Computing Tests of Comparisons (4 of 6)

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Comparisons among means can be tested with F as well as with t. The formula for F is:

F = MSB/MSE

where MSB (the mean square between) is equal to the sum of squares between (SSB) divided by the degrees of freedom numerator (dfn): MSB = SSB/dfn.

The formula for SSB for a comparison is:



where L, a_i, and n_i are as defined previously. The dfn for a planned comparison is always one. Therefore, MSB = SSB.

MSE, as defined previously, is taken from the analysis of variance.

The degrees of freedom for the F test are:

dfn = 1
dfe = N-a.

An F with one dfn is equal to t² . Therefore, the F test of a comparison is equal to the square of the t-test of the comparison described previously. For the example data,

MSB = SSB = 10.3²/0.85 = 124.812.