Question

Name two common post hoc procedure for the comparison of means in an ANOVA.

Answer 1

1. Duncan’s new multiple range test (MRT)
When you run Analysis of Variance (ANOVA), the results will tell you if there is a difference in means. However, it won’t pinpoint the pairs of means that are different. Duncan’s Multiple Range Test will identify the pairs of means (from at least three) that differ. The MRT is similar to the LSD, but instead of a t-value, a Q Value is used.

2.  LSD test.

The original solution to this problem, developed by Fisher, was to explore all possible pair-wise comparisons of means comprising a factor using the equivalent of multiple t-tests. This procedure was named the Least Significant Difference (LSD) test.

Tukey’s HSD was designed for a situation with equal sample sizes per group, but can be adapted to unequal sample sizes as well (the simplest adaptation uses the harmonic mean of n-sizes as n*).

3. Scheffe’s test.

Scheffe’s procedure is perhaps the most popular of the post hoc procedures, the most flexible, and the most conservative. Scheffe’s procedure corrects alpha for all pair-wise or simple comparisons of means, but also for all complex comparisons of means as well. Complex comparisons involve contrasts of more than two means at a time. As a result, Scheffe’s is also the least statistically powerful procedure. Scheffe’s is presented and calculated below for our pairwise situation for purposes of comparison and because Scheffe’s is commonly applied in this situation, but it should be recognized that Scheffe’s is a poor choice of procedures unless complex comparisons are being made.

Critical Difference

LSD 0.6360

Tukey 1.1957

Scheffe 1.3027