powerWelchT: Power of Two-Sided Two Sample T Test With Unequal Variances...

In powerSurvEpi: Power and Sample Size Calculation for Survival Analysis of Epidemiological Studies

Power of Two-Sided Two Sample T Test With Unequal Variances And Unequal Sample Sizes

Description

Power of two-sided 2 sample t test with unequal variances and unequal sample sizes.

Usage

powerWelchT(
  n1, 
  n2, 
  meanDiff, 
  sd1, 
  sd2, 
  alpha = 0.05)

Arguments

n1	sample size for group 1
n2	sample size for group 2
meanDiff	mean difference between 2 groups
sd1	standard deviation of group 1
sd2	standard deviation of group 2
alpha	Type I error rate

Details

The power formula is

power = Pr\left(|T| > t_{1-\alpha/2, \nu} | T \sim t_{\nu, \lambda}\right),

where \lambda is the noncentrality parameter of the t distribution with degree of freedom \nu. t_{1-\alpha/2, \nu} is the upper 100\alpha/2 percentile of the t distribution with degree of freedom \nu. \alpha is the significance level. The noncentrality parameter \lambda is defined as

\lambda = \frac{|\mu_1 - \mu_2|}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}.

The degree \nu of freedom is the Satterthwaite approximation and is defined as

\nu = \frac{\left(\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}\right)^2}{ \frac{\left(\frac{\sigma_1^2}{n_1}\right)^2}{n_1-1} + \frac{\left(\frac{\sigma_2^2}{n_2}\right)^2}{n_2-1} }

Value

power

Examples

powerWelchT(
    n1 = 64, # sample size for group 1 
    n2 = 30, # sample size for group 2
    meanDiff = 1, # mean difference between 2 groups
    sd1 = 2, # SD of group 1
    sd2 = 1, # SD of group 2
    alpha = 0.05 # type I error rate
)
# 0.8918191

powerSurvEpi documentation built on June 23, 2025, 1:06 a.m.