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I can see why you might not use a more powerful method, such as the Hochberg method, over the Bonferroni correction, as they may have extra assumptions, such as the independence of hypotheses in this case, but I don't understand why you would ever use the Bonferroni correction over Holm's sequentially rejective modification, as the latter is more powerful and has no more assumptions than Bonferroni. Have I missed something?

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One big distinction: The Bonferroni (or Šidák) method allows you to compute a confidence interval. The Holm method does not.

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You're correct that the Holm-Bonferroni procedure is uniformly more powerful.

I can see only one advantage Bonferroni has over Holm-Bonferroni. The Bonferroni correction is simple to carry out - just divide the comparison-wise error rate by k # of hypothesis tests being performed.

If you're in a time crunch and need to perform a lot of hypothesis tests, the Bonferroni correction is already coded in many SAS procedures.

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    $\begingroup$ +1 Ease of calculation has certainly played its role in the popularity of Bonferroni. Perhaps more so historically - for instance, it's commonly cited that the need to calculate fractional powers limited the use of the more powerful Šidák correction. By the time that became computationally trivial, the tradition of using Bonferroni had already been well established. $\endgroup$
    – M. Berk
    Commented Feb 17, 2014 at 16:35
  • $\begingroup$ @M.Berk: I'm sure it is cited, but another consideration may have been that Sidak's correction assumes each test is independent. $\endgroup$
    – Scortchi ♦
    Commented Feb 17, 2014 at 23:12
  • $\begingroup$ Perhaps it would be better to say in this answer: 1): Bonferroni is much easier to do by hand, and computational statistics packages are just a few decades old. 2): Bonferroni was more widely implemented in computational statistics packages of the past. I think those factors probably matter more these days than time crunch. Any decent statistics package (like R) will implement both correction methods, and more besides. $\endgroup$
    – John Doucette
    Commented Apr 17, 2018 at 4:12

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