All Pairwise Comparisons among Means: Recapitulation and Recommendations (2 of 3)
There is no "correct" procedure to use; the various procedures trade off power for control of the EER in different ways. There is a consensus that the Duncan's and Fisher's LSD procedures result in too high an EER and should not be used. The choice between the Newman-Keuls and Tukey HSD is a close call. You have to decide how important it is to control the EER completely. If you want to be sure that you have controlled the EER, then the Tukey HSD should be used. Most statisticians now consider the Newman-Keuls unacceptably liberal because of situations in which it allows an inflated EER. However, it is up to the researcher to weigh the balance between power and controlling the EER.
Be careful not to accept the null hypothesis for comparisons for which the null hypothesis is not rejected. Otherwise you may be left with contradictory conclusions. You may find, for example, that M1 is significantly different from M3 but that M1 is not significantly different from M2 and that M2 is not significantly different from M3.