A researcher conducts an independent-measures, two-factor study with two levels of factor A and three levels of factor B, using a separate sample of n = 10 participants in each treatment condition. What are the df values for the F-ratio evaluating the main effect of factor A? (Hint: Enter in the degrees of freedom for the numerator first and the degrees of freedom for the denominator second.)

(1, 36)

Step-by-step explanation:

Degrees of freedom for the F-test of the two way ANOVA

Here, we use a two factors, independent measures ANOVA, where, factor has 2 level and a factor also has 2 levels.

So, here,

= number of levels of A = 2

= number of levels of B = 2

And n = sample size in each treatment condition = 10

So we have,

= df of the main effect A = ( - 1) = 2 - 1 = 1

= df of the main effect A = ( - 1) = 2 - 1 = 1

= df of interaction effect (A x B) = ( - 1)( - 1)

                                                        = (2-1)(2-1)

                                                         = 1

And = df of within variation (i.e. error variation) =

                                                                                 = 2 x 2 x (10 - 1)

                                                                                  = 36

So, the df value for the F-ratio evaluating the main effect of factors-A is

=  ()

= (1, 36)