Page "Statistical power" Paragraph 14

Many statistical analyses involve the estimation of several unknown quantities.

In simple cases, all but one of these quantities is a nuisance parameter.

In this setting, the only relevant power pertains to the single quantity that will undergo formal statistical inference.

In some settings, particularly if the goals are more " exploratory ", there may be a number of quantities of interest in the analysis.

For example, in a multiple regression analysis we may include several covariates of potential interest.

In situations such as this where several hypotheses are under consideration, it is common that the powers associated with the different hypotheses differ.

For instance, in multiple regression analysis, the power for detecting an effect of a given size is related to the variance of the covariate.

Since different covariates will have different variances, their powers will differ as well.