Participants in each treatment condition. The results are evaluated using an ANO

Question

Participants in each treatment condition. The results are evaluated using an ANOVA and the researcher reports an F-ratio with df= 2, 108 for factor A, and an F-ratio with df = 3, 108 for factor B.a. How many levels of factor A were used in the a. U study? b. How many levels of factor B were used in the study? c. What are the df values for the F-ratio evaluating the interaction? The following results are from an independent- measures, two-factor study with n = 10 participants measures. a. Use a two-factor ANOVA with alpha = 05 to evaluate the main effects and the interaction. b. Compute eta^2 to measure the effect size for each of the main effects and the interaction. The following results are from an independent- to measures, two-factor study with n = 5 participants

Explanation / Answer

Two-Way ANOVA Table

It is assumed that main effect A has 'a' levels (and A = a-1 df), main effect B has 'b' levels (and B = b-1 df), n is the sample size of each treatment, and N = abn is the total sample size.

(a)Here, df for factor A is a-1=2 , hence levels of factor A is a=2+1=3.

(b) df for factor B is b-1=3 , hence levels of factor B is b=3+1=4.

(c) df for interaction AB is (a-1)*(b-1)=2*3=6

Source SS df MS F Main Effect A SS(A) A,
a-1 SS / df MS(A) / MS(W) Main Effect B SS(B) B,
b-1 SS / df MS(B) / MS(W) Interaction Effect SS(A*B) A*B,
(a-1)(b-1) SS / df MS(A*B) / MS(W) Within SS(W) N - ab,
ab(n-1) SS / df Total SS(T) N - 1,
abn - 1

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