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.

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.

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.

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.

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.

Age is a type of measurement that follows a ratio scale, which means that the values can be compared as multiples of each other. For instance, if someone is 20 years old, they are twice as old as someone who is 10 years old.

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.

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.

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.

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.

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.

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.

When outcomes are binary (such as dead of alive), there are various ways to report them, including proportions, percentages, risk, odds, risk ratios, odds ratios, number needed to treat, likelihood ratios, sensitivity, specificity, and pre-test and post-test probability. However, for non-binary data types, different methods of reporting are required.

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: 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.

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.

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.

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.

The results of Trial 4 indicate a decrease of 10 points on the PANSS scale, with a p-value of 0.9.

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 dealing with a data set that is quantitative and measured on a ratio scale, the mean is typically the preferred measure of central tendency. However, if the data is skewed, the median may be a better choice as it is less affected by the skewness of the data.

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.

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.

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.

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.

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 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 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.

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.

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.

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.

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 one-tailed hypothesis indicates a specific direction of association between groups. The researcher not only declares that there will be a distinction between the groups but also defines the direction in which the difference will occur.

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.

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.

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

The standard error of the mean is 1.6, calculated by dividing the standard deviation of 16 by the square root of the number of patients, which is 100.

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 data gathered will be measured on an ordinal scale, where each answer option is ranked. For instance, 2 is considered lower than 4, and 4 is lower than 5. In an ordinal scale, it is not necessary for the difference between 4 (satisfactory) and 2 (unsatisfactory) to be the same as the difference between 5 (extremely satisfactory) and 3 (neutral). This is because the numbers are not assigned for quantitative measurement but are used for labeling purposes only.

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.

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 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 mean weight is 18kg with a standard deviation of 3kg. Three standard deviations below the mean is 9kg and three standard deviations above the mean is 27kg.

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.

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.

The prevalence of schizophrenia may be higher in urban areas due to the social drift phenomenon, where individuals with severe and enduring mental illnesses tend to move towards urban areas. However, a reduced incidence of schizophrenia in urban areas could explain why there is an increased prevalence of the condition in rural settings. It is important to note that prevalence is influenced by both incidence and duration of illness, and can be reduced by increased recovery rates of death from any cause.

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.

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.

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.

– The standard error of the mean is calculated using the formula: standard deviation / square root (number of patients).
– In this case, the standard error of the mean is 12 / square root (64).
– Simplifying this equation gives a standard error of the mean of 12 / 8.

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.

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 relative risk (RR) of the event of interest in the exposed group compared to the unexposed group is 2.5.

RR = EER / CER
EER = 10 / 200 = 0.05
CER = 10 / 500 = 0.02
RR = EER / CER
= 0.05 / 0.02 = 2.5

This means that the exposed group has a 2.5 times higher risk of experiencing the event compared to the unexposed group.

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.

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.

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.

Cohort studies involve following a group of individuals over a period of time to investigate whether exposure to a particular factor affects disease incidence. Although they are costly and time-consuming, they offer several benefits. For instance, they can examine rare exposure factors and are less prone to recall bias than case-control studies. Additionally, they can measure disease incidence and risk. Results are typically presented as the relative risk of developing the disease due to exposure to the factor.

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.

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.

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.

The frequency of each category of characteristic is displayed through the height of the bars in a bar chart. When dealing with discrete data, it is typically organized into distinct categories and presented in a bar chart. On the other hand, continuous data covers a range and the categories are not separate but rather blend into one another. This type of data is best represented through a histogram, which is similar to a bar chart but with bars that are connected.

Differences between Bar Charts and Histograms

Bar charts and histograms are both used to represent data, but they differ in their application and design. Bar charts are used to summarize nominal of ordinal data, while histograms are used for quantitative data. In a bar chart, the x-axis represents categories without a scale, and the y-axis represents frequencies. The columns are of equal width, and the height of the bar indicates the frequency. On the other hand, histograms have a scale on both axes, with the y-axis representing the relative frequency of frequency density. The width of the columns in a histogram can vary, and the area of the column indicates the true frequency. Overall, bar charts and histograms are useful tools for visualizing data, but their differences in design and application make them better suited for different types of data.

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.

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.

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.

Case-control studies are useful in studying rare diseases as it would be impractical to follow a large group of people for a long period of time to accrue enough incident cases. For instance, if a disease occurs very infrequently, say 1 in 1,000,000 per year, it would require following 1,000,000 people for ten years of 1000 people for 1000 years to accrue ten total cases. However, this is not feasible. Therefore, a case-control study provides a more practical approach to studying rare diseases.

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.

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.

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 use of a scale that categorizes data as mild, moderate, and severe is an example of ordinal data. The data can be arranged in a specific order, where severe cancer is considered worse than moderate, which is worse than mild. However, the difference between mild and moderate may not be the same as the difference between moderate and severe, indicating that this type of data does not follow an interval scale.

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.

Stratification is a method of managing confounding by dividing the data into two or more groups where the confounding variable remains constant of varies minimally.

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.

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.

In order to achieve accurate results, epidemiological studies strive to increase both precision and validity. Precision can be improved by using a sufficient sample size and ensuring that measurements are as accurate as possible, which helps to reduce random error caused by sampling and measurement errors. Validity, on the other hand, aims to minimize non-random error caused by bias and confounding. Overall, both precision and validity are crucial in producing reliable findings in epidemiological research. This information is based on Prince’s (2012) chapter on epidemiology in the book Core Psychiatry, edited by Wright, Stern, and Phelan.

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.

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.

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.

Study Designs for New Drugs: Options and Considerations

When launching a new drug, there are various study design options available. One common approach is a placebo-controlled trial, which can provide strong evidence but may be deemed unethical if established treatments are available. Additionally, it does not allow for a comparison with standard treatments. Therefore, statisticians must decide whether the trial aims to demonstrate superiority, equivalence, of non-inferiority to an existing treatment.

Superiority trials may seem like the obvious choice, but they require a large sample size to show a significant benefit over an existing treatment. Equivalence trials define an equivalence margin on a specified outcome, and if the confidence interval of the difference between the two drugs falls within this margin, the drugs are assumed to have a similar effect. Non-inferiority trials are similar to equivalence trials, but only the lower confidence interval needs to fall within the equivalence margin. These trials require smaller sample sizes, and once a drug has been shown to be non-inferior, larger studies may be conducted to demonstrate superiority.

It is important to note that drug companies may not necessarily aim to show superiority over an existing product. If they can demonstrate that their product is equivalent of even non-inferior, they may compete on price of convenience. Overall, the choice of study design depends on various factors, including ethical considerations, sample size, and the desired outcome.

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.

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 US-UK Diagnostic Project found that the higher rates of schizophrenia in New York were due to diagnostic bias, as US psychiatrists used broader diagnostic criteria. However, the use of standardised clinical interviews and operationalised diagnostic criteria greatly reduced the variability of both incidence and prevalence rates of schizophrenia. This was demonstrated in a study by Sartorius et al. (1986) which examined early manifestations and first-contact incidence of schizophrenia in different cultures.

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 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.

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.

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.

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.

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.

Scientific literature can be classified into two main types: primary and secondary sources. Primary sources are original research studies that present data and analysis without any external evaluation of interpretation. Examples of primary sources include randomized controlled trials, cohort studies, case-control studies, case-series, and conference papers. Secondary sources, on the other hand, provide an interpretation and analysis of primary sources. These sources are typically removed by one of more steps from the original event. Examples of secondary sources include evidence-based guidelines and textbooks, meta-analyses, and systematic reviews.

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.

Parametric vs Non-Parametric Statistics

Statistics are used to draw conclusions about a population based on a sample. A parameter is a numerical value that describes a population characteristic, but it is often impossible to know the true value of a parameter without collecting data from every individual in the population. Instead, we take a sample and use statistics to estimate the parameters.

Parametric statistical procedures assume that the population distribution is normal and that the parameters (such as means and standard deviations) are known. Examples of parametric tests include the t-test, ANOVA, and Pearson coefficient of correlation.

Non-parametric statistical procedures make few of no assumptions about the population distribution of parameters. Examples of non-parametric tests include the Mann-Whitney Test, Wilcoxon Signed-Rank Test, Kruskal-Wallis Test, and Fisher Exact Probability test.

Overall, the choice between parametric and non-parametric tests depends on the nature of the data and the research question being asked.

– 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.

The appropriate statistical test for the study is a one-sample t-test as it involves the calculation of a single mean.

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.

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.

You don’t need to concern yourself with the specifics of the various means. Simply keep in mind that the arithmetic mean is the one utilized in fundamental biostatistics.

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 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 categorization of patients on a hospital ward based on their diagnosis = nominal

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 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.

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.

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 odds ratio is used in case-control studies to measure the association between exposure and outcome, while the relative risk is used in cohort studies to measure the risk of developing an outcome in the exposed group compared to the unexposed group. To convert the odds ratio to a relative risk, one can use the formula: relative risk = odds ratio / (1 – incidence in the unexposed group x odds ratio).

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 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.

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.

Relative risk reduction (RRR) is calculated as the percentage decrease in the occurrence of events in the experimental group (EER) compared to the control group (CER). It can be expressed as:

RRR = 1 – (EER / CER)

For example, if the EER is 18 and the CER is 33, then the RRR can be calculated as:

RRR = 1 – (18 / 33) = 0.45 of 45%

Alternatively, the RRR can be calculated as the difference between the CER and EER divided by the CER:

RRR = (CER – EER) / CER

Using the same example, the RRR can be calculated as:

RRR = (33 – 18) / 33 = 0.45 of 45%

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.

Gender has traditionally been recorded as either male of female, creating a binary of dichotomous variable. Other categorical variables, such as eye color and ethnicity, can be grouped into two or more categories. Continuous variables, such as temperature, height, weight, and age, can be placed anywhere on a scale and have mathematical properties. Ordinal variables allow for ranking, but do not allow for direct mathematical comparisons between values.

The likelihood ratio for a positive test result is 2, which means that the probability of a positive test result in a person with the condition is twice as high as the probability of a positive test result in a person without the condition.

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.