In a two-factor ANOVA, A (fixed factor) has 3 levels, and B (random factor) has 5 levels. Each cell has 5 observations. The F_A ratio has degrees of freedom equal to? A) 2, 8 B) 2, 15 C) 2, 60 D) 2, 74 E) None of the above.

Question

Quizplus · Accepted Answer

The degrees of freedom for the numerator (F_A) are determined by the interaction between factors A and B, which is (levels of A - 1) * (levels of B - 1) = (3-1)*(5-1) = 2*4 = 8. The denominator's degrees of freedom are for the error term, which is calculated as the number of observations per cell minus 1, multiplied by the total number of cells: (5-1)*(3*5) = 4*15 = 60. However, the question specifically asks for the F_A ratio's degrees of freedom, which are correctly identified in option A as 2 for the numerator (interaction term) and 8 for the denominator (error term within the interaction), indicating a misunderstanding in the explanation of the denominator's calculation. The correct interpretation focuses on the interaction term's degrees of freedom and the specific structure of the ANOVA design, leading to the correct answer of 2, 8.

In a Two-Factor ANOVA, a (Fixed Factor) Has 3 Levels