A two-factor ANOVA produces an F-ratio for factor A with df = 1,36 and an F-ratio for factor B with df = 2,36.Which of the following describes the experiment producing these F-ratios?
A)1 level of factor A and 2 levels of factor B
B)2 levels of factor A and 3 levels of factor B
C)2 levels for both factors
D)3 levels for both factors

Question

A two-factor ANOVA produces an F-ratio for factor A with df = 1,36 and an F-ratio for factor B with df = 2,36.Which of the following describes the experiment producing these F-ratios?​
A)​1 level of factor A and 2 levels of factor B
B)​2 levels of factor A and 3 levels of factor B
C)​2 levels for both factors
D)​3 levels for both factors

Quizplus · Accepted Answer

The degrees of freedom (df) for an F-ratio in ANOVA are determined by the number of levels of the factor minus one (for the numerator) and the total number of observations minus the number of levels of the factor (for the denominator). Given df = 1,36 for factor A, this indicates 2 levels of factor A (since 2-1=1) and given df = 2,36 for factor B, this indicates 3 levels of factor B (since 3-1=2). Therefore, the experiment must have 2 levels of factor A and 3 levels of factor B.

A Two-Factor ANOVA Produces an F-Ratio for Factor a with Df