# Which post-hoc test use after ANOVA? - Tukey, Newman-Keuls or Bonferroni? (Mar/02/2010 )

I use Prism to do all my statistics. When I do an ANOVA I have the choice of a few post-hoc tests (Tukey, Newman-Keuls and Bonferroni). I am wondering which one should I use in which circumpstances. I’ve read that Newman-Keuls is more powerful than Tukey, but can’t find anything about the Bonferroni. Why should I use one or the other? I find that they usually give similar results.

LAB Tech on Mar 2 2010, 10:21 AM said:

Slight differences in how pairwise comparisons are calculated. It really boils down to how conservative each is. I know Bonferroni is more strict than Tukey, but not sure where Newman-Keuls is in the range. By that I mean that Tukey's adjustments will most likely result in a lower P-value than Bonferroni's. So if you use Tukey's, you may end up with values that are signficant where if you used Bonferroni's, the value would be insignificant. I think any of the three are generally accepted without much fuss. I don't think any one applies to any situation, just which one is preferred. I generally use Tukey's, based on what my stats professor taught, but I think it's more of a personal preference type of thing.

You have the right approach, trying out a few tests and looking to see where and why they are different. And in the end do what we all do and chose the one that gives the results that best suits our purposes .

The Bonferroni is basically the same as doing a whole series of t-tests, except that it winds up the cut off point for significance according to the number of comparisons that are to be made. Thus the more means you have the stingier it will get.

The other two take a slightly different approach by altering the T-distribution with a studentised range to set the significance cut off. In practical terms I would favour the Tukey results if you have more than 5 factors because the probability of declaring false differences becomes dangerously likely with the N-K test.

Thanks for your answers

So basically, if I write in the material & methods of an article that I'm using any of these post test I shouldn't have any problems, right?

Re Bonferroni:

see Bland JM & Altman DG, "Multiple significance tests: the Bonferroni method", British Medical Journal, 310:170, 1995