Question

How does the Fisher’s least significant difference test differ from Tukey’s honestly significant difference test? Provide examples of when you would use each, and explain the differences between these two post-hoc test.

Answer 1

SOLUTION:

Fisher’s LSD:

We begin with a one-way analysis of variance. If the F-ratio overall is statistically significant, we can safely conclude that not all of the treatment means are identical. Then only then...we carry out all possible t tests! Yes, the same "all possible t tests" that were just soundly criticized. The difference is that the t tests can't be performed unless the overall F-ratio is statistically significant. There is only a 5% chance of that the overall F ratio will reach statistical significance when there are no differences. Therefore, the chance of reporting a significant difference when there are none is held to 5%. It is not uncommon to see the term Fisher's LSD used to describe all possible t tests without a preliminary F test, so stay alert and be a careful consumer of statistics.

Tukey's HSD:

Tukey attacked the problem a different way by following in Student's (WS Gosset) footsteps. Student discovered the distribution of the t statistic when there were [b]two[/b] groups to be compared and there was no underlying mean difference between them. When there are g groups, there are g(g-1)/2 pairwise comparisons that can be made. Tukey found the distribution of the largest of these t statistic when there were no underlying differences. For example, when there are 4 treatements and 6 subjects per treatment, there are 20 degrees of freedom for the various test statistics. For Student's t test, the critcal value is 2.09. To be statistically significant according to Tukey's HSD, a t statistic must exceed 2.80. Because the number of groups is accounted for, there is only a 5% chance that Tukey's HSD will declare something to be statistically significant when all groups have the same population mean. While HSD and LSD are the most commonly used procedures, there are many more in the statistical literature and some see frequent use.