Question

The partially completed ANOVA table for a 3 x 4 factorial experiment (i.e., there are 3 levels of factor A and 4 levels of factor B) with two replications is shown below:

Source          df          SS          MS          F   

Total                          18.1

Factor A                     0.8

Factor B                     5.3

A x B                           9.6

Error                                                            

What are the degrees of freedom for total, factor A, factor B, the A x B interaction, and error?

Group of answer choices

Degrees of freedom = 24, 3, 4, 12, and 5 for total, factor A, factor B, the A x B interaction, and error, respectively.

Degrees of freedom = 23, 2, 3, 5, and 13 for total, factor A, factor B, the A x B interaction, and error, respectively.

Degrees of freedom = 24, 12, 1, 1, and 10 for total, factor A, factor B, the A x B interaction, and error, respectively.

Degrees of freedom = 23, 2, 3 , 6, and 12 for total, factor A, factor B, the A x B interaction, and error, respectively.

Answer 1

The degrees of freedom for the main effect that is for factors A and B are computed as the number of levels - 1

Therefore DF for A would be 3 - 1 = 2 and that for B would be 4 - 1 = 3

For the cross interaction term, the degree of freedom is computed as the product of the individual degree of freedoms for the 2 factors. Therefore it is computed here as: 2*3 = 6

Therefore DF for the interaction term are given as 6

For the error term the degree of freedom are computed as the product of the individual number of levels, computed here as: DF = 3*4 = 12

Therefore DF for the error term are given here as 12

Total DF = 12 + 6 + 2 + 3 = 23

Therefore Degrees of freedom = 23, 2, 3 , 6, and 12 for total, factor A, factor B, the A x B interaction, and error, respectively is the required answer here.