If the assumption of equality of variances is not met, Tamhane's test is preferred. When this assumption is satisfied we can choose amongst several tests. Although the LSD (Fisher's Least Significant Difference) is a very strong test in detecting pairs of means differences, it is applied only when the F test is significant, and it is mostly less preferable since its method fails in protecting low error rate. Bonferroni test is a good choice due to its correction suggested by his method. This correction states that if n independent tests are to be applied then the α in each test should be equal to α /n. Tukey's method is also preferable by many statisticians because it controls the overall error rate. (More information on this issue can be found in any ANOVA book, such as Douglas C. Montgomery's Design and Analysis of Experiments).