Question

A two-factor research study has 2 levels of factor A and 3 levels of factor B with a separate sample of n = 5 subjects in each treatment condition. Based on this information, what are the df values for the F-ratio evaluating the main effect of factor A?

a. df=1,29
b. df= 1,24
c. df= 2,29
d. df= 2,24

Answer 1

option (b) df = 1, 24

Explanation:

Data provided in the question:

levels of factor A, a = 2

levels of factor B, b = 3

Subjects in each Sample, s = 5

n = 5 × 3 × 2 = 30

Now

df for Factor A = a - 1

= 2 - 1

= 1

df for Factor B = b - 1

= 3 - 1

= 2

df for Interaction AB = ( a - 1 ) × ( b - 1 )

= 1 × 2

= 2

df for Total = n - 1

= 30 - 1

= 29

df for error = 29 - 5

= 24

Hence,

df values for the F-ratio evaluating the main effect of factor A is 1, 24

The correct answer is option (b) df = 1, 24