Categorical variables are very prevalent in medicine. Measures like presence of comorbidities, mortality, and test results are categorical in nature. Here are some general caveats associated with categorical measurement and sample size:  

1. Categorical outcomes will always DECREASE statistical power and INCREASE the needed sample size. This is due to the lack of precision and accuracy in categorical measurement.

2. The underlying algebra associated with calculating 95% confidence intervals of odds ratios and relative risk is 100% dependent upon the sample size. With smaller sample sizes, by default, wider and less precise 95% confidence intervals will be found. If one of the cells of a cross-tabulation table has fewer observations that the other cells, then the 95% confidence interval will be wider and potentially not truly interpretable. A 95% confidence interval will become narrower or more precise only with larger sample sizes.  

3. When using categorical variables for diagnostic testing purposes, larger samples sizes will be needed to calculate precise measures of sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV). With smaller sample sizes in diagnostic studies, a change in one or two observations can have drastic effects on the diagnostic values.

This is especially true when there is a subjective rating used for purposes of diagnosing someone as "positive" or "negative" for a given disease state (radiologist reading an X-ray). Inter-rater reliability coefficients such as Kappa or ICC should be employed to ensure consistency and reliability among subsequent ratings and raters. Sensitivity, specificity, and PPV will be affected by inter-rater reliability. Receiver Operator Characteristic (ROC) curves can be used to find a given value where sensitivity and specificity of a test is maximized. ROC curves can also be used to compare the area under the curve (AUC) between several diagnostic tests at the same time so that the best can be chosen.  

4. For each predictor categorical parameter (or variable) that you want to include in a multivariate model, you have to increase your sample size by at least 20-40 observations of the outcome. This due to the limited precision, accuracy, and statistical power associated with categorical measurement. Researchers HAVE to collect more observations in order to detect any potential significant multivariate associations.  

In the case that a polychotomous variable is to be used in a model, create (a-1), where a is the number of categories, dichotomous variables with "0" as not being that category and "1" as being that category. For each level, 20-40 more observations of the outcome will be needed to have enough statistical power to detect differences amongst the multiple groups.        

By far, the prospective cohort design is the most powerful observational design. The design can yield a measure of incidence (number of new cases in a population), longitudinal effects (etiology and disease progression), and the potential for decreased observation bias (more control on study design and data collection).

Retrospective cohort designs can yield some measures of incidence in patient populations. However, researchers are limited to the variables that have been collected in an objective fashion within homogeneous populations. Incidence is a much more valid measure when generated using a prospective cohort design. Researchers choose in an a priori fashion exactly what variables will be collected in the measured.

Incidence is a much more precise measure of association versus prevalence. Prospective and experimental designs can yield measures of incidence and establish the relative risk of developing an outcome. Researchers and clinicians also have a better understanding of incidence and relative risk versus prevalence and odds ratios.

Longitudinal data is data collected over an extended period of time. Longitudinal data is necessary for understanding the etiology and progression of disease states. Survival and time-to-event analyses produce popular measures in medicine such as 1-year, 3-year, and 5-year survival and recurrence. The primary issue with collecting longitudinal data is attrition and loss to follow-up with the prospective sample. As participants fall out of the study or are lost, the validity of the data greatly decreases.

Again, it is important to state that prospective designs give more control to researchers in regards to what data is collected. Every variable that you find pertinent for establishing causal effects between predictor and outcome variables, when controlling for all important demographic, prognostic, clinical, and confounding variables, can be chosen and collected. Observational biases associated with retrospective research do not apply with these studies because you can collect all of the data on all the variables that you chose, given that there is a theoretical, conceptual, or physiological reason for doing so.

As we continue our journey to break through the barriers associated with statistical lexicons, here is another dichotomy of popular statistical terms that are spoken commonly but not always understood by everyone.  

Parametric statistics are used to assess differences and effects for continuous outcomes. These statistical tests include one-sample t-tests, independent samples t-tests, one-way ANOVA, repeated-measures ANOVA, ANCOVA, factorial ANOVA, multiple regression, MANOVA, and MANCOVA. 

Non-parametric statistics are used to assess differences and effects for:

1. Ordinal outcomes - One-sample median tests, Mann-Whitney U, Wilcoxon, Kruskal-Wallis, Friedman's ANOVA, Proportional odds regression

2. Categorical outcomes - Chi-square, Chi-square Goodness-of-fit, odds ratio, relative risk, McNemar's, Cochran's Q, Kaplan-Meier, log-rank test, Cochran-Mantel-Haenszel, Cox regression, logistic regression, multinomial logistic regression

3. Small sample sizes (n < 30) - Smaller sample sizes make it harder to meet the statistical assumptions associated with parametric statistics.  Non-parametric statistics can generate valid statistical inferences in these situations.

4. Violations of statistical assumptions for parametric tests - Normality, Homogeneity of variance, Normality of difference scores

If there is ANY statistical calculation that holds true value for researchers and clinicians on a day-to-day basis, it is the 95% confidence interval wrapped around the findings of inferential analyses. Statistics is not an exact mathematical science as far as other exact mathematical sciences go, measurement error is inherent when attempting to measure for anything related to human beings, and FEW tried and true causal effects have been proven scientifically. Statistics' strength as a mathematical science is in its ability to build confidence intervals around findings to put them into a relative context.  

Also, 95% confidence intervals act as the primary inference associated with unadjusted odds ratios, relative risk, hazard ratios, and adjusted odds ratios. If the confidence interval crosses over 1.0, there is a non-significant effect. Wide 95% confidence intervals are indicative of small sample sizes and lead to decreased precision of the effect. Constricted or narrow 95% confidence intervals reflect increased precision and consistency of a treatment effect.

In essence, p-values should not be what people get excited about when it comes to statistical analyses. The interpretation of your findings within the context of the subsequent population means, odds, risk, hazard, and 95% confidence intervals IS the real "meat" of applied statistics.

Most people that need statistics are focused only on the almighty p-value of less than .05. When running Chi-square analyses between a dichotomous categorical predictor and a dichotomous categorical outcome, p-values are not the primary inference that should be interpreted for practical purposes. The lack of precision and accuracy in categorical measures coupled with sampling error makes the p-values yielded from Chi-square analyses virtually worthless in the applied sense.

The correct statistic to run is an unadjusted odds ratio with 95% confidence interval. This is the best measure for interpreting the magnitude of the association between two dichotomous categorical variables collected in a retrospective fashion. Relative risk can be calculated when the association is assessed in a prospective fashion.

The width of the 95% confidence interval and it crossing over 1.0 dictate the significance and precision of the association between the variables.  With smaller sample sizes, the 95% confidence interval will be wider and less precise. Larger sample sizes will yield more precise effects.

There are terms in statistics that many people do not understand from a practical standpoint. I'm a biostatistical scientist and it took me YEARS to wrap my head around some fundamental aspects of statistical reasoning, much less the lexicon. I would hypothesize that 90% of the statistics reported in the empirical literature as a whole fall between two different categories of statistics, between-subjects and within-subjects. Here is a basic breakdown of the differences in these types of statistical tests:

1. Between-subjects - When you are comparing independent groups on a categorical, ordinal, or continuous outcome variable, you are conducting between-subjects analyses. The "between-" denotes the differences between mutually exclusive groups or levels of a categorical predictor variable. Chi-square, Mann-Whitney U, independent-samples t-tests, odds ratio, Kruskal-Wallis, and one-way ANOVA are all considered between-subjects analyses because of the comparison of independent groups.  

2. Within-subjects - When you are comparing THE SAME GROUP on a categorical, ordinal, or continuous outcome ACROSS TIME OR WITHIN THE SAME OBJECT OF MEASUREMENT MULTIPLE TIMES, then you are conducting within-subjects analyses. The "within-" relates to the differences within the same object of measurement across multiple observations, time, or literally, "within-subjects." Chi-square Goodness-of-fit, Wilcoxon, repeated-measures t-tests, relative risk, Friedman's ANOVA, and repeated-measures ANOVA are within-subjects analyses because the same group or cohort of individuals is measured at several different time-points or observations.

The terms prevalence and incidence are often used interchangeably. However, they are extremely different in their utility and interpretability within epidemiology.

Prevalence is the proportion of cases or disease states that exist in a population at any given time.  Prevalence is established using cross-sectional research designs.  Measures of prevalence can be used to generate odds ratios for outcomes occurring given an exposure or non-exposure.  It is calculated when data is collected in a retrospective fashion. 

Incidence is the number of new cases or disease states that occur in a population.  Incidence is established in cohort designs.  Measures of incidence are used to establish the relative risk of an outcome given treatment or no treatment.  It is calculated when data is collected in a prospective fashion.

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