Tests Supplementing Main Effects in Factorial Designs
(2 of 3)
The marginal mean for A
1 (5.125) is the average of A
1B
1
and A
1B
2 which is: (5.00 + 5.25)/2 = 5.125. Similarly,
the marginal mean for A
2 is the average of A
2B
1
and A
2B
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.