powertools (version 1.0.0)

mlrF.overall: Power calculation for a multiple linear regression overall F test

Description

Conducts power and sample size calculations for an overall (or omnibus) F test in a multiple linear regression model. This is a test that all coefficients other than the intercept are equal to zero. Can solve for power, N or alpha.

Usage

mlrF.overall(
  N = NULL,
  p = NULL,
  Rsq = NULL,
  fsq = NULL,
  alpha = 0.05,
  power = NULL,
  random = FALSE,
  v = FALSE
)

Value

A list of the arguments (including the computed one).

Arguments

N

The sample size.

p

The number of predictors.

Rsq

The squared population multiple correlation coefficient.

fsq

The f-squared effect size. Either Rsq OR fsq must be specified.

alpha

The significance level or type 1 error rate; defaults to 0.05.

power

The specified level of power.

random

Whether the values of the predictors are random; defaults to FALSE.

v

Either TRUE for verbose output or FALSE to output computed argument only.

Details

Either Rsq OR fsq must be specified. These are related as fsq = Rsq/(1-Rsq). Rsq is the proportion of the total variation in Y that is explained by linear relationship with the predictors. Specifying random = TRUE yields a calculation in which Y and the predictors are assumed to have a multivariate normal distribution; see Crespi (2025).

Examples

mlrF.overall(N = 400, p = 2, Rsq = 0.02)
mlrF.overall(N = 400, p = 2, fsq = 0.02 / (1 - 0.02))
mlrF.overall(N = 109, p = 1, Rsq = 0.3^2)
mlrF.overall(N = 50, p = 1, Rsq = 0.2)
mlrF.overall(N = 50, p = 3, Rsq = 0.2)
mlrF.overall(N = 50, p = 5, Rsq = 0.2)
mlrF.overall(N = 400, p = 2, Rsq = 0.02, random = TRUE)