The p.adjust function in R can produce P value adjustments based on methods from Hochberg and Hommel, which are both more powerful than methods from Bonferroni and Holm. However, and as stated in the R documentation:
Hochberg's and Hommel's methods are valid when the hypothesis tests are independent or when they are non-negatively associated (Sarkar, 1998; Sarkar and Chang, 1997).
Can anyone explain what this means in a more accessible language?
Also, is there a way to empirically determine whether your hypothesis tests (data) meet this assumption?
