cited in more than 3,000 scientific papers!

Below you will find descriptions and details for the 9 formulas that are used to compute post-hoc statistical power values for hierarchical multiple regression studies.

Beta function:

Effect size for hierarchical multiple regression:

where R

Error function:

F-distribution cumulative distribution function (CDF):

where

Lower incomplete beta function:

Noncentral F-distribution cumulative distribution function (CDF):

where

Noncentral F-distribution noncentrality parameter:

where

Normal distribution cumulative distribution function (CDF):

where

Regularized lower incomplete beta function:

where the numerator is the lower incomplete beta function, and the denominator is the beta function.

Related Resources