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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.)

Respuesta :

Answer:

(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 [tex]A[/tex] has 2 level and a factor [tex]B[/tex] also has 2 levels.

So, here,

[tex]$k_1$[/tex] = number of levels of A = 2

[tex]k_2[/tex] = number of levels of B = 2

And n = sample size in each treatment condition = 10

So we have,

[tex]d_1[/tex] = df of the main effect A = ([tex]$k_1$[/tex] - 1) = 2 - 1 = 1

[tex]d_2[/tex] = df of the main effect A = ([tex]$k_2$[/tex] - 1) = 2 - 1 = 1

[tex]d_3[/tex] = df of interaction effect (A x B) = ([tex]$k_1$[/tex] - 1)([tex]$k_2$[/tex] - 1)

                                                        = (2-1)(2-1)

                                                         = 1

And [tex]d_4[/tex] = df of within variation (i.e. error variation) = [tex]$k_1k_2(n-1)$[/tex]

                                                                                 = 2 x 2 x (10 - 1)

                                                                                  = 36

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

=  ([tex]d_1, d_4[/tex])

= (1, 36)

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