How to calculate power (or sample size) for a multiple comparison when Bonferroni-adjusted p-value?

General
2

Without a reprex (see the FAQ), the best I can do is to relay a chat, which I haven't tested.

To calculate power or sample size for multiple comparison experiments (ANOVA or Kruskal-Wallis non-parametric test) when using the Bonferroni-adjusted p-value method, you can use the MultNonParam package in R for the Kruskal-Wallis test[1]. For ANOVA, you can use the pwr package in R.

For the Kruskal-Wallis test, you can use the kwpower function from the MultNonParam package[3]:

# Install the package if not already installed
if (!requireNamespace("MultNonParam", quietly = TRUE)) {
  install.packages("MultNonParam")
}

# Load the package
library(MultNonParam)

# Calculate power for Kruskal-Wallis test
kwpower(nreps, shifts, distname = c("normal", "logistic"), level = 0.05, ...)

For ANOVA, you can use the pwr.anova.test function from the pwr package:

# Install the package if not already installed
if (!requireNamespace("pwr", quietly = TRUE)) {
  install.packages("pwr")
}

# Load the package
library(pwr)

# Calculate power for ANOVA
pwr.anova.test(k, n, f, sig.level = 0.05, power = NULL)

For a more user-friendly tool, you can use GPower to calculate the required sample size for the Kruskal-Wallis test[2]. GPower is a free software that can be downloaded from the following website: http://www.gpower.hhu.de/

Please note that the Bonferroni-adjusted p-value method is used for multiple comparisons after the initial ANOVA or Kruskal-Wallis test. The power or sample size calculations mentioned above are for the initial tests, and the Bonferroni adjustment is applied afterward to control the family-wise error rate.

Citations:
[1] nonparametric - Power analysis for Kruskal-Wallis or Mann-Whitney U test using R? - Cross Validated
[2] Kruskal-Wallis-Test - calculate required sample size with G*Power - YouTube
[3] kwpower: Power for the Kruskal-Wallis test. in MultNonParam: Multivariate Nonparametric Methods
[4] https://www.datanovia.com/en/lessons/kruskal-wallis-test-in-r/
[5] https://med.und.edu/research/daccota/_files/pdfs/berdc_resource_pdfs/sample_size_r_module.pdf
[6] https://med.und.edu/research/daccota/_files/pdfs/berdc_resource_pdfs/sample_size_