Consider a repeated measures factorial ANOVA in which Factor A has 3 levels and Factor B has 6 levels.

What will be the sum of the numerator degrees of freedom for the main effect of Factor A, the main effect of Factor B, and the AB interaction?

Question

Consider a repeated measures factorial ANOVA in which Factor A has 3 levels and Factor B has 6 levels.

What will be the sum of the numerator degrees of freedom for the main effect of Factor A, the main effect of Factor B, and the AB interaction?

BlackTom AI · Accepted Answer

The question asks for the sum of the numerator degrees of freedom (df) for three effects in a repeated measures factorial ANOVA with Factor A having 3 levels and Factor B having 6 levels.

First, determine the df for each effect in a factorial design:
- Main effect A: df_A = a - 1, where a is the number of levels of A. Here a = 3, so df_A = 3 - 1 = 2.
- Main effect B: df_B = b - 1, where b is the number of levels of B. Here b = 6, so df_B = 6 - 1 = 5.
- Interaction AB: df_AB = (a - 1) × (b - 1). With a = 3 and b = 6, this is (3 - 1) × (6 - 1) = 2 × 5 = 10.

Next, sum the numerator degrees of freedom for these effects as requested:
- Add df_A, df_B, and df_AB: 2 + 5 + 10.

Therefore, the total numerator degrees of freedom contributed by the main effects and their interaction is 2 + 5 + 10, i.e., the sum of the individual components equals 2, 5, and 10 respectively; adding them yields the total required for these three terms.

Consider a repeated measures factorial ANOVA in which Factor A has 3 levels and Factor B has 6 levels. What will be the sum of the numerator degrees of freedom for the main effect of Factor A, the main effect of Factor B, and the AB interaction?数值题

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