If you specify covariates in a univariate model (whether continuous or categorical), then two adjustments are made in order to compute approximate power in the presence of the covariates. Let denote the number of covariates (counting dummy variables for categorical covariates individually) as specified in the NCOVARIATES= option in the POWER statement. In other words, is the total degrees of freedom used by the covariates. The adjustments are as follows:
The error degrees of freedom decrease by .
The error standard deviation shrinks by a factor of (if the CORRXY= option is used to specify the correlation between covariates and response) or (if the PROPVARREDUCTION= option is used to specify the proportional reduction in total incurred by the covariates). Let represent the updated value of .
As a result of these changes, the power is computed as
where is calculated using rather than :