Computing Tests of Comparisons (6 of 6)


The section on planned comparisons has a computational example of a planned comparison. For that example, assume that the comparison between the classical music and the rock music was not planned in advance. This makes it necessary to do Scheffé's test. In the example, the values: SSB = 124.812 and
MSE = 21.722 have already been computed.

MSB = 124.812/dfn = 124.812/(5-1) = 31.203
F = 31.203/21.722 = 1.44

An F table shows that the probability of an F with 4 and 18 degrees of freedom being 1.44 or larger is 0.26. Compare this value with the probability value of 0.028 obtained when the comparison was assumed to be planned in advance. Scheffé's test is not a powerful test. If at all possible, you should plan your comparison(s) among means in advance.

Planned comparisons are sometimes called "a priori" comparisons. Unplanned comparisons are sometimes called "post hoc" comparisons and at other times are called "a posteriori" comparisons.