# Effects of categorical measurement

## Decrease statistical power and increase 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.