When we perform experiments (on small sample sizes (usually the sample size per treatment group is about 7~8)) on two groups, we use a t-test to test for difference. However, when we perform an ANOVA (obviously for more than two groups), we use something along the lines of Bonferroni (LSD/# of pairwise comparisons) or Tukey's as a post hoc, and as a student, I have been warned off from using Fisher's Least Significant Difference (LSD).
Now the thing is, LSD is similar to pairwise t-test (am I right?), and so the only thing it doesn't account for is that we're doing multiple comparisons. How important is that when dealing with say 6 groups, if the ANOVA is itself significant?
Or in other words, is there any scientific/statistical reason for using a Fisher's LSD?
Best Answer
Fisher's LSD is indeed a series of pairwise t-tests, with each test using the mean squared error from the significant ANOVA as its pooled variance estimate (and naturally taking the associated degrees of freedom). That the ANOVA be significant is an additional constraint of this test.
It restricts family-wise error rate to alpha in the special case of 3 groups only. Howell has a very good and relatively simple explanation of how it does so in Chapter 16 of his book Fundamental Statistics for the Behavioral Sciences, 8th edition, David C. Howell.
Above 3 groups alpha inflates rapidly (as @Alexis has noted above). It is not certainly appropriate for 6 groups. I believe that it is this limited applicability that causes most people to suggest ignoring it as an option.