I have a bit of trouble understanding the Holm-Bonferroni correction. For the normal Bonferroni correction you simply divide your alpha level by the number of tests. For example, if I have 3 tests, I will test all 3 test against a alpha level of .016. Note: I´m adjusting alpha instead of p, because I´m doing a power analysis.
Now, for the Holm-Bonferroni correction, I understood that you apply the Bonferroni correction sequentially. That is: Test 1: Alpha = .05. Test 2: Alpha = .025 Test 3: Alpha = .016. However, that seems to be incorrect. Consider the following code in R:
> pvalues <- c(0.049, 0.049, 0.049) > p.adjust(pvalues, method = "holm")  0.147 0.147 0.147 > p.adjust(pvalues, method = "bonferroni")  0.147 0.147 0.147
Both methods return exactly the same output for all three p-values. Can anyone explain where I get the Holm-Bonferroni correction wrong and how I can adjust my alpha appropriately? Please note that the output remains identical with more p-values.