ssizeWelchT: Sample Size Calculation For Two-Sided Two Sample T Test With...

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

Sample Size Calculation For Two-Sided Two Sample T Test With Unequal Variances And Unequal Sample Sizes

Description

Sample size calculation for two-sided two sample t test with unequal variances and unequal sample sizes

Usage

ssizeWelchT(
  ratioN2toN1, 
  meanDiff, 
  sd1, 
  sd2, 
  power = 0.8, 
  alpha = 0.05, 
  minN1 = 3)

Arguments

ratioN2toN1	numeric. The ratio of sample size for group 2 to sample size for group 1
meanDiff	mean difference between 2 groups
sd1	standard deviation of group 1
sd2	standard deviation of group 2
power	power
alpha	Type I error rate
minN1	minimum sample size for group 1

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

A list with 2 elements

n1	sample size for group 1
n2	sample size for group 2

Examples

ssizeWelchT(
    ratioN2toN1=30/64, # ratio of sample size for group 2 to sample size for group 1
    meanDiff = 1, # mean difference between 2 groups
    sd1 = 2, # SD of group 1
    sd2 = 1, # SD of group 2
    power = 0.8918191, # power
    alpha = 0.05, # type I error rate
    minN1 = 3 # minimu possible sample size for group 1
)
# n1 = 64 and n2 = 30

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