to search for evidence, including Medline and PubMed, Embase, the Cochrane Library, PsycINFO, CINAHL, and OpenGrey. Boolean logic can be used to combine search terms in PubMed, and phrase searching and truncation can also be used. Medical Subject Headings (MeSH) are used by indexers to describe articles for MEDLINE records, and the MeSH Database is like a thesaurus that enables exploration of this vocabulary.

An observed p-value of 0.0125 means that there is a 1.25% chance of obtaining the observed result by chance, assuming the null hypothesis is true. This also means that the Type I error rate (the probability of falsely rejecting the null hypothesis) is 1/80 of 1.25%. In comparison, a p-value of 0.05 indicates a 5% chance of obtaining the observed result by chance, of a Type I error rate of 1/20.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

Measures of dispersion are used to indicate the variation of spread of a data set, often in conjunction with a measure of central tendency such as the mean of median. The range, which is the difference between the largest and smallest value, is the simplest measure of dispersion. The interquartile range, which is the difference between the 3rd and 1st quartiles, is another useful measure. Quartiles divide a data set into quarters, and the interquartile range can provide additional information about the spread of the data. However, to get a more representative idea of spread, measures such as the variance and standard deviation are needed. The variance gives an indication of how much the items in the data set vary from the mean, while the standard deviation reflects the distribution of individual scores around their mean. The standard deviation is expressed in the same units as the data set and can be used to indicate how confident we are that data points lie within a particular range. The standard error of the mean is an inferential statistic used to estimate the population mean and is a measure of the spread expected for the mean of the observations. Confidence intervals are often presented alongside sample results such as the mean value, indicating a range that is likely to contain the true value.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

Standard Deviation and Standard Error of the Mean

Standard deviation (SD) and standard error of the mean (SEM) are two important statistical measures used to describe data. SD is a measure of how much the data varies, while SEM is a measure of how precisely we know the true mean of the population. The normal distribution, also known as the Gaussian distribution, is a symmetrical bell-shaped curve that describes the spread of many biological and clinical measurements.

68.3% of the data lies within 1 SD of the mean, 95.4% of the data lies within 2 SD of the mean, and 99.7% of the data lies within 3 SD of the mean. The SD is calculated by taking the square root of the variance and is expressed in the same units as the data set. A low SD indicates that data points tend to be very close to the mean.

On the other hand, SEM is an inferential statistic that quantifies the precision of the mean. It is expressed in the same units as the data and is calculated by dividing the SD of the sample mean by the square root of the sample size. The SEM gets smaller as the sample size increases, and it takes into account both the value of the SD and the sample size.

Both SD and SEM are important measures in statistical analysis, and they are used to calculate confidence intervals and test hypotheses. While SD quantifies scatter, SEM quantifies precision, and both are essential in understanding and interpreting data.

Types of Bias in Statistics

Bias is a systematic error that can lead to incorrect conclusions. Confounding factors are variables that are associated with both the outcome and the exposure but have no causative role. Confounding can be addressed in the design and analysis stage of a study. The main method of controlling confounding in the analysis phase is stratification analysis. The main methods used in the design stage are matching, randomization, and restriction of participants.

There are two main types of bias: selection bias and information bias. Selection bias occurs when the selected sample is not a representative sample of the reference population. Disease spectrum bias, self-selection bias, participation bias, incidence-prevalence bias, exclusion bias, publication of dissemination bias, citation bias, and Berkson’s bias are all subtypes of selection bias. Information bias occurs when gathered information about exposure, outcome, of both is not correct and there was an error in measurement. Detection bias, recall bias, lead time bias, interviewer/observer bias, verification and work-up bias, Hawthorne effect, and ecological fallacy are all subtypes of information bias.

Disease Rates and Their Interpretation

Disease rates are a measure of the occurrence of a disease in a population. They are used to establish causation, monitor interventions, and measure the impact of exposure on disease rates. The attributable risk is the difference in the rate of disease between the exposed and unexposed groups. It tells us what proportion of deaths in the exposed group were due to the exposure. The relative risk is the risk of an event relative to exposure. It is calculated by dividing the rate of disease in the exposed group by the rate of disease in the unexposed group. A relative risk of 1 means there is no difference between the two groups. A relative risk of <1 means that the event is less likely to occur in the exposed group, while a relative risk of >1 means that the event is more likely to occur in the exposed group. The population attributable risk is the reduction in incidence that would be observed if the population were entirely unexposed. It can be calculated by multiplying the attributable risk by the prevalence of exposure in the population. The attributable proportion is the proportion of the disease that would be eliminated in a population if its disease rate were reduced to that of the unexposed group.

The Importance of Power in Statistical Analysis

Power is a crucial concept in statistical analysis as it helps researchers determine the number of participants needed in a study to detect a clinically significant difference of effect. It represents the probability of correctly rejecting the null hypothesis when it is false, which means avoiding a Type II error. Power values range from 0 to 1, with 0 indicating 0% and 1 indicating 100%. A power of 0.80 is generally considered the minimum acceptable level.

Several factors influence the power of a study, including sample size, effect size, and significance level. Larger sample sizes lead to more precise parameter estimations and increase the study’s ability to detect a significant effect. Effect size, which is determined at the beginning of a study, refers to the size of the difference between two means that leads to rejecting the null hypothesis. Finally, the significance level, also known as the alpha level, represents the probability of a Type I error. By considering these factors, researchers can optimize the power of their studies and increase the likelihood of detecting meaningful effects.

Recall bias pertains to how a person’s illness status can influence their tendency to report past exposure to a risk factor. Confounding arises when an additional variable is associated with both an independent and dependent variable. Observer bias refers to the possibility that researchers’ cognitive biases may unconsciously impact the results of a study. Publication bias refers to the tendency for studies with positive results to be more likely to be published. Selection bias occurs when certain individuals of groups are overrepresented, leading to inadequate randomization.

To address the issue of drop-outs in a study, an intention to treat (ITT) analysis can be employed. Drop-outs can lead to attrition bias, which creates systematic differences in attrition across treatment groups. In an ITT analysis, all patients are included in the groups they were initially assigned to through random allocation. To handle missing data, two common methods are last observation carried forward and worst case scenario analysis.

Negative predictive value = 172 / 177

Clinical tests are used to determine the presence of absence of a disease of condition. To interpret test results, it is important to have a working knowledge of statistics used to describe them. Two by two tables are commonly used to calculate test statistics such as sensitivity and specificity. Sensitivity refers to the proportion of people with a condition that the test correctly identifies, while specificity refers to the proportion of people without a condition that the test correctly identifies. Accuracy tells us how closely a test measures to its true value, while predictive values help us understand the likelihood of having a disease based on a positive of negative test result. Likelihood ratios combine sensitivity and specificity into a single figure that can refine our estimation of the probability of a disease being present. Pre and post-test odds and probabilities can also be calculated to better understand the likelihood of having a disease before and after a test is carried out. Fagan’s nomogram is a useful tool for calculating post-test probabilities.

Types of Bias in Statistics

Bias is a systematic error that can lead to incorrect conclusions. Confounding factors are variables that are associated with both the outcome and the exposure but have no causative role. Confounding can be addressed in the design and analysis stage of a study. The main method of controlling confounding in the analysis phase is stratification analysis. The main methods used in the design stage are matching, randomization, and restriction of participants.

There are two main types of bias: selection bias and information bias. Selection bias occurs when the selected sample is not a representative sample of the reference population. Disease spectrum bias, self-selection bias, participation bias, incidence-prevalence bias, exclusion bias, publication of dissemination bias, citation bias, and Berkson’s bias are all subtypes of selection bias. Information bias occurs when gathered information about exposure, outcome, of both is not correct and there was an error in measurement. Detection bias, recall bias, lead time bias, interviewer/observer bias, verification and work-up bias, Hawthorne effect, and ecological fallacy are all subtypes of information bias.

The use of allocation concealment is being implemented by the researchers to prevent interference from investigators of patients in the randomisation process. This is important as knowledge of group allocation can lead to patient refusal to participate of researchers manipulating the allocation process. By using distant call centres for allocation concealment, the risk of selection bias, which refers to systematic differences between comparison groups, is reduced.

T-tests are appropriate for parametric data, which means that the data should conform to a normal distribution.

Choosing the right statistical test can be challenging, but understanding the basic principles can help. Different tests have different assumptions, and using the wrong one can lead to inaccurate results. To identify the appropriate test, a flow chart can be used based on three main factors: the type of dependent variable, the type of data, and whether the groups/samples are independent of dependent. It is important to know which tests are parametric and non-parametric, as well as their alternatives. For example, the chi-squared test is used to assess differences in categorical variables and is non-parametric, while Pearson’s correlation coefficient measures linear correlation between two variables and is parametric. T-tests are used to compare means between two groups, and ANOVA is used to compare means between more than two groups. Non-parametric equivalents to ANOVA include the Kruskal-Wallis analysis of ranks, the Median test, Friedman’s two-way analysis of variance, and Cochran Q test. Understanding these tests and their assumptions can help researchers choose the appropriate statistical test for their data.

Methods of Economic Evaluation

There are four main methods of economic evaluation: cost-effectiveness analysis (CEA), cost-benefit analysis (CBA), cost-utility analysis (CUA), and cost-minimisation analysis (CMA). While all four methods capture costs, they differ in how they assess health effects.

Cost-effectiveness analysis (CEA) compares interventions by relating costs to a single clinical measure of effectiveness, such as symptom reduction of improvement in activities of daily living. The cost-effectiveness ratio is calculated as total cost divided by units of effectiveness. CEA is typically used when CBA cannot be performed due to the inability to monetise benefits.

Cost-benefit analysis (CBA) measures all costs and benefits of an intervention in monetary terms to establish which alternative has the greatest net benefit. CBA requires that all consequences of an intervention, such as life-years saved, treatment side-effects, symptom relief, disability, pain, and discomfort, are allocated a monetary value. CBA is rarely used in mental health service evaluation due to the difficulty in converting benefits from mental health programmes into monetary values.

Cost-utility analysis (CUA) is a special form of CEA in which health benefits/outcomes are measured in broader, more generic ways, enabling comparisons between treatments for different diseases and conditions. Multidimensional health outcomes are measured by a single preference- of utility-based index such as the Quality-Adjusted-Life-Years (QALY). QALYs are a composite measure of gains in life expectancy and health-related quality of life. CUA allows for comparisons across treatments for different conditions.

Cost-minimisation analysis (CMA) is an economic evaluation in which the consequences of competing interventions are the same, and only inputs, i.e. costs, are taken into consideration. The aim is to decide the least costly way of achieving the same outcome.

Costs in Economic Evaluation Studies

There are three main types of costs in economic evaluation studies: direct, indirect, and intangible. Direct costs are associated directly with the healthcare intervention, such as staff time, medical supplies, cost of travel for the patient, childcare costs for the patient, and costs falling on other social sectors such as domestic help from social services. Indirect costs are incurred by the reduced productivity of the patient, such as time off work, reduced work productivity, and time spent caring for the patient by relatives. Intangible costs are difficult to measure, such as pain of suffering on the part of the patient.

Measures of dispersion are used to indicate the variation of spread of a data set, often in conjunction with a measure of central tendency such as the mean of median. The range, which is the difference between the largest and smallest value, is the simplest measure of dispersion. The interquartile range, which is the difference between the 3rd and 1st quartiles, is another useful measure. Quartiles divide a data set into quarters, and the interquartile range can provide additional information about the spread of the data. However, to get a more representative idea of spread, measures such as the variance and standard deviation are needed. The variance gives an indication of how much the items in the data set vary from the mean, while the standard deviation reflects the distribution of individual scores around their mean. The standard deviation is expressed in the same units as the data set and can be used to indicate how confident we are that data points lie within a particular range. The standard error of the mean is an inferential statistic used to estimate the population mean and is a measure of the spread expected for the mean of the observations. Confidence intervals are often presented alongside sample results such as the mean value, indicating a range that is likely to contain the true value.

Methods of Economic Evaluation

There are four main methods of economic evaluation: cost-effectiveness analysis (CEA), cost-benefit analysis (CBA), cost-utility analysis (CUA), and cost-minimisation analysis (CMA). While all four methods capture costs, they differ in how they assess health effects.

Cost-effectiveness analysis (CEA) compares interventions by relating costs to a single clinical measure of effectiveness, such as symptom reduction of improvement in activities of daily living. The cost-effectiveness ratio is calculated as total cost divided by units of effectiveness. CEA is typically used when CBA cannot be performed due to the inability to monetise benefits.

Cost-benefit analysis (CBA) measures all costs and benefits of an intervention in monetary terms to establish which alternative has the greatest net benefit. CBA requires that all consequences of an intervention, such as life-years saved, treatment side-effects, symptom relief, disability, pain, and discomfort, are allocated a monetary value. CBA is rarely used in mental health service evaluation due to the difficulty in converting benefits from mental health programmes into monetary values.

Cost-utility analysis (CUA) is a special form of CEA in which health benefits/outcomes are measured in broader, more generic ways, enabling comparisons between treatments for different diseases and conditions. Multidimensional health outcomes are measured by a single preference- of utility-based index such as the Quality-Adjusted-Life-Years (QALY). QALYs are a composite measure of gains in life expectancy and health-related quality of life. CUA allows for comparisons across treatments for different conditions.

Cost-minimisation analysis (CMA) is an economic evaluation in which the consequences of competing interventions are the same, and only inputs, i.e. costs, are taken into consideration. The aim is to decide the least costly way of achieving the same outcome.

Costs in Economic Evaluation Studies

There are three main types of costs in economic evaluation studies: direct, indirect, and intangible. Direct costs are associated directly with the healthcare intervention, such as staff time, medical supplies, cost of travel for the patient, childcare costs for the patient, and costs falling on other social sectors such as domestic help from social services. Indirect costs are incurred by the reduced productivity of the patient, such as time off work, reduced work productivity, and time spent caring for the patient by relatives. Intangible costs are difficult to measure, such as pain of suffering on the part of the patient.

Calculation of Standardised Mortality Ratio (SMR)

To calculate the SMR, age and sex-specific death rates in the standard population are obtained. An estimate for the number of people in each category for both the standard and study populations is needed. The number of expected deaths in each age-sex group of the study population is calculated by multiplying the age-sex-specific rates in the standard population by the number of people in each category of the study population. The sum of all age- and sex-specific expected deaths gives the expected number of deaths for the whole study population. The observed number of deaths is then divided by the expected number of deaths to obtain the SMR.

The SMR can be standardised using the direct of indirect method. The direct method is used when the age-sex-specific rates for the study population and the age-sex-structure of the standard population are known. The indirect method is used when the age-specific rates for the study population are unknown of not available. This method uses the observed number of deaths in the study population and compares it to the number of deaths that would be expected if the age distribution was the same as that of the standard population.

The SMR can be interpreted as follows: an SMR less than 1.0 indicates fewer than expected deaths in the study population, an SMR of 1.0 indicates the number of observed deaths equals the number of expected deaths in the study population, and an SMR greater than 1.0 indicates more than expected deaths in the study population (excess deaths). It is sometimes expressed after multiplying by 100.

A case-control design is more suitable than a cohort study for studying sudden infant death syndrome due to its low incidence.

Types of Primary Research Studies and Their Advantages and Disadvantages

Primary research studies can be categorized into six types based on the research question they aim to address. The best type of study for each question type is listed in the table below. There are two main types of study design: experimental and observational. Experimental studies involve an intervention, while observational studies do not. The advantages and disadvantages of each study type are summarized in the table below.

Type of Question Best Type of Study

Therapy Randomized controlled trial (RCT), cohort, case control, case series
Diagnosis Cohort studies with comparison to gold standard test
Prognosis Cohort studies, case control, case series
Etiology/Harm RCT, cohort studies, case control, case series
Prevention RCT, cohort studies, case control, case series
Cost Economic analysis

Study Type Advantages Disadvantages

Randomized Controlled Trial – Unbiased distribution of confounders – Blinding more likely – Randomization facilitates statistical analysis – Expensive – Time-consuming – Volunteer bias – Ethically problematic at times
Cohort Study – Ethically safe – Subjects can be matched – Can establish timing and directionality of events – Eligibility criteria and outcome assessments can be standardized – Administratively easier and cheaper than RCT – Controls may be difficult to identify – Exposure may be linked to a hidden confounder – Blinding is difficult – Randomization not present – For rare disease, large sample sizes of long follow-up necessary
Case-Control Study – Quick and cheap – Only feasible method for very rare disorders of those with long lag between exposure and outcome – Fewer subjects needed than cross-sectional studies – Reliance on recall of records to determine exposure status – Confounders – Selection of control groups is difficult – Potential bias: recall, selection
Cross-Sectional Survey – Cheap and simple – Ethically safe – Establishes association at most, not causality – Recall bias susceptibility – Confounders may be unequally distributed – Neyman bias – Group sizes may be unequal
Ecological Study – Cheap and simple – Ethically safe – Ecological fallacy (when relationships which exist for groups are assumed to also be true for individuals)

In conclusion, the choice of study type depends on the research question being addressed. Each study type has its own advantages and disadvantages, and researchers should carefully consider these when designing their studies.

There are several reporting guidelines available for different types of research studies. The COREQ checklist, consisting of 32 items, is designed for reporting qualitative research that involves interviews and focus groups. The CONSORT Statement provides a 25-item checklist to aid in reporting randomized controlled trials (RCTs). For reporting the pooled findings of multiple studies, the QUOROM and PRISMA guidelines are useful. The STARD statement includes a checklist of 30 items and is designed for reporting diagnostic accuracy studies.

Simpson’s Paradox is a real phenomenon where the comparison of association between variables can change direction when data from multiple groups are merged into one. The other three options are not valid terms.

Types of Bias in Statistics

Bias is a systematic error that can lead to incorrect conclusions. Confounding factors are variables that are associated with both the outcome and the exposure but have no causative role. Confounding can be addressed in the design and analysis stage of a study. The main method of controlling confounding in the analysis phase is stratification analysis. The main methods used in the design stage are matching, randomization, and restriction of participants.

There are two main types of bias: selection bias and information bias. Selection bias occurs when the selected sample is not a representative sample of the reference population. Disease spectrum bias, self-selection bias, participation bias, incidence-prevalence bias, exclusion bias, publication of dissemination bias, citation bias, and Berkson’s bias are all subtypes of selection bias. Information bias occurs when gathered information about exposure, outcome, of both is not correct and there was an error in measurement. Detection bias, recall bias, lead time bias, interviewer/observer bias, verification and work-up bias, Hawthorne effect, and ecological fallacy are all subtypes of information bias.

Clinical tests are used to determine the presence of absence of a disease of condition. To interpret test results, it is important to have a working knowledge of statistics used to describe them. Two by two tables are commonly used to calculate test statistics such as sensitivity and specificity. Sensitivity refers to the proportion of people with a condition that the test correctly identifies, while specificity refers to the proportion of people without a condition that the test correctly identifies. Accuracy tells us how closely a test measures to its true value, while predictive values help us understand the likelihood of having a disease based on a positive of negative test result. Likelihood ratios combine sensitivity and specificity into a single figure that can refine our estimation of the probability of a disease being present. Pre and post-test odds and probabilities can also be calculated to better understand the likelihood of having a disease before and after a test is carried out. Fagan’s nomogram is a useful tool for calculating post-test probabilities.

The odds of being married are 3.77 times higher in individuals with panic disorder compared to controls.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

Understanding Stats Variables

Variables are characteristics, numbers, of quantities that can be measured of counted. They are also known as data items. Examples of variables include age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour, and vehicle type. The value of a variable may vary between data units in a population. In a typical study, there are three main variables: independent, dependent, and controlled variables.

The independent variable is something that the researcher purposely changes during the investigation. The dependent variable is the one that is observed and changes in response to the independent variable. Controlled variables are those that are not changed during the experiment. Dependent variables are affected by independent variables but not by controlled variables, as these do not vary throughout the study.

For instance, a researcher wants to test the effectiveness of a new weight loss medication. Participants are divided into three groups, with the first group receiving a placebo (0mg dosage), the second group a 10 mg dose, and the third group a 40 mg dose. After six months, the participants’ weights are measured. In this case, the independent variable is the dosage of the medication, as that is what is being manipulated. The dependent variable is the weight, as that is what is being measured.

Measures of Central Tendency

Measures of central tendency are used in descriptive statistics to summarize the middle of typical value of a data set. There are three common measures of central tendency: the mean, median, and mode.

The median is the middle value in a data set that has been arranged in numerical order. It is not affected by outliers and is used for ordinal data. The mode is the most frequent value in a data set and is used for categorical data. The mean is calculated by adding all the values in a data set and dividing by the number of values. It is sensitive to outliers and is used for interval and ratio data.

The appropriate measure of central tendency depends on the measurement scale of the data. For nominal and categorical data, the mode is used. For ordinal data, the median of mode is used. For interval data with a normal distribution, the mean is preferable, but the median of mode can also be used. For interval data with skewed distribution, the median is used. For ratio data, the mean is preferable, but the median of mode can also be used for skewed data.

In addition to measures of central tendency, the range is also used to describe the spread of a data set. It is calculated by subtracting the smallest value from the largest value.

This set of numbers has no mode as no number occurs more than once: 3, 6, 9, 16, 27, 37, 48.

Measures of Central Tendency

Measures of central tendency are used in descriptive statistics to summarize the middle of typical value of a data set. There are three common measures of central tendency: the mean, median, and mode.

The median is the middle value in a data set that has been arranged in numerical order. It is not affected by outliers and is used for ordinal data. The mode is the most frequent value in a data set and is used for categorical data. The mean is calculated by adding all the values in a data set and dividing by the number of values. It is sensitive to outliers and is used for interval and ratio data.

The appropriate measure of central tendency depends on the measurement scale of the data. For nominal and categorical data, the mode is used. For ordinal data, the median of mode is used. For interval data with a normal distribution, the mean is preferable, but the median of mode can also be used. For interval data with skewed distribution, the median is used. For ratio data, the mean is preferable, but the median of mode can also be used for skewed data.

In addition to measures of central tendency, the range is also used to describe the spread of a data set. It is calculated by subtracting the smallest value from the largest value.

Triangulation is a technique commonly employed in research to ensure the accuracy and reliability of results. It involves using multiple methods to verify findings, also known as ‘cross examination’. This approach increases confidence in the results by demonstrating consistency across different methods. Investigator triangulation involves using researchers with diverse backgrounds, while method triangulation involves using different techniques such as interviews and focus groups. The goal of triangulation in qualitative research is to enhance the credibility and validity of the findings by addressing potential biases and limitations associated with single-method, single-observer studies.

An NNT of 1 indicates that every patient who receives the treatment experiences a positive outcome, while no patient in the control group experiences the same outcome. This represents an ideal outcome.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

Stats Publication Bias

Publication bias refers to the tendency for studies with positive findings to be published more than studies with negative findings, leading to incomplete data sets in meta-analyses and erroneous conclusions. Graphical methods such as funnel plots, Galbraith plots, ordered forest plots, and normal quantile plots can be used to detect publication bias. Funnel plots are the most commonly used and offer an easy visual way to ensure that published literature is evenly weighted. The x-axis represents the effect size, and the y-axis represents the study size. A symmetrical, inverted funnel shape indicates that publication bias is unlikely, while an asymmetrical funnel indicates a relationship between treatment effect and study size, indicating either publication bias of small study effects.

Skewed Data: Understanding the Relationship between Mean, Median, and Mode

When analyzing a data set, it is important to consider the shape of the distribution. In a normally distributed data set, the curve is symmetrical and bell-shaped, with the median, mode, and mean all equal. However, in skewed data sets, the distribution is asymmetrical, with the bulk of the data concentrated on one side of the figure.

In a negatively skewed distribution, the left tail is longer, and the bulk of the data is concentrated to the right of the figure. In contrast, a positively skewed distribution has a longer right tail, with the bulk of the data concentrated to the left of the figure. In both cases, the median is positioned between the mode and the mean, as it represents the halfway point of the distribution.

However, the mean is affected by extreme values of outliers, causing it to move away from the median in the direction of the tail. In positively skewed data, the mean is greater than the median, which is greater than the mode. In negatively skewed data, the mode is greater than the median, which is greater than the mean.

Understanding the relationship between mean, median, and mode in skewed data sets is crucial for accurate data analysis and interpretation. By recognizing the shape of the distribution, researchers can make informed decisions about which measures of central tendency to use and how to interpret their results.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

The formula for the standard error of the mean is equal to the standard deviation divided by the square root of the number of patients.

Measures of dispersion are used to indicate the variation of spread of a data set, often in conjunction with a measure of central tendency such as the mean of median. The range, which is the difference between the largest and smallest value, is the simplest measure of dispersion. The interquartile range, which is the difference between the 3rd and 1st quartiles, is another useful measure. Quartiles divide a data set into quarters, and the interquartile range can provide additional information about the spread of the data. However, to get a more representative idea of spread, measures such as the variance and standard deviation are needed. The variance gives an indication of how much the items in the data set vary from the mean, while the standard deviation reflects the distribution of individual scores around their mean. The standard deviation is expressed in the same units as the data set and can be used to indicate how confident we are that data points lie within a particular range. The standard error of the mean is an inferential statistic used to estimate the population mean and is a measure of the spread expected for the mean of the observations. Confidence intervals are often presented alongside sample results such as the mean value, indicating a range that is likely to contain the true value.

Stats Publication Bias

Publication bias refers to the tendency for studies with positive findings to be published more than studies with negative findings, leading to incomplete data sets in meta-analyses and erroneous conclusions. Graphical methods such as funnel plots, Galbraith plots, ordered forest plots, and normal quantile plots can be used to detect publication bias. Funnel plots are the most commonly used and offer an easy visual way to ensure that published literature is evenly weighted. The x-axis represents the effect size, and the y-axis represents the study size. A symmetrical, inverted funnel shape indicates that publication bias is unlikely, while an asymmetrical funnel indicates a relationship between treatment effect and study size, indicating either publication bias of small study effects.

To determine the number needed to treat (NNT), we first calculated the absolute risk reduction (ARR) using the formula ARR = CER – EER, where CER is the control event rate and EER is the experimental event rate. In this case, the ARR was 0.47, which is the reciprocal of the NNT. Therefore, the NNT was calculated as 2.12. This means that for every two patients treated with the active medication, at least one patient will have a better outcome compared to those treated with a placebo.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

Types of Bias in Statistics

Bias is a systematic error that can lead to incorrect conclusions. Confounding factors are variables that are associated with both the outcome and the exposure but have no causative role. Confounding can be addressed in the design and analysis stage of a study. The main method of controlling confounding in the analysis phase is stratification analysis. The main methods used in the design stage are matching, randomization, and restriction of participants.

There are two main types of bias: selection bias and information bias. Selection bias occurs when the selected sample is not a representative sample of the reference population. Disease spectrum bias, self-selection bias, participation bias, incidence-prevalence bias, exclusion bias, publication of dissemination bias, citation bias, and Berkson’s bias are all subtypes of selection bias. Information bias occurs when gathered information about exposure, outcome, of both is not correct and there was an error in measurement. Detection bias, recall bias, lead time bias, interviewer/observer bias, verification and work-up bias, Hawthorne effect, and ecological fallacy are all subtypes of information bias.

Qualitative research is a method of inquiry that seeks to understand the meaning and experience dimensions of human lives and social worlds. There are different approaches to qualitative research, such as ethnography, phenomenology, and grounded theory, each with its own purpose, role of the researcher, stages of research, and method of data analysis. The most common methods used in healthcare research are interviews and focus groups. Sampling techniques include convenience sampling, purposive sampling, quota sampling, snowball sampling, and case study sampling. Sample size can be determined by data saturation, which occurs when new categories, themes, of explanations stop emerging from the data. Validity can be assessed through triangulation, respondent validation, bracketing, and reflexivity. Analytical approaches include content analysis and constant comparison.

The Delphi Method: A Widely Used Technique for Achieving Convergence of Opinion

The Delphi method is a well-established technique for soliciting expert opinions on real-world knowledge within specific topic areas. The process involves multiple rounds of questionnaires, with each round building on the previous one to achieve convergence of opinion among the participants. However, there are potential issues with the Delphi method, such as the time-consuming nature of the process, low response rates, and the potential for investigators to influence the opinions of the participants. Despite these challenges, the Delphi method remains a valuable tool for generating consensus among experts in various fields.

If the odds ratio is less than 1, it means that the likelihood of experiencing a stroke is lower for individuals who are taking the new drug compared to those who are receiving the usual treatment.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

Understanding the Kappa Statistic for Measuring Interobserver Variation

The kappa statistic, also known as Cohen’s kappa coefficient, is a useful tool for quantifying the level of agreement between independent observers. This measure can be applied in any situation where multiple observers are evaluating the same thing, such as in medical diagnoses of research studies. The kappa coefficient ranges from 0 to 1, with 0 indicating complete disagreement and 1 indicating perfect agreement. By using the kappa statistic, researchers and practitioners can gain insight into the level of interobserver variation present in their data, which can help to improve the accuracy and reliability of their findings. Overall, the kappa statistic is a valuable tool for understanding and measuring interobserver variation in a variety of contexts.

The distinction between interval and ratio scales is illustrated by the fact that ratio scales have a non-arbitrary zero point and meaningful ratios between values. Celsius and Fahrenheit temperature measurements are examples of interval scales, while the Kelvin scale is a ratio scale due to its zero point representing the complete absence of heat and the meaningful ratios between its values.

Scales of Measurement in Statistics

In the 1940s, Stanley Smith Stevens introduced four scales of measurement to categorize data variables. Knowing the scale of measurement for a variable is crucial in selecting the appropriate statistical analysis. The four scales of measurement are ratio, interval, ordinal, and nominal.

Ratio scales are similar to interval scales, but they have true zero points. Examples of ratio scales include weight, time, and length. Interval scales measure the difference between two values, and one unit on the scale represents the same magnitude on the trait of characteristic being measured across the whole range of the scale. The Fahrenheit scale for temperature is an example of an interval scale.

Ordinal scales categorize observed values into set categories that can be ordered, but the intervals between each value are uncertain. Examples of ordinal scales include social class, education level, and income level. Nominal scales categorize observed values into set categories that have no particular order of hierarchy. Examples of nominal scales include genotype, blood type, and political party.

Data can also be categorized as quantitative of qualitative. Quantitative variables take on numeric values and can be further classified into discrete and continuous types. Qualitative variables do not take on numerical values and are usually names. Some qualitative variables have an inherent order in their categories and are described as ordinal. Qualitative variables are also called categorical of nominal variables. When a qualitative variable has only two categories, it is called a binary variable.

The probability of detecting a difference by chance is 1 in 20 times when the p-value is 0.05, which is the conventional cutoff. In this case, the answer is 1 in 14 times, which is equivalent to a p-value of 0.07.

Understanding Hypothesis Testing in Statistics

In statistics, it is not feasible to investigate hypotheses on entire populations. Therefore, researchers take samples and use them to make estimates about the population they are drawn from. However, this leads to uncertainty as there is no guarantee that the sample taken will be truly representative of the population, resulting in potential errors. Statistical hypothesis testing is the process used to determine if claims from samples to populations can be made and with what certainty.

The null hypothesis (Ho) is the claim that there is no real difference between two groups, while the alternative hypothesis (H1 of Ha) suggests that any difference is due to some non-random chance. The alternative hypothesis can be one-tailed of two-tailed, depending on whether it seeks to establish a difference of a change in one direction.

Two types of errors may occur when testing the null hypothesis: Type I and Type II errors. Type I error occurs when the null hypothesis is rejected when it is true, while Type II error occurs when the null hypothesis is accepted when it is false. The power of a study is the probability of correctly rejecting the null hypothesis when it is false, and it can be increased by increasing the sample size.

P-values provide information on statistical significance and help researchers decide if study results have occurred due to chance. The p-value is the probability of obtaining a result that is as large of larger when in reality there is no difference between two groups. The cutoff for the p-value is called the significance level (alpha level), typically set at 0.05. If the p-value is less than the cutoff, the null hypothesis is rejected, and if it is greater or equal to the cut off, the null hypothesis is not rejected. However, the p-value does not indicate clinical significance, which may be too small to be meaningful.

To make predictions about systolic blood pressure, linear regression is necessary in this situation.

Stats: Correlation and Regression

Correlation and regression are related but not interchangeable terms. Correlation is used to test for association between variables, while regression is used to predict values of dependent variables from independent variables. Correlation can be linear, non-linear, of non-existent, and can be strong, moderate, of weak. The strength of a linear relationship is measured by the correlation coefficient, which can be positive of negative and ranges from very weak to very strong. However, the interpretation of a correlation coefficient depends on the context and purposes. Correlation can suggest association but cannot prove of disprove causation. Linear regression, on the other hand, can be used to predict how much one variable changes when a second variable is changed. Scatter graphs are used in correlation and regression analyses to visually determine if variables are associated and to detect outliers. When constructing a scatter graph, the dependent variable is typically placed on the vertical axis and the independent variable on the horizontal axis.

Publication bias refers to the tendency of researchers, editors, and pharmaceutical companies to favor the publication of studies with positive results over those with negative of inconclusive results. This bias can have various causes and can result in a skewed representation of the literature. The file drawer problem refers to the phenomenon of unpublished negative studies. HARKing, of hypothesizing after the results are known, is a form of outcome reporting bias where outcomes are selectively reported based on the strength and direction of observed associations. Begg’s funnel plot is an analytical tool used to quantify the presence of publication bias.

Kappa is used to assess the consistency of agreement between different raters.

Understanding the Kappa Statistic for Measuring Interobserver Variation

The kappa statistic, also known as Cohen’s kappa coefficient, is a useful tool for quantifying the level of agreement between independent observers. This measure can be applied in any situation where multiple observers are evaluating the same thing, such as in medical diagnoses of research studies. The kappa coefficient ranges from 0 to 1, with 0 indicating complete disagreement and 1 indicating perfect agreement. By using the kappa statistic, researchers and practitioners can gain insight into the level of interobserver variation present in their data, which can help to improve the accuracy and reliability of their findings. Overall, the kappa statistic is a valuable tool for understanding and measuring interobserver variation in a variety of contexts.

Choosing the right statistical test can be challenging, but understanding the basic principles can help. Different tests have different assumptions, and using the wrong one can lead to inaccurate results. To identify the appropriate test, a flow chart can be used based on three main factors: the type of dependent variable, the type of data, and whether the groups/samples are independent of dependent. It is important to know which tests are parametric and non-parametric, as well as their alternatives. For example, the chi-squared test is used to assess differences in categorical variables and is non-parametric, while Pearson’s correlation coefficient measures linear correlation between two variables and is parametric. T-tests are used to compare means between two groups, and ANOVA is used to compare means between more than two groups. Non-parametric equivalents to ANOVA include the Kruskal-Wallis analysis of ranks, the Median test, Friedman’s two-way analysis of variance, and Cochran Q test. Understanding these tests and their assumptions can help researchers choose the appropriate statistical test for their data.

To examine differences between various groups, researchers may conduct subgroup analyses by dividing participant data into subsets. These subsets may include specific demographics (e.g. gender) of study characteristics (e.g. location). Subgroup analyses can help explain inconsistent findings of provide insights into particular patient populations, interventions, of study types.

Qualitative research is a method of inquiry that seeks to understand the meaning and experience dimensions of human lives and social worlds. There are different approaches to qualitative research, such as ethnography, phenomenology, and grounded theory, each with its own purpose, role of the researcher, stages of research, and method of data analysis. The most common methods used in healthcare research are interviews and focus groups. Sampling techniques include convenience sampling, purposive sampling, quota sampling, snowball sampling, and case study sampling. Sample size can be determined by data saturation, which occurs when new categories, themes, of explanations stop emerging from the data. Validity can be assessed through triangulation, respondent validation, bracketing, and reflexivity. Analytical approaches include content analysis and constant comparison.

Measures of dispersion are used to indicate the variation of spread of a data set, often in conjunction with a measure of central tendency such as the mean of median. The range, which is the difference between the largest and smallest value, is the simplest measure of dispersion. The interquartile range, which is the difference between the 3rd and 1st quartiles, is another useful measure. Quartiles divide a data set into quarters, and the interquartile range can provide additional information about the spread of the data. However, to get a more representative idea of spread, measures such as the variance and standard deviation are needed. The variance gives an indication of how much the items in the data set vary from the mean, while the standard deviation reflects the distribution of individual scores around their mean. The standard deviation is expressed in the same units as the data set and can be used to indicate how confident we are that data points lie within a particular range. The standard error of the mean is an inferential statistic used to estimate the population mean and is a measure of the spread expected for the mean of the observations. Confidence intervals are often presented alongside sample results such as the mean value, indicating a range that is likely to contain the true value.

Measures of dispersion are used to indicate the variation of spread of a data set, often in conjunction with a measure of central tendency such as the mean of median. The range, which is the difference between the largest and smallest value, is the simplest measure of dispersion. The interquartile range, which is the difference between the 3rd and 1st quartiles, is another useful measure. Quartiles divide a data set into quarters, and the interquartile range can provide additional information about the spread of the data. However, to get a more representative idea of spread, measures such as the variance and standard deviation are needed. The variance gives an indication of how much the items in the data set vary from the mean, while the standard deviation reflects the distribution of individual scores around their mean. The standard deviation is expressed in the same units as the data set and can be used to indicate how confident we are that data points lie within a particular range. The standard error of the mean is an inferential statistic used to estimate the population mean and is a measure of the spread expected for the mean of the observations. Confidence intervals are often presented alongside sample results such as the mean value, indicating a range that is likely to contain the true value.

Qualitative research is a method of inquiry that seeks to understand the meaning and experience dimensions of human lives and social worlds. There are different approaches to qualitative research, such as ethnography, phenomenology, and grounded theory, each with its own purpose, role of the researcher, stages of research, and method of data analysis. The most common methods used in healthcare research are interviews and focus groups. Sampling techniques include convenience sampling, purposive sampling, quota sampling, snowball sampling, and case study sampling. Sample size can be determined by data saturation, which occurs when new categories, themes, of explanations stop emerging from the data. Validity can be assessed through triangulation, respondent validation, bracketing, and reflexivity. Analytical approaches include content analysis and constant comparison.

Stats Confounding

A confounding factor is a factor that can obscure the relationship between an exposure and an outcome in a study. This factor is associated with both the exposure and the disease. For example, in a study that finds a link between coffee consumption and heart disease, smoking could be a confounding factor because it is associated with both drinking coffee and heart disease. Confounding occurs when there is a non-random distribution of risk factors in the population, such as age, sex, and social class.

To control for confounding in the design stage of an experiment, researchers can use randomization, restriction, of matching. Randomization aims to produce an even distribution of potential risk factors in two populations. Restriction involves limiting the study population to a specific group to ensure similar age distributions. Matching involves finding and enrolling participants who are similar in terms of potential confounding factors.

In the analysis stage of an experiment, researchers can control for confounding by using stratification of multivariate models such as logistic regression, linear regression, of analysis of covariance (ANCOVA). Stratification involves creating categories of strata in which the confounding variable does not vary of varies minimally.

Overall, controlling for confounding is important in ensuring that the relationship between an exposure and an outcome is accurately assessed in a study.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

Funnel plots are utilized in meta-analyses to visually display the potential presence of publication bias. However, it is important to note that an asymmetric funnel plot does not necessarily confirm the existence of publication bias, as other factors may contribute to its formation.

Stats Publication Bias

Publication bias refers to the tendency for studies with positive findings to be published more than studies with negative findings, leading to incomplete data sets in meta-analyses and erroneous conclusions. Graphical methods such as funnel plots, Galbraith plots, ordered forest plots, and normal quantile plots can be used to detect publication bias. Funnel plots are the most commonly used and offer an easy visual way to ensure that published literature is evenly weighted. The x-axis represents the effect size, and the y-axis represents the study size. A symmetrical, inverted funnel shape indicates that publication bias is unlikely, while an asymmetrical funnel indicates a relationship between treatment effect and study size, indicating either publication bias of small study effects.

Methods of Economic Evaluation

There are four main methods of economic evaluation: cost-effectiveness analysis (CEA), cost-benefit analysis (CBA), cost-utility analysis (CUA), and cost-minimisation analysis (CMA). While all four methods capture costs, they differ in how they assess health effects.

Cost-effectiveness analysis (CEA) compares interventions by relating costs to a single clinical measure of effectiveness, such as symptom reduction of improvement in activities of daily living. The cost-effectiveness ratio is calculated as total cost divided by units of effectiveness. CEA is typically used when CBA cannot be performed due to the inability to monetise benefits.

Cost-benefit analysis (CBA) measures all costs and benefits of an intervention in monetary terms to establish which alternative has the greatest net benefit. CBA requires that all consequences of an intervention, such as life-years saved, treatment side-effects, symptom relief, disability, pain, and discomfort, are allocated a monetary value. CBA is rarely used in mental health service evaluation due to the difficulty in converting benefits from mental health programmes into monetary values.

Cost-utility analysis (CUA) is a special form of CEA in which health benefits/outcomes are measured in broader, more generic ways, enabling comparisons between treatments for different diseases and conditions. Multidimensional health outcomes are measured by a single preference- of utility-based index such as the Quality-Adjusted-Life-Years (QALY). QALYs are a composite measure of gains in life expectancy and health-related quality of life. CUA allows for comparisons across treatments for different conditions.

Cost-minimisation analysis (CMA) is an economic evaluation in which the consequences of competing interventions are the same, and only inputs, i.e. costs, are taken into consideration. The aim is to decide the least costly way of achieving the same outcome.

Costs in Economic Evaluation Studies

There are three main types of costs in economic evaluation studies: direct, indirect, and intangible. Direct costs are associated directly with the healthcare intervention, such as staff time, medical supplies, cost of travel for the patient, childcare costs for the patient, and costs falling on other social sectors such as domestic help from social services. Indirect costs are incurred by the reduced productivity of the patient, such as time off work, reduced work productivity, and time spent caring for the patient by relatives. Intangible costs are difficult to measure, such as pain of suffering on the part of the patient.

Sampling Methods in Statistics

When collecting data from a population, it is often impractical and unnecessary to gather information from every single member. Instead, taking a sample is preferred. However, it is crucial that the sample accurately represents the population from which it is drawn. There are two main types of sampling methods: probability (random) sampling and non-probability (non-random) sampling.

Non-probability sampling methods, also known as judgement samples, are based on human choice rather than random selection. These samples are convenient and cheaper than probability sampling methods. Examples of non-probability sampling methods include voluntary sampling, convenience sampling, snowball sampling, and quota sampling.

Probability sampling methods give a more representative sample of the population than non-probability sampling. In each probability sampling technique, each population element has a known (non-zero) chance of being selected for the sample. Examples of probability sampling methods include simple random sampling, systematic sampling, cluster sampling, stratified sampling, and multistage sampling.

Simple random sampling is a sample in which every member of the population has an equal chance of being chosen. Systematic sampling involves selecting every kth member of the population. Cluster sampling involves dividing a population into separate groups (called clusters) and selecting a random sample of clusters. Stratified sampling involves dividing a population into groups (strata) and taking a random sample from each strata. Multistage sampling is a more complex method that involves several stages and combines two of more sampling methods.

Overall, probability sampling methods give a more representative sample of the population, but non-probability sampling methods are often more convenient and cheaper. It is important to choose the appropriate sampling method based on the research question and available resources.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

The study used the CGI scale, which produces ordinal data. However, the data was transformed into dichotomous data by dividing it into two categories. The CGI-I is a simple seven-point scale that compares a patient’s overall clinical condition to the one week period just prior to the initiation of medication use. The ratings range from very much improved to very much worse since the initiation of treatment.

Scales of Measurement in Statistics

In the 1940s, Stanley Smith Stevens introduced four scales of measurement to categorize data variables. Knowing the scale of measurement for a variable is crucial in selecting the appropriate statistical analysis. The four scales of measurement are ratio, interval, ordinal, and nominal.

Ratio scales are similar to interval scales, but they have true zero points. Examples of ratio scales include weight, time, and length. Interval scales measure the difference between two values, and one unit on the scale represents the same magnitude on the trait of characteristic being measured across the whole range of the scale. The Fahrenheit scale for temperature is an example of an interval scale.

Ordinal scales categorize observed values into set categories that can be ordered, but the intervals between each value are uncertain. Examples of ordinal scales include social class, education level, and income level. Nominal scales categorize observed values into set categories that have no particular order of hierarchy. Examples of nominal scales include genotype, blood type, and political party.

Data can also be categorized as quantitative of qualitative. Quantitative variables take on numeric values and can be further classified into discrete and continuous types. Qualitative variables do not take on numerical values and are usually names. Some qualitative variables have an inherent order in their categories and are described as ordinal. Qualitative variables are also called categorical of nominal variables. When a qualitative variable has only two categories, it is called a binary variable.

The scenario described above highlights the issue of information bias, which can arise due to errors in measuring, collecting, of interpreting data related to the exposure of disease. Specifically, interviewer/observer bias is a type of information bias that can occur when a single psychiatrist has a tendency to either over of under diagnose a condition, potentially skewing the study results.

Types of Bias in Statistics

Bias is a systematic error that can lead to incorrect conclusions. Confounding factors are variables that are associated with both the outcome and the exposure but have no causative role. Confounding can be addressed in the design and analysis stage of a study. The main method of controlling confounding in the analysis phase is stratification analysis. The main methods used in the design stage are matching, randomization, and restriction of participants.

There are two main types of bias: selection bias and information bias. Selection bias occurs when the selected sample is not a representative sample of the reference population. Disease spectrum bias, self-selection bias, participation bias, incidence-prevalence bias, exclusion bias, publication of dissemination bias, citation bias, and Berkson’s bias are all subtypes of selection bias. Information bias occurs when gathered information about exposure, outcome, of both is not correct and there was an error in measurement. Detection bias, recall bias, lead time bias, interviewer/observer bias, verification and work-up bias, Hawthorne effect, and ecological fallacy are all subtypes of information bias.

To calculate the ARR, we first need to find the CER and EER. The CER is the conversion rate of the control group, which is 200 out of 800, of 0.25. The EER is the conversion rate of the experimental group, which is 120 out of 1,200, of 0.1.

To find the ARR, we subtract the EER from the CER:

ARR = CER – EER
ARR = 0.25 – 0.1
ARR = 0.15

Therefore, the ARR is 0.15 of 15%.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

The search ‘Psychosis AND (cannabis AND sexual abuse)’ would also return citations with all three terms, but it allows for the possibility of citations that include both cannabis and sexual abuse, but not necessarily psychosis.

Evidence-based medicine involves four basic steps: developing a focused clinical question, searching for the best evidence, critically appraising the evidence, and applying the evidence and evaluating the outcome. When developing a question, it is important to understand the difference between background and foreground questions. Background questions are general questions about conditions, illnesses, syndromes, and pathophysiology, while foreground questions are more often about issues of care. The PICO system is often used to define the components of a foreground question: patient group of interest, intervention of interest, comparison, and primary outcome.

When searching for evidence, it is important to have a basic understanding of the types of evidence and sources of information. Scientific literature is divided into two basic categories: primary (empirical research) and secondary (interpretation and analysis of primary sources). Unfiltered sources are large databases of articles that have not been pre-screened for quality, while filtered resources summarize and appraise evidence from several studies.

There are several databases and search engines that can be used to search for evidence, including Medline and PubMed, Embase, the Cochrane Library, PsycINFO, CINAHL, and OpenGrey. Boolean logic can be used to combine search terms in PubMed, and phrase searching and truncation can also be used. Medical Subject Headings (MeSH) are used by indexers to describe articles for MEDLINE records, and the MeSH Database is like a thesaurus that enables exploration of this vocabulary.

When a study has good external validity, its findings can be applied to other populations with confidence.

Validity in statistics refers to how accurately something measures what it claims to measure. There are two main types of validity: internal and external. Internal validity refers to the confidence we have in the cause and effect relationship in a study, while external validity refers to the degree to which the conclusions of a study can be applied to other people, places, and times. There are various threats to both internal and external validity, such as sampling, measurement instrument obtrusiveness, and reactive effects of setting. Additionally, there are several subtypes of validity, including face validity, content validity, criterion validity, and construct validity. Each subtype has its own specific focus and methods for testing validity.

When investigating prognosis, the hierarchy of study designs starts with a systematic review of cohort studies, followed by a cohort study, follow-up of untreated patients from randomized controlled trials, case series, and expert opinion. The strength of evidence provided by a study depends on its ability to minimize bias and maximize attribution. The Agency for Healthcare Policy and Research hierarchy of study types is widely accepted as reliable, with systematic reviews and meta-analyses of randomized controlled trials at the top, followed by randomized controlled trials, non-randomized intervention studies, observational studies, and non-experimental studies.

Disease Rates and Their Interpretation

Disease rates are a measure of the occurrence of a disease in a population. They are used to establish causation, monitor interventions, and measure the impact of exposure on disease rates. The attributable risk is the difference in the rate of disease between the exposed and unexposed groups. It tells us what proportion of deaths in the exposed group were due to the exposure. The relative risk is the risk of an event relative to exposure. It is calculated by dividing the rate of disease in the exposed group by the rate of disease in the unexposed group. A relative risk of 1 means there is no difference between the two groups. A relative risk of <1 means that the event is less likely to occur in the exposed group, while a relative risk of >1 means that the event is more likely to occur in the exposed group. The population attributable risk is the reduction in incidence that would be observed if the population were entirely unexposed. It can be calculated by multiplying the attributable risk by the prevalence of exposure in the population. The attributable proportion is the proportion of the disease that would be eliminated in a population if its disease rate were reduced to that of the unexposed group.

Stats Association and Causation

When two variables are found to be more commonly present together, they are said to be associated. However, this association can be of three types: spurious, indirect, of direct. Spurious association is one that has arisen by chance and is not real, while indirect association is due to the presence of another factor, known as a confounding variable. Direct association, on the other hand, is a true association not linked by a third variable.

Once an association has been established, the next question is whether it is causal. To determine causation, the Bradford Hill Causal Criteria are used. These criteria include strength, temporality, specificity, coherence, and consistency. The stronger the association, the more likely it is to be truly causal. Temporality refers to whether the exposure precedes the outcome. Specificity asks whether the suspected cause is associated with a specific outcome of disease. Coherence refers to whether the association fits with other biological knowledge. Finally, consistency asks whether the same association is found in many studies.

An ecological fallacy is a potential error that can occur when generalizing relationships observed among groups to individuals. This is a concern when conducting analyses of ecological studies.

Types of Primary Research Studies and Their Advantages and Disadvantages

Primary research studies can be categorized into six types based on the research question they aim to address. The best type of study for each question type is listed in the table below. There are two main types of study design: experimental and observational. Experimental studies involve an intervention, while observational studies do not. The advantages and disadvantages of each study type are summarized in the table below.

Type of Question Best Type of Study

Therapy Randomized controlled trial (RCT), cohort, case control, case series
Diagnosis Cohort studies with comparison to gold standard test
Prognosis Cohort studies, case control, case series
Etiology/Harm RCT, cohort studies, case control, case series
Prevention RCT, cohort studies, case control, case series
Cost Economic analysis

Study Type Advantages Disadvantages

Randomized Controlled Trial – Unbiased distribution of confounders – Blinding more likely – Randomization facilitates statistical analysis – Expensive – Time-consuming – Volunteer bias – Ethically problematic at times
Cohort Study – Ethically safe – Subjects can be matched – Can establish timing and directionality of events – Eligibility criteria and outcome assessments can be standardized – Administratively easier and cheaper than RCT – Controls may be difficult to identify – Exposure may be linked to a hidden confounder – Blinding is difficult – Randomization not present – For rare disease, large sample sizes of long follow-up necessary
Case-Control Study – Quick and cheap – Only feasible method for very rare disorders of those with long lag between exposure and outcome – Fewer subjects needed than cross-sectional studies – Reliance on recall of records to determine exposure status – Confounders – Selection of control groups is difficult – Potential bias: recall, selection
Cross-Sectional Survey – Cheap and simple – Ethically safe – Establishes association at most, not causality – Recall bias susceptibility – Confounders may be unequally distributed – Neyman bias – Group sizes may be unequal
Ecological Study – Cheap and simple – Ethically safe – Ecological fallacy (when relationships which exist for groups are assumed to also be true for individuals)

In conclusion, the choice of study type depends on the research question being addressed. Each study type has its own advantages and disadvantages, and researchers should carefully consider these when designing their studies.

Normality Testing in Statistics

In statistics, parametric tests are based on the assumption that the data set follows a normal distribution. On the other hand, non-parametric tests do not require this assumption but are less powerful. To check if a distribution is normally distributed, there are several tests available, including the Kolmogorov-Smirnov (Goodness-of-Fit) Test, Jarque-Bera test, Wilk-Shapiro test, P-plot, and Q-plot. However, it is important to note that if a data set is not normally distributed, it may be possible to transform it to make it follow a normal distribution, such as by taking the logarithm of the values.

Understanding Hypothesis Testing in Statistics

In statistics, it is not feasible to investigate hypotheses on entire populations. Therefore, researchers take samples and use them to make estimates about the population they are drawn from. However, this leads to uncertainty as there is no guarantee that the sample taken will be truly representative of the population, resulting in potential errors. Statistical hypothesis testing is the process used to determine if claims from samples to populations can be made and with what certainty.

The null hypothesis (Ho) is the claim that there is no real difference between two groups, while the alternative hypothesis (H1 of Ha) suggests that any difference is due to some non-random chance. The alternative hypothesis can be one-tailed of two-tailed, depending on whether it seeks to establish a difference of a change in one direction.

Two types of errors may occur when testing the null hypothesis: Type I and Type II errors. Type I error occurs when the null hypothesis is rejected when it is true, while Type II error occurs when the null hypothesis is accepted when it is false. The power of a study is the probability of correctly rejecting the null hypothesis when it is false, and it can be increased by increasing the sample size.

P-values provide information on statistical significance and help researchers decide if study results have occurred due to chance. The p-value is the probability of obtaining a result that is as large of larger when in reality there is no difference between two groups. The cutoff for the p-value is called the significance level (alpha level), typically set at 0.05. If the p-value is less than the cutoff, the null hypothesis is rejected, and if it is greater or equal to the cut off, the null hypothesis is not rejected. However, the p-value does not indicate clinical significance, which may be too small to be meaningful.

The task assigned to the researcher is to conduct a cost-effectiveness analysis, which involves comparing two interventions based on their costs and their impact on a single clinical measure of effectiveness, specifically the reduction in symptom severity as measured by the PANSS.

Methods of Economic Evaluation

There are four main methods of economic evaluation: cost-effectiveness analysis (CEA), cost-benefit analysis (CBA), cost-utility analysis (CUA), and cost-minimisation analysis (CMA). While all four methods capture costs, they differ in how they assess health effects.

Cost-effectiveness analysis (CEA) compares interventions by relating costs to a single clinical measure of effectiveness, such as symptom reduction of improvement in activities of daily living. The cost-effectiveness ratio is calculated as total cost divided by units of effectiveness. CEA is typically used when CBA cannot be performed due to the inability to monetise benefits.

Cost-benefit analysis (CBA) measures all costs and benefits of an intervention in monetary terms to establish which alternative has the greatest net benefit. CBA requires that all consequences of an intervention, such as life-years saved, treatment side-effects, symptom relief, disability, pain, and discomfort, are allocated a monetary value. CBA is rarely used in mental health service evaluation due to the difficulty in converting benefits from mental health programmes into monetary values.

Cost-utility analysis (CUA) is a special form of CEA in which health benefits/outcomes are measured in broader, more generic ways, enabling comparisons between treatments for different diseases and conditions. Multidimensional health outcomes are measured by a single preference- of utility-based index such as the Quality-Adjusted-Life-Years (QALY). QALYs are a composite measure of gains in life expectancy and health-related quality of life. CUA allows for comparisons across treatments for different conditions.

Cost-minimisation analysis (CMA) is an economic evaluation in which the consequences of competing interventions are the same, and only inputs, i.e. costs, are taken into consideration. The aim is to decide the least costly way of achieving the same outcome.

Costs in Economic Evaluation Studies

There are three main types of costs in economic evaluation studies: direct, indirect, and intangible. Direct costs are associated directly with the healthcare intervention, such as staff time, medical supplies, cost of travel for the patient, childcare costs for the patient, and costs falling on other social sectors such as domestic help from social services. Indirect costs are incurred by the reduced productivity of the patient, such as time off work, reduced work productivity, and time spent caring for the patient by relatives. Intangible costs are difficult to measure, such as pain of suffering on the part of the patient.

Odds Ratio Calculation for Birth Difficulties in Case and Control Groups

The odds ratio is a statistical measure that compares the likelihood of an event occurring in one group to that of another group. In this case, we are interested in the odds of birth difficulties in a case group compared to a control group.

To calculate the odds ratio, we need to determine the number of individuals in each group who had birth difficulties and those who did not. In the case group, 67 individuals had birth difficulties, while 229 did not. In the control group, 61 individuals had birth difficulties, while 235 did not.

Using these numbers, we can calculate the odds ratio as follows:

Odds ratio = (67/229) / (61/235) = 1.13

This means that the odds of birth difficulties are 1.13 times higher in the case group compared to the control group.

Skewed Data: Understanding the Relationship between Mean, Median, and Mode

When analyzing a data set, it is important to consider the shape of the distribution. In a normally distributed data set, the curve is symmetrical and bell-shaped, with the median, mode, and mean all equal. However, in skewed data sets, the distribution is asymmetrical, with the bulk of the data concentrated on one side of the figure.

In a negatively skewed distribution, the left tail is longer, and the bulk of the data is concentrated to the right of the figure. In contrast, a positively skewed distribution has a longer right tail, with the bulk of the data concentrated to the left of the figure. In both cases, the median is positioned between the mode and the mean, as it represents the halfway point of the distribution.

However, the mean is affected by extreme values of outliers, causing it to move away from the median in the direction of the tail. In positively skewed data, the mean is greater than the median, which is greater than the mode. In negatively skewed data, the mode is greater than the median, which is greater than the mean.

Understanding the relationship between mean, median, and mode in skewed data sets is crucial for accurate data analysis and interpretation. By recognizing the shape of the distribution, researchers can make informed decisions about which measures of central tendency to use and how to interpret their results.

Measures of Disease Frequency: Incidence and Prevalence

Incidence and prevalence are two important measures of disease frequency. Incidence measures the speed at which new cases of a disease are emerging, while prevalence measures the burden of disease within a population. Cumulative incidence and incidence rate are two types of incidence measures, while point prevalence and period prevalence are two types of prevalence measures.

Cumulative incidence is the average risk of getting a disease over a certain period of time, while incidence rate is a measure of the speed at which new cases are emerging. Prevalence is a proportion and is a measure of the burden of disease within a population. Point prevalence measures the number of cases in a defined population at a specific point in time, while period prevalence measures the number of identified cases during a specified period of time.

It is important to note that prevalence is equal to incidence multiplied by the duration of the condition. In chronic diseases, the prevalence is much greater than the incidence. The incidence rate is stated in units of person-time, while cumulative incidence is always a proportion. When describing cumulative incidence, it is necessary to give the follow-up period over which the risk is estimated. In acute diseases, the prevalence and incidence may be similar, while for conditions such as the common cold, the incidence may be greater than the prevalence.

Incidence is a useful measure to study disease etiology and risk factors, while prevalence is useful for health resource planning. Understanding these measures of disease frequency is important for public health professionals and researchers in order to effectively monitor and address the burden of disease within populations.

Clinical tests are used to determine the presence of absence of a disease of condition. To interpret test results, it is important to have a working knowledge of statistics used to describe them. Two by two tables are commonly used to calculate test statistics such as sensitivity and specificity. Sensitivity refers to the proportion of people with a condition that the test correctly identifies, while specificity refers to the proportion of people without a condition that the test correctly identifies. Accuracy tells us how closely a test measures to its true value, while predictive values help us understand the likelihood of having a disease based on a positive of negative test result. Likelihood ratios combine sensitivity and specificity into a single figure that can refine our estimation of the probability of a disease being present. Pre and post-test odds and probabilities can also be calculated to better understand the likelihood of having a disease before and after a test is carried out. Fagan’s nomogram is a useful tool for calculating post-test probabilities.

To ensure validity in qualitative studies, a technique called member checking of respondent validation is used. This involves interviewing a subset of the participants (typically around 11) to confirm that their perspectives align with the study’s findings.

Qualitative research is a method of inquiry that seeks to understand the meaning and experience dimensions of human lives and social worlds. There are different approaches to qualitative research, such as ethnography, phenomenology, and grounded theory, each with its own purpose, role of the researcher, stages of research, and method of data analysis. The most common methods used in healthcare research are interviews and focus groups. Sampling techniques include convenience sampling, purposive sampling, quota sampling, snowball sampling, and case study sampling. Sample size can be determined by data saturation, which occurs when new categories, themes, of explanations stop emerging from the data. Validity can be assessed through triangulation, respondent validation, bracketing, and reflexivity. Analytical approaches include content analysis and constant comparison.

Validity in statistics refers to how accurately something measures what it claims to measure. There are two main types of validity: internal and external. Internal validity refers to the confidence we have in the cause and effect relationship in a study, while external validity refers to the degree to which the conclusions of a study can be applied to other people, places, and times. There are various threats to both internal and external validity, such as sampling, measurement instrument obtrusiveness, and reactive effects of setting. Additionally, there are several subtypes of validity, including face validity, content validity, criterion validity, and construct validity. Each subtype has its own specific focus and methods for testing validity.

The t test is limited to parametric data that follows a normal distribution. However, inadequate statistical power due to a small sample size does not necessarily invalidate the t test results. While it is likely that a small sample size may not reveal any significant differences, it is still possible that large differences may be observed regardless of prior power calculations.

Kappa is used to assess the consistency of reliability between different raters.

Understanding the Kappa Statistic for Measuring Interobserver Variation

The kappa statistic, also known as Cohen’s kappa coefficient, is a useful tool for quantifying the level of agreement between independent observers. This measure can be applied in any situation where multiple observers are evaluating the same thing, such as in medical diagnoses of research studies. The kappa coefficient ranges from 0 to 1, with 0 indicating complete disagreement and 1 indicating perfect agreement. By using the kappa statistic, researchers and practitioners can gain insight into the level of interobserver variation present in their data, which can help to improve the accuracy and reliability of their findings. Overall, the kappa statistic is a valuable tool for understanding and measuring interobserver variation in a variety of contexts.

A sensitivity analysis is a tool utilized to evaluate the degree to which the outcomes of a study of systematic review are influenced by modifications in the methodology employed. It is employed to determine the resilience of the findings to uncertain judgments of assumptions regarding the data and techniques employed.

Type I errors occur when we reject a null hypothesis that is actually true, leading us to believe that there is a significant difference of effect when there is not.

Understanding Hypothesis Testing in Statistics

In statistics, it is not feasible to investigate hypotheses on entire populations. Therefore, researchers take samples and use them to make estimates about the population they are drawn from. However, this leads to uncertainty as there is no guarantee that the sample taken will be truly representative of the population, resulting in potential errors. Statistical hypothesis testing is the process used to determine if claims from samples to populations can be made and with what certainty.

The null hypothesis (Ho) is the claim that there is no real difference between two groups, while the alternative hypothesis (H1 of Ha) suggests that any difference is due to some non-random chance. The alternative hypothesis can be one-tailed of two-tailed, depending on whether it seeks to establish a difference of a change in one direction.

Two types of errors may occur when testing the null hypothesis: Type I and Type II errors. Type I error occurs when the null hypothesis is rejected when it is true, while Type II error occurs when the null hypothesis is accepted when it is false. The power of a study is the probability of correctly rejecting the null hypothesis when it is false, and it can be increased by increasing the sample size.

P-values provide information on statistical significance and help researchers decide if study results have occurred due to chance. The p-value is the probability of obtaining a result that is as large of larger when in reality there is no difference between two groups. The cutoff for the p-value is called the significance level (alpha level), typically set at 0.05. If the p-value is less than the cutoff, the null hypothesis is rejected, and if it is greater or equal to the cut off, the null hypothesis is not rejected. However, the p-value does not indicate clinical significance, which may be too small to be meaningful.

Methods of Economic Evaluation

There are four main methods of economic evaluation: cost-effectiveness analysis (CEA), cost-benefit analysis (CBA), cost-utility analysis (CUA), and cost-minimisation analysis (CMA). While all four methods capture costs, they differ in how they assess health effects.

Cost-effectiveness analysis (CEA) compares interventions by relating costs to a single clinical measure of effectiveness, such as symptom reduction of improvement in activities of daily living. The cost-effectiveness ratio is calculated as total cost divided by units of effectiveness. CEA is typically used when CBA cannot be performed due to the inability to monetise benefits.

Cost-benefit analysis (CBA) measures all costs and benefits of an intervention in monetary terms to establish which alternative has the greatest net benefit. CBA requires that all consequences of an intervention, such as life-years saved, treatment side-effects, symptom relief, disability, pain, and discomfort, are allocated a monetary value. CBA is rarely used in mental health service evaluation due to the difficulty in converting benefits from mental health programmes into monetary values.

Cost-utility analysis (CUA) is a special form of CEA in which health benefits/outcomes are measured in broader, more generic ways, enabling comparisons between treatments for different diseases and conditions. Multidimensional health outcomes are measured by a single preference- of utility-based index such as the Quality-Adjusted-Life-Years (QALY). QALYs are a composite measure of gains in life expectancy and health-related quality of life. CUA allows for comparisons across treatments for different conditions.

Cost-minimisation analysis (CMA) is an economic evaluation in which the consequences of competing interventions are the same, and only inputs, i.e. costs, are taken into consideration. The aim is to decide the least costly way of achieving the same outcome.

Costs in Economic Evaluation Studies

There are three main types of costs in economic evaluation studies: direct, indirect, and intangible. Direct costs are associated directly with the healthcare intervention, such as staff time, medical supplies, cost of travel for the patient, childcare costs for the patient, and costs falling on other social sectors such as domestic help from social services. Indirect costs are incurred by the reduced productivity of the patient, such as time off work, reduced work productivity, and time spent caring for the patient by relatives. Intangible costs are difficult to measure, such as pain of suffering on the part of the patient.

Choosing the right statistical test can be challenging, but understanding the basic principles can help. Different tests have different assumptions, and using the wrong one can lead to inaccurate results. To identify the appropriate test, a flow chart can be used based on three main factors: the type of dependent variable, the type of data, and whether the groups/samples are independent of dependent. It is important to know which tests are parametric and non-parametric, as well as their alternatives. For example, the chi-squared test is used to assess differences in categorical variables and is non-parametric, while Pearson’s correlation coefficient measures linear correlation between two variables and is parametric. T-tests are used to compare means between two groups, and ANOVA is used to compare means between more than two groups. Non-parametric equivalents to ANOVA include the Kruskal-Wallis analysis of ranks, the Median test, Friedman’s two-way analysis of variance, and Cochran Q test. Understanding these tests and their assumptions can help researchers choose the appropriate statistical test for their data.

Stats: Correlation and Regression

Correlation and regression are related but not interchangeable terms. Correlation is used to test for association between variables, while regression is used to predict values of dependent variables from independent variables. Correlation can be linear, non-linear, of non-existent, and can be strong, moderate, of weak. The strength of a linear relationship is measured by the correlation coefficient, which can be positive of negative and ranges from very weak to very strong. However, the interpretation of a correlation coefficient depends on the context and purposes. Correlation can suggest association but cannot prove of disprove causation. Linear regression, on the other hand, can be used to predict how much one variable changes when a second variable is changed. Scatter graphs are used in correlation and regression analyses to visually determine if variables are associated and to detect outliers. When constructing a scatter graph, the dependent variable is typically placed on the vertical axis and the independent variable on the horizontal axis.

Skewed Data: Understanding the Relationship between Mean, Median, and Mode

When analyzing a data set, it is important to consider the shape of the distribution. In a normally distributed data set, the curve is symmetrical and bell-shaped, with the median, mode, and mean all equal. However, in skewed data sets, the distribution is asymmetrical, with the bulk of the data concentrated on one side of the figure.

In a negatively skewed distribution, the left tail is longer, and the bulk of the data is concentrated to the right of the figure. In contrast, a positively skewed distribution has a longer right tail, with the bulk of the data concentrated to the left of the figure. In both cases, the median is positioned between the mode and the mean, as it represents the halfway point of the distribution.

However, the mean is affected by extreme values of outliers, causing it to move away from the median in the direction of the tail. In positively skewed data, the mean is greater than the median, which is greater than the mode. In negatively skewed data, the mode is greater than the median, which is greater than the mean.

Understanding the relationship between mean, median, and mode in skewed data sets is crucial for accurate data analysis and interpretation. By recognizing the shape of the distribution, researchers can make informed decisions about which measures of central tendency to use and how to interpret their results.

The benefits of conducting a case-control study include its suitability for examining rare diseases, the ability to investigate a broad range of risk factors, no loss to follow-up, and its relatively low cost and quick turnaround time. The findings of such studies are typically presented as an odds ratio.

The key characteristic that sets ratio variables apart from interval variables is the presence of a meaningful zero point. On a ratio scale, this zero point signifies the absence of the measured attribute, while on an interval scale, the zero point is simply a point on the scale with no inherent significance.

Scales of Measurement in Statistics

In the 1940s, Stanley Smith Stevens introduced four scales of measurement to categorize data variables. Knowing the scale of measurement for a variable is crucial in selecting the appropriate statistical analysis. The four scales of measurement are ratio, interval, ordinal, and nominal.

Ratio scales are similar to interval scales, but they have true zero points. Examples of ratio scales include weight, time, and length. Interval scales measure the difference between two values, and one unit on the scale represents the same magnitude on the trait of characteristic being measured across the whole range of the scale. The Fahrenheit scale for temperature is an example of an interval scale.

Ordinal scales categorize observed values into set categories that can be ordered, but the intervals between each value are uncertain. Examples of ordinal scales include social class, education level, and income level. Nominal scales categorize observed values into set categories that have no particular order of hierarchy. Examples of nominal scales include genotype, blood type, and political party.

Data can also be categorized as quantitative of qualitative. Quantitative variables take on numeric values and can be further classified into discrete and continuous types. Qualitative variables do not take on numerical values and are usually names. Some qualitative variables have an inherent order in their categories and are described as ordinal. Qualitative variables are also called categorical of nominal variables. When a qualitative variable has only two categories, it is called a binary variable.

Understanding ROC Curves and AUC Values

ROC (receiver operating characteristic) curves are graphs used to evaluate the effectiveness of a test in distinguishing between two groups, such as those with and without a disease. The curve plots the true positive rate against the false positive rate at different threshold settings. The goal is to find the best trade-off between sensitivity and specificity, which can be adjusted by changing the threshold. AUC (area under the curve) is a measure of the overall performance of the test, with higher values indicating better accuracy. The conventional grading of AUC values ranges from excellent to fail. ROC curves and AUC values are useful in evaluating diagnostic and screening tools, comparing different tests, and studying inter-observer variability.

While many individuals can readily remember that the systematic review is at the highest level and case-series at the lowest, it can be difficult to correctly sequence the intermediate levels.

Levels and Grades of Evidence in Evidence-Based Medicine

To evaluate the quality of evidence on a subject of question, levels of grades are used. The traditional hierarchy approach places systematic reviews of randomized control trials at the top and case-series/report at the bottom. However, this approach is overly simplistic as certain research questions cannot be answered using RCTs. To address this, the Oxford Centre for Evidence-Based Medicine introduced their 2011 Levels of Evidence system, which separates the type of study questions and gives a hierarchy for each.

The grading approach to be aware of is the GRADE system, which classifies the quality of evidence as high, moderate, low, of very low. The process begins by formulating a study question and identifying specific outcomes. Outcomes are then graded as critical of important. The evidence is then gathered and criteria are used to grade the evidence, with the type of evidence being a significant factor. Evidence can be promoted of downgraded based on certain criteria, such as limitations to study quality, inconsistency, uncertainty about directness, imprecise of sparse data, and reporting bias. The GRADE system allows for the promotion of observational studies to high-quality evidence under the right circumstances.

Epidemiology Key Terms

– Epidemic (Outbreak): A rise in disease cases above the anticipated level in a specific population during a particular time frame.
– Endemic: The regular of anticipated level of disease in a particular population.
– Pandemic: Epidemics that affect a significant number of individuals across multiple countries, regions, of continents.

Making a false positive conclusion by rejecting the null hypothesis.

Understanding Hypothesis Testing in Statistics

In statistics, it is not feasible to investigate hypotheses on entire populations. Therefore, researchers take samples and use them to make estimates about the population they are drawn from. However, this leads to uncertainty as there is no guarantee that the sample taken will be truly representative of the population, resulting in potential errors. Statistical hypothesis testing is the process used to determine if claims from samples to populations can be made and with what certainty.

The null hypothesis (Ho) is the claim that there is no real difference between two groups, while the alternative hypothesis (H1 of Ha) suggests that any difference is due to some non-random chance. The alternative hypothesis can be one-tailed of two-tailed, depending on whether it seeks to establish a difference of a change in one direction.

Two types of errors may occur when testing the null hypothesis: Type I and Type II errors. Type I error occurs when the null hypothesis is rejected when it is true, while Type II error occurs when the null hypothesis is accepted when it is false. The power of a study is the probability of correctly rejecting the null hypothesis when it is false, and it can be increased by increasing the sample size.

P-values provide information on statistical significance and help researchers decide if study results have occurred due to chance. The p-value is the probability of obtaining a result that is as large of larger when in reality there is no difference between two groups. The cutoff for the p-value is called the significance level (alpha level), typically set at 0.05. If the p-value is less than the cutoff, the null hypothesis is rejected, and if it is greater or equal to the cut off, the null hypothesis is not rejected. However, the p-value does not indicate clinical significance, which may be too small to be meaningful.

A negative SMR is not possible. An SMR less than 1.0 suggests that there were fewer deaths than expected in the study population, while an SMR of 1.0 indicates that the observed and expected deaths were equal. An SMR greater than 1.0 indicates that there were excess deaths in the study population.

Calculation of Standardised Mortality Ratio (SMR)

To calculate the SMR, age and sex-specific death rates in the standard population are obtained. An estimate for the number of people in each category for both the standard and study populations is needed. The number of expected deaths in each age-sex group of the study population is calculated by multiplying the age-sex-specific rates in the standard population by the number of people in each category of the study population. The sum of all age- and sex-specific expected deaths gives the expected number of deaths for the whole study population. The observed number of deaths is then divided by the expected number of deaths to obtain the SMR.

The SMR can be standardised using the direct of indirect method. The direct method is used when the age-sex-specific rates for the study population and the age-sex-structure of the standard population are known. The indirect method is used when the age-specific rates for the study population are unknown of not available. This method uses the observed number of deaths in the study population and compares it to the number of deaths that would be expected if the age distribution was the same as that of the standard population.

The SMR can be interpreted as follows: an SMR less than 1.0 indicates fewer than expected deaths in the study population, an SMR of 1.0 indicates the number of observed deaths equals the number of expected deaths in the study population, and an SMR greater than 1.0 indicates more than expected deaths in the study population (excess deaths). It is sometimes expressed after multiplying by 100.

Measures of Central Tendency

Measures of central tendency are used in descriptive statistics to summarize the middle of typical value of a data set. There are three common measures of central tendency: the mean, median, and mode.

The median is the middle value in a data set that has been arranged in numerical order. It is not affected by outliers and is used for ordinal data. The mode is the most frequent value in a data set and is used for categorical data. The mean is calculated by adding all the values in a data set and dividing by the number of values. It is sensitive to outliers and is used for interval and ratio data.

The appropriate measure of central tendency depends on the measurement scale of the data. For nominal and categorical data, the mode is used. For ordinal data, the median of mode is used. For interval data with a normal distribution, the mean is preferable, but the median of mode can also be used. For interval data with skewed distribution, the median is used. For ratio data, the mean is preferable, but the median of mode can also be used for skewed data.

In addition to measures of central tendency, the range is also used to describe the spread of a data set. It is calculated by subtracting the smallest value from the largest value.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

Types of Bias in Statistics

Bias is a systematic error that can lead to incorrect conclusions. Confounding factors are variables that are associated with both the outcome and the exposure but have no causative role. Confounding can be addressed in the design and analysis stage of a study. The main method of controlling confounding in the analysis phase is stratification analysis. The main methods used in the design stage are matching, randomization, and restriction of participants.

There are two main types of bias: selection bias and information bias. Selection bias occurs when the selected sample is not a representative sample of the reference population. Disease spectrum bias, self-selection bias, participation bias, incidence-prevalence bias, exclusion bias, publication of dissemination bias, citation bias, and Berkson’s bias are all subtypes of selection bias. Information bias occurs when gathered information about exposure, outcome, of both is not correct and there was an error in measurement. Detection bias, recall bias, lead time bias, interviewer/observer bias, verification and work-up bias, Hawthorne effect, and ecological fallacy are all subtypes of information bias.

Foreground questions are specific and focused, and can lead to a clinical decision. In contrast, background questions are more general and broad in scope.

Evidence-based medicine involves four basic steps: developing a focused clinical question, searching for the best evidence, critically appraising the evidence, and applying the evidence and evaluating the outcome. When developing a question, it is important to understand the difference between background and foreground questions. Background questions are general questions about conditions, illnesses, syndromes, and pathophysiology, while foreground questions are more often about issues of care. The PICO system is often used to define the components of a foreground question: patient group of interest, intervention of interest, comparison, and primary outcome.

When searching for evidence, it is important to have a basic understanding of the types of evidence and sources of information. Scientific literature is divided into two basic categories: primary (empirical research) and secondary (interpretation and analysis of primary sources). Unfiltered sources are large databases of articles that have not been pre-screened for quality, while filtered resources summarize and appraise evidence from several studies.

There are several databases and search engines that can be used to search for evidence, including Medline and PubMed, Embase, the Cochrane Library, PsycINFO, CINAHL, and OpenGrey. Boolean logic can be used to combine search terms in PubMed, and phrase searching and truncation can also be used. Medical Subject Headings (MeSH) are used by indexers to describe articles for MEDLINE records, and the MeSH Database is like a thesaurus that enables exploration of this vocabulary.

As an AI language model, I do not have personal opinions of beliefs. However, I can provide information and guidance on the standards of reporting for different types of research studies. The guidelines mentioned above are essential for ensuring that research studies are reported accurately and transparently, which is crucial for the scientific community to evaluate and replicate the findings. It is important for researchers to be familiar with these standards and follow them when reporting their studies to ensure the quality and integrity of their research.

Understanding Hypothesis Testing in Statistics

In statistics, it is not feasible to investigate hypotheses on entire populations. Therefore, researchers take samples and use them to make estimates about the population they are drawn from. However, this leads to uncertainty as there is no guarantee that the sample taken will be truly representative of the population, resulting in potential errors. Statistical hypothesis testing is the process used to determine if claims from samples to populations can be made and with what certainty.

The null hypothesis (Ho) is the claim that there is no real difference between two groups, while the alternative hypothesis (H1 of Ha) suggests that any difference is due to some non-random chance. The alternative hypothesis can be one-tailed of two-tailed, depending on whether it seeks to establish a difference of a change in one direction.

Two types of errors may occur when testing the null hypothesis: Type I and Type II errors. Type I error occurs when the null hypothesis is rejected when it is true, while Type II error occurs when the null hypothesis is accepted when it is false. The power of a study is the probability of correctly rejecting the null hypothesis when it is false, and it can be increased by increasing the sample size.

P-values provide information on statistical significance and help researchers decide if study results have occurred due to chance. The p-value is the probability of obtaining a result that is as large of larger when in reality there is no difference between two groups. The cutoff for the p-value is called the significance level (alpha level), typically set at 0.05. If the p-value is less than the cutoff, the null hypothesis is rejected, and if it is greater or equal to the cut off, the null hypothesis is not rejected. However, the p-value does not indicate clinical significance, which may be too small to be meaningful.

The α value, also known as the type I error, is the predetermined probability that is considered acceptable for making an error. If the P value is lower than the predetermined α value, then the null hypothesis (Ho) is rejected, and it is concluded that the observed difference, association, of correlation is statistically significant.

Understanding Hypothesis Testing in Statistics

In statistics, it is not feasible to investigate hypotheses on entire populations. Therefore, researchers take samples and use them to make estimates about the population they are drawn from. However, this leads to uncertainty as there is no guarantee that the sample taken will be truly representative of the population, resulting in potential errors. Statistical hypothesis testing is the process used to determine if claims from samples to populations can be made and with what certainty.

The null hypothesis (Ho) is the claim that there is no real difference between two groups, while the alternative hypothesis (H1 of Ha) suggests that any difference is due to some non-random chance. The alternative hypothesis can be one-tailed of two-tailed, depending on whether it seeks to establish a difference of a change in one direction.

Two types of errors may occur when testing the null hypothesis: Type I and Type II errors. Type I error occurs when the null hypothesis is rejected when it is true, while Type II error occurs when the null hypothesis is accepted when it is false. The power of a study is the probability of correctly rejecting the null hypothesis when it is false, and it can be increased by increasing the sample size.

P-values provide information on statistical significance and help researchers decide if study results have occurred due to chance. The p-value is the probability of obtaining a result that is as large of larger when in reality there is no difference between two groups. The cutoff for the p-value is called the significance level (alpha level), typically set at 0.05. If the p-value is less than the cutoff, the null hypothesis is rejected, and if it is greater or equal to the cut off, the null hypothesis is not rejected. However, the p-value does not indicate clinical significance, which may be too small to be meaningful.

The Kaplan-Meier plot is the most effective graphical representation of survival probability. It presents the overall likelihood of an individual’s survival over time from a baseline, and the comparison of two lines on the plot can indicate whether there is a survival advantage. To determine if the distinction between the two groups is significant, a log rank test can be employed.

Understanding Hypothesis Testing in Statistics

In statistics, it is not feasible to investigate hypotheses on entire populations. Therefore, researchers take samples and use them to make estimates about the population they are drawn from. However, this leads to uncertainty as there is no guarantee that the sample taken will be truly representative of the population, resulting in potential errors. Statistical hypothesis testing is the process used to determine if claims from samples to populations can be made and with what certainty.

The null hypothesis (Ho) is the claim that there is no real difference between two groups, while the alternative hypothesis (H1 of Ha) suggests that any difference is due to some non-random chance. The alternative hypothesis can be one-tailed of two-tailed, depending on whether it seeks to establish a difference of a change in one direction.

Two types of errors may occur when testing the null hypothesis: Type I and Type II errors. Type I error occurs when the null hypothesis is rejected when it is true, while Type II error occurs when the null hypothesis is accepted when it is false. The power of a study is the probability of correctly rejecting the null hypothesis when it is false, and it can be increased by increasing the sample size.

P-values provide information on statistical significance and help researchers decide if study results have occurred due to chance. The p-value is the probability of obtaining a result that is as large of larger when in reality there is no difference between two groups. The cutoff for the p-value is called the significance level (alpha level), typically set at 0.05. If the p-value is less than the cutoff, the null hypothesis is rejected, and if it is greater or equal to the cut off, the null hypothesis is not rejected. However, the p-value does not indicate clinical significance, which may be too small to be meaningful.

When faced with a question, it’s helpful to consider what the letters in the question might represent, even if you don’t know the answer right away. Don’t become overwhelmed and keep this strategy in mind.

Evidence-based medicine involves four basic steps: developing a focused clinical question, searching for the best evidence, critically appraising the evidence, and applying the evidence and evaluating the outcome. When developing a question, it is important to understand the difference between background and foreground questions. Background questions are general questions about conditions, illnesses, syndromes, and pathophysiology, while foreground questions are more often about issues of care. The PICO system is often used to define the components of a foreground question: patient group of interest, intervention of interest, comparison, and primary outcome.

When searching for evidence, it is important to have a basic understanding of the types of evidence and sources of information. Scientific literature is divided into two basic categories: primary (empirical research) and secondary (interpretation and analysis of primary sources). Unfiltered sources are large databases of articles that have not been pre-screened for quality, while filtered resources summarize and appraise evidence from several studies.

There are several databases and search engines that can be used to search for evidence, including Medline and PubMed, Embase, the Cochrane Library, PsycINFO, CINAHL, and OpenGrey. Boolean logic can be used to combine search terms in PubMed, and phrase searching and truncation can also be used. Medical Subject Headings (MeSH) are used by indexers to describe articles for MEDLINE records, and the MeSH Database is like a thesaurus that enables exploration of this vocabulary.

Clinical tests are used to determine the presence of absence of a disease of condition. To interpret test results, it is important to have a working knowledge of statistics used to describe them. Two by two tables are commonly used to calculate test statistics such as sensitivity and specificity. Sensitivity refers to the proportion of people with a condition that the test correctly identifies, while specificity refers to the proportion of people without a condition that the test correctly identifies. Accuracy tells us how closely a test measures to its true value, while predictive values help us understand the likelihood of having a disease based on a positive of negative test result. Likelihood ratios combine sensitivity and specificity into a single figure that can refine our estimation of the probability of a disease being present. Pre and post-test odds and probabilities can also be calculated to better understand the likelihood of having a disease before and after a test is carried out. Fagan’s nomogram is a useful tool for calculating post-test probabilities.

Stats: Correlation and Regression

Correlation and regression are related but not interchangeable terms. Correlation is used to test for association between variables, while regression is used to predict values of dependent variables from independent variables. Correlation can be linear, non-linear, of non-existent, and can be strong, moderate, of weak. The strength of a linear relationship is measured by the correlation coefficient, which can be positive of negative and ranges from very weak to very strong. However, the interpretation of a correlation coefficient depends on the context and purposes. Correlation can suggest association but cannot prove of disprove causation. Linear regression, on the other hand, can be used to predict how much one variable changes when a second variable is changed. Scatter graphs are used in correlation and regression analyses to visually determine if variables are associated and to detect outliers. When constructing a scatter graph, the dependent variable is typically placed on the vertical axis and the independent variable on the horizontal axis.

In the analytic stage of a study, confounding cannot be controlled for by the technique of stratification. (This is false, as stratification is a technique commonly used to control for confounding in observational studies.)

Stats Confounding

A confounding factor is a factor that can obscure the relationship between an exposure and an outcome in a study. This factor is associated with both the exposure and the disease. For example, in a study that finds a link between coffee consumption and heart disease, smoking could be a confounding factor because it is associated with both drinking coffee and heart disease. Confounding occurs when there is a non-random distribution of risk factors in the population, such as age, sex, and social class.

To control for confounding in the design stage of an experiment, researchers can use randomization, restriction, of matching. Randomization aims to produce an even distribution of potential risk factors in two populations. Restriction involves limiting the study population to a specific group to ensure similar age distributions. Matching involves finding and enrolling participants who are similar in terms of potential confounding factors.

In the analysis stage of an experiment, researchers can control for confounding by using stratification of multivariate models such as logistic regression, linear regression, of analysis of covariance (ANCOVA). Stratification involves creating categories of strata in which the confounding variable does not vary of varies minimally.

Overall, controlling for confounding is important in ensuring that the relationship between an exposure and an outcome is accurately assessed in a study.

In qualitative research, data saturation refers to the point where additional data collection becomes unnecessary as the responses obtained are repetitive and do not provide any new insights. This is when the researcher has heard the same information repeatedly and there is no need to continue recruiting participants. Understanding data saturation is crucial in qualitative research.

Measures of dispersion are used to indicate the variation of spread of a data set, often in conjunction with a measure of central tendency such as the mean of median. The range, which is the difference between the largest and smallest value, is the simplest measure of dispersion. The interquartile range, which is the difference between the 3rd and 1st quartiles, is another useful measure. Quartiles divide a data set into quarters, and the interquartile range can provide additional information about the spread of the data. However, to get a more representative idea of spread, measures such as the variance and standard deviation are needed. The variance gives an indication of how much the items in the data set vary from the mean, while the standard deviation reflects the distribution of individual scores around their mean. The standard deviation is expressed in the same units as the data set and can be used to indicate how confident we are that data points lie within a particular range. The standard error of the mean is an inferential statistic used to estimate the population mean and is a measure of the spread expected for the mean of the observations. Confidence intervals are often presented alongside sample results such as the mean value, indicating a range that is likely to contain the true value.

A p-value represents the likelihood of rejecting a null hypothesis that is actually true. A smaller p-value indicates a lower chance of mistakenly rejecting the null hypothesis, providing evidence in favor of the alternative hypothesis.

Understanding Hypothesis Testing in Statistics

In statistics, it is not feasible to investigate hypotheses on entire populations. Therefore, researchers take samples and use them to make estimates about the population they are drawn from. However, this leads to uncertainty as there is no guarantee that the sample taken will be truly representative of the population, resulting in potential errors. Statistical hypothesis testing is the process used to determine if claims from samples to populations can be made and with what certainty.

The null hypothesis (Ho) is the claim that there is no real difference between two groups, while the alternative hypothesis (H1 of Ha) suggests that any difference is due to some non-random chance. The alternative hypothesis can be one-tailed of two-tailed, depending on whether it seeks to establish a difference of a change in one direction.

Two types of errors may occur when testing the null hypothesis: Type I and Type II errors. Type I error occurs when the null hypothesis is rejected when it is true, while Type II error occurs when the null hypothesis is accepted when it is false. The power of a study is the probability of correctly rejecting the null hypothesis when it is false, and it can be increased by increasing the sample size.

P-values provide information on statistical significance and help researchers decide if study results have occurred due to chance. The p-value is the probability of obtaining a result that is as large of larger when in reality there is no difference between two groups. The cutoff for the p-value is called the significance level (alpha level), typically set at 0.05. If the p-value is less than the cutoff, the null hypothesis is rejected, and if it is greater or equal to the cut off, the null hypothesis is not rejected. However, the p-value does not indicate clinical significance, which may be too small to be meaningful.

– The median is the point with half the values above and half below.
– In the given data set, there are an even number of values.
– The median value is halfway between the two middle values.
– The middle values are 56 and 58.
– Therefore, the median is (56 + 58) / 2.

Measures of Central Tendency

Measures of central tendency are used in descriptive statistics to summarize the middle of typical value of a data set. There are three common measures of central tendency: the mean, median, and mode.

The median is the middle value in a data set that has been arranged in numerical order. It is not affected by outliers and is used for ordinal data. The mode is the most frequent value in a data set and is used for categorical data. The mean is calculated by adding all the values in a data set and dividing by the number of values. It is sensitive to outliers and is used for interval and ratio data.

The appropriate measure of central tendency depends on the measurement scale of the data. For nominal and categorical data, the mode is used. For ordinal data, the median of mode is used. For interval data with a normal distribution, the mean is preferable, but the median of mode can also be used. For interval data with skewed distribution, the median is used. For ratio data, the mean is preferable, but the median of mode can also be used for skewed data.

In addition to measures of central tendency, the range is also used to describe the spread of a data set. It is calculated by subtracting the smallest value from the largest value.

Measures of dispersion are used to indicate the variation of spread of a data set, often in conjunction with a measure of central tendency such as the mean of median. The range, which is the difference between the largest and smallest value, is the simplest measure of dispersion. The interquartile range, which is the difference between the 3rd and 1st quartiles, is another useful measure. Quartiles divide a data set into quarters, and the interquartile range can provide additional information about the spread of the data. However, to get a more representative idea of spread, measures such as the variance and standard deviation are needed. The variance gives an indication of how much the items in the data set vary from the mean, while the standard deviation reflects the distribution of individual scores around their mean. The standard deviation is expressed in the same units as the data set and can be used to indicate how confident we are that data points lie within a particular range. The standard error of the mean is an inferential statistic used to estimate the population mean and is a measure of the spread expected for the mean of the observations. Confidence intervals are often presented alongside sample results such as the mean value, indicating a range that is likely to contain the true value.

The number needed to treat (NNT) is equal to 100. This means that for every 100 patients treated, one patient will benefit from the treatment. The absolute risk reduction (ARR) is 0.01, which is the difference between the control event rate (CER) of 0.04 and the experimental event rate (EER) of 0.03.

Measures of Effect in Clinical Studies

When conducting clinical studies, we often want to know the effect of treatments of exposures on health outcomes. Measures of effect are used in randomized controlled trials (RCTs) and include the odds ratio (of), risk ratio (RR), risk difference (RD), and number needed to treat (NNT). Dichotomous (binary) outcome data are common in clinical trials, where the outcome for each participant is one of two possibilities, such as dead of alive, of clinical improvement of no improvement.

To understand the difference between of and RR, it’s important to know the difference between risks and odds. Risk is a proportion that describes the probability of a health outcome occurring, while odds is a ratio that compares the probability of an event occurring to the probability of it not occurring. Absolute risk is the basic risk, while risk difference is the difference between the absolute risk of an event in the intervention group and the absolute risk in the control group. Relative risk is the ratio of risk in the intervention group to the risk in the control group.

The number needed to treat (NNT) is the number of patients who need to be treated for one to benefit. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen. The odds ratio is the odds of an outcome given a particular exposure versus the odds of an outcome in the absence of the exposure. It is commonly used in case-control studies and can also be used in cross-sectional and cohort study designs. An odds ratio of 1 indicates no difference in risk between the two groups, while an odds ratio >1 indicates an increased risk and an odds ratio <1 indicates a reduced risk.

The Normal distribution is a probability distribution that is continuous in nature.

Standard Deviation and Standard Error of the Mean

Standard deviation (SD) and standard error of the mean (SEM) are two important statistical measures used to describe data. SD is a measure of how much the data varies, while SEM is a measure of how precisely we know the true mean of the population. The normal distribution, also known as the Gaussian distribution, is a symmetrical bell-shaped curve that describes the spread of many biological and clinical measurements.

68.3% of the data lies within 1 SD of the mean, 95.4% of the data lies within 2 SD of the mean, and 99.7% of the data lies within 3 SD of the mean. The SD is calculated by taking the square root of the variance and is expressed in the same units as the data set. A low SD indicates that data points tend to be very close to the mean.

On the other hand, SEM is an inferential statistic that quantifies the precision of the mean. It is expressed in the same units as the data and is calculated by dividing the SD of the sample mean by the square root of the sample size. The SEM gets smaller as the sample size increases, and it takes into account both the value of the SD and the sample size.

Both SD and SEM are important measures in statistical analysis, and they are used to calculate confidence intervals and test hypotheses. While SD quantifies scatter, SEM quantifies precision, and both are essential in understanding and interpreting data.

Stats: Correlation and Regression

Correlation and regression are related but not interchangeable terms. Correlation is used to test for association between variables, while regression is used to predict values of dependent variables from independent variables. Correlation can be linear, non-linear, of non-existent, and can be strong, moderate, of weak. The strength of a linear relationship is measured by the correlation coefficient, which can be positive of negative and ranges from very weak to very strong. However, the interpretation of a correlation coefficient depends on the context and purposes. Correlation can suggest association but cannot prove of disprove causation. Linear regression, on the other hand, can be used to predict how much one variable changes when a second variable is changed. Scatter graphs are used in correlation and regression analyses to visually determine if variables are associated and to detect outliers. When constructing a scatter graph, the dependent variable is typically placed on the vertical axis and the independent variable on the horizontal axis.

Since the data is normally distributed and the study aims to evaluate the correlation between two variables, the most suitable test to use is Pearson’s product-moment coefficient. On the other hand, if the data is non-parametric, Spearman’s coefficient would be more appropriate.

Choosing the right statistical test can be challenging, but understanding the basic principles can help. Different tests have different assumptions, and using the wrong one can lead to inaccurate results. To identify the appropriate test, a flow chart can be used based on three main factors: the type of dependent variable, the type of data, and whether the groups/samples are independent of dependent. It is important to know which tests are parametric and non-parametric, as well as their alternatives. For example, the chi-squared test is used to assess differences in categorical variables and is non-parametric, while Pearson’s correlation coefficient measures linear correlation between two variables and is parametric. T-tests are used to compare means between two groups, and ANOVA is used to compare means between more than two groups. Non-parametric equivalents to ANOVA include the Kruskal-Wallis analysis of ranks, the Median test, Friedman’s two-way analysis of variance, and Cochran Q test. Understanding these tests and their assumptions can help researchers choose the appropriate statistical test for their data.

While quantitative methods are typically used for treatment evaluation, qualitative studies can also provide valuable insights by interpreting, qualifying, of illuminating findings. This is especially beneficial when examining unexpected results, as they can help to test the primary hypothesis.

Qualitative research is a method of inquiry that seeks to understand the meaning and experience dimensions of human lives and social worlds. There are different approaches to qualitative research, such as ethnography, phenomenology, and grounded theory, each with its own purpose, role of the researcher, stages of research, and method of data analysis. The most common methods used in healthcare research are interviews and focus groups. Sampling techniques include convenience sampling, purposive sampling, quota sampling, snowball sampling, and case study sampling. Sample size can be determined by data saturation, which occurs when new categories, themes, of explanations stop emerging from the data. Validity can be assessed through triangulation, respondent validation, bracketing, and reflexivity. Analytical approaches include content analysis and constant comparison.

Stats: Correlation and Regression

Correlation and regression are related but not interchangeable terms. Correlation is used to test for association between variables, while regression is used to predict values of dependent variables from independent variables. Correlation can be linear, non-linear, of non-existent, and can be strong, moderate, of weak. The strength of a linear relationship is measured by the correlation coefficient, which can be positive of negative and ranges from very weak to very strong. However, the interpretation of a correlation coefficient depends on the context and purposes. Correlation can suggest association but cannot prove of disprove causation. Linear regression, on the other hand, can be used to predict how much one variable changes when a second variable is changed. Scatter graphs are used in correlation and regression analyses to visually determine if variables are associated and to detect outliers. When constructing a scatter graph, the dependent variable is typically placed on the vertical axis and the independent variable on the horizontal axis.

Opportunity Cost in Economics: Understanding the Value of Choices

Opportunity cost is a crucial concept in economics that helps us make informed decisions. It refers to the value of the next-best alternative that we give up when we choose one option over another. This concept is particularly relevant when we have limited resources, such as a fixed budget, and need to make choices about how to allocate them.

For instance, if we decide to spend our money on antidepressants, we cannot use that same money to pay for cognitive-behavioral therapy (CBT). Both options have a value, but we have to choose one over the other. The opportunity cost of choosing antidepressants over CBT is the value of the benefits we would have received from CBT but did not because we chose antidepressants instead.

To compare the opportunity cost of different choices, economists often use quality-adjusted life years (QALYs). QALYs measure the value of health outcomes in terms of both quantity (life years gained) and quality (health-related quality of life). By using QALYs, we can compare the opportunity cost of different healthcare interventions and choose the one that provides the best value for our resources.

In summary, understanding opportunity cost is essential for making informed decisions in economics and healthcare. By recognizing the value of the alternatives we give up, we can make better choices and maximize the benefits we receive from our limited resources.