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When do you use which test and which test is best for isolating the differences in multiple comparisons?

gung - Reinstate Monica
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user5943954
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1 Answers1

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It appears you are asking about procedures for doing all pairwise comparisons. The LSD is considered too liberal since it is essentially doing all pairwise comparisons with t tests. The Bonferroni is too conservative since it corrects for the worst case (independent comparisons). This makes the hsd the best of this group. It is also worth noting that the Tukey hsd controls the Type I error rate even if you do not due an ANOVA. Ironically, most people call it a post hoc test when it should be planned a priori.

David Lane
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  • So if you have T1(49.17, 48.19, 48.93) and T2 (4.48, 4.43, 4.79), you'll obviously find a difference here via LSD because of the huge gap. But when comparing T2 and T3(6.36, 7.03, 5.36), you probably won't find a difference because of how liberal the LSD test is? But Bonferroni and HsD probably will because they're more conservative? – user5943954 Mar 17 '17 at 03:46
  • Liberal generally means you are more likely to find a significant difference but the cost is the Type I error rate is not controlled. LSD will always be significant if HSD is significant. – David Lane Mar 17 '17 at 04:32
  • And since bonferroni is conservative, it means that it has a low type 1 error rate but you're less likely to find a significant difference? – user5943954 Mar 17 '17 at 07:32
  • Yes, that is correct. – David Lane Mar 17 '17 at 14:37