Tests Supplementing Main Effects in Factorial Designs (2 of 3)

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The marginal mean for A1 (5.125) is the average of A1B1 and A1B2 which is: (5.00 + 5.25)/2 = 5.125. Similarly, the marginal mean for A2 is the average of A2B1 and A2B2, etc. The significant main effect of A means that the marginal means for A1, A2, and A3 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:
  1. All pairwise comparisons among means

  2. Specific comparisons among means

  3. 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.
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