Sample size and power for continuous and categorical variables

When relating one or more predictors to a dependent variable, data analysts sometimes categorize continuous variables. The effect of such categorization on power and sample size was examined via simulation, in several situations. These include the case where the correct model is in fact linear dependence of outcomes on continuous predictors; that in which the relationship is correctly modeled by a categorical predictor; and situations which fall between these poles. Additionally, linear and logistic regressions using continuous and categorized versions of the same dependent variable are analyzed. Comparisons depend on effect size and on correlations among independent variables in multiple regression.

Differences in power, and in sample size needed to detect a given effect with given power, are substantial. Differences in both power and sample size are threefold or more in some cases.

The existence of differences is not unexpected, in view of the statistical theory of efficient estimators and most powerful tests. However, their magnitude may be surprising. Therefore it can be important to have sound reasons for deciding whether and how to categorize.