Complete the following ANOVA summary table for a two-factor fixed-effects ANOVA, where there are two levels of factor A (type of counseling) and four levels of factor B (frequency of counseling). Each cell includes six people and $\alpha$= .01.

$\begin{array}{ccccccc}
\hline \text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \mathrm{A} & 60 & & & 6 & \
\mathrm{~B} & & & & & \
\mathrm{AB} & 60 & & & & \
\text { Within } & & & & & \
\text { Total } & 640 & & & & \
\hline
\end{array}$

Question

Complete the following ANOVA summary table for a two-factor fixed-effects ANOVA, where there are two levels of factor A (type of counseling) and four levels of factor B (frequency of counseling). Each cell includes six people and $\alpha$= .01.

$\begin{array}{ccccccc}
\hline \text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \mathrm{A} & 60 & & & 6 & \
\mathrm{~B} & & & & & \
\mathrm{AB} & 60 & & & & \
\text { Within } & & & & & \
\text { Total } & 640 & & & & \
\hline
\end{array}$

Quizplus · Accepted Answer

The Answer is A has 2 levels, so J = 2. B has 4 levels, so K = 4.

Each cell has 6 people, so n = 6. N = 2*4*6 = 48.

df_A= J - 1 = 2 - 1 = 1, df_B = K - 1 = 4 - 1 = 3, df_A_B = (J - 1)(K - 1) = 1*3 = 3, df_with = N - JK = 48 - 2*4 = 40, df_total = N - 1 = 48 - 1 = 47.

MS_A = SS_A/df_A = 60/1 = 60, MS_AB = SS_AB/df_AB = 60/3 = 20,
MS_with = MS_A/F_A = 60/6 = 10; SS_with = MS_with*df_with = 10*40 = 400,
SS_B = SS_total - SS_A - SS_AB - SS_with = 640 - 60 - 60 - 400 = 120;
MS_B = MS_B/F_B = 120/3 = 40
F_A = MS_A/MS_with = 60/10 = 6; critical value = _.0₁F_1,40 = 7.31 > F_A, fail to reject H₀.

F_B = MS_B/MS_with = 40/10 = 4; critical value = _.0₁F₃_,₄₀ = 4.31 > F_B, fail to reject H₀.
F_AB= MS_AB/MS_with= 20/10 = 2; critical value = _.0₁F₃_,₄₀= 4.31 > F_AB, fail to reject H₀.

\begin{array}{crrrrcc} ext { Source } & S S & d f & M S & F & ext { Critical Value } & ext { Decision } \\hline \mathrm{A} & 60 & 1 & 60 & 6 & .01 F_{1,40}=7.31 & ext { Fail to reject } H_{0} \\mathrm{~B} & 120 & 3 & 40 & 4 & .01 F_{3,40}=4.31 & ext { Fail to reject } H_{0} \\mathrm{AB} & 60 & 3 & 20 & 2 & .01 F_{3,40}=4.31 & ext { Fail to reject } H_{0} \ ext { Within } & 400 & 40 & 10 & & & \\hline\end{array}

Complete the Following ANOVA Summary Table for a Two-Factor Fixed-Effects α\alphaα

Complete the Following ANOVA Summary Table for a Two-Factor Fixed-Effects $\alpha$