# Tests Supplementing Main Effects in Factorial Designs
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The marginal mean for A

_{1} (5.125) is the average of A

_{1}B

_{1}
and A

_{1}B

_{2} which is: (5.00 + 5.25)/2 = 5.125. Similarly,
the marginal mean for A

_{2} is the average of A

_{2}B

_{1}
and A

_{2}B

_{2}, etc. The significant

main effect of A means that the marginal means for A

_{1},
A

_{2}, and A

_{3} are not all equal. It does not reveal
which population means are different from which others. Procedures for
following up a significant main effect such as this one are analogous
to the procedures used to

follow up a significant
effect in a one-factor ANOVA. These procedures are:

- All pairwise comparisons among means

- Specific comparisons among
means

- Comparing all means with a control

The formulas used in these procedures

all involve the

sample size (n).

When
applying these formulas to multi-factor experiments, n refers to the
number of scores in each of the means being compared.