Complete the following ANOVA summary table for a two-factor fixed-effects ANOVA, where there are three levels of factor A (teaching method) and two levels of factor B (time of class).
Each cell includes six students and $\alpha$ = .05.

$\begin{array}{ccccccc}
\hline \text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \text { A } & & & 6.5 & & & \
\text { B } & & & & & \
\mathrm{AB} & & & 5.2 & & \
\text { Within } & 39 & & & & \
\text { Total } & 65 & & & & \
\hline
\end{array}$

Question

Complete the following ANOVA summary table for a two-factor fixed-effects ANOVA, where there are three levels of factor A (teaching method) and two levels of factor B (time of class).
 Each cell includes six students and $\alpha$ = .05.

$\begin{array}{ccccccc}
\hline \text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \text { A } & & & 6.5 & & & \
\text { B } & & & & & \
\mathrm{AB} & & & 5.2 & & \
\text { Within } & 39 & & & & \
\text { Total } & 65 & & & & \
\hline
\end{array}$

Quizplus · Accepted Answer

The Answer is There are 3 levels of factor A, so J = 3. There are 2 levels of factor B, so K = 2. Each cell has 6 students, so n = 6. N = 3*2*6 = 36.

df_A= J - 1 = 3 - 1 = 2, df_B = K- 1 = 2 - 1 = 1, df_A_B = (J - 1)(K - 1) = 2*1 = 2, df_with = N - JK = 36 - 3*2 = 30, df_total = N- 1 = 36 - 1 = 35.

SS_A = df_A*MS_A = 2*6.5 = 13, SS_AB = df_AB*MS_AB = 2*5.2 = 10.4,
SS_B = SS_total -SS_A - SS_AB -SS_with = 65 - 13 - 10.4- 39 = 2.6.

MS_B = SS_B/df_B = 2.6/1 = 2.6; MS_with = SS_with/df_with = 39/30 = 1.3.

F_A = MS_A/MS_with = 6.5/1.3 = 5; critical value = _.05F_2,30 = 3.32 < F_A, reject H₀.
F_B=MS_B/MS_with = 2.6/1.3 = 2; critical value = _.05F₁_,₃₀ = 4.17 > F_B, fail to reject H₀.

F_AB =MS_AB/MS_with =5.2/1.3 = 4; critical value = _.05F_2,₃₀ = 3.32 < F_AB, reject H₀.

\begin{array}{ccccccc}\hline ext { Source } & S S & \boldsymbol{d f} & M S & F & ext { Critical Value } & ext { Decision } \\hline \mathrm{A} & 13.0 & 2 & 6.5 & 5 & .05 F_{2,00}=3.32 & ext { Reject } H_{0} \\mathrm{~B} & 2.6 & 1 & 2.6 & 2 & .05 F_{1,30}=4.17 & ext { Fail toreject } H_{0} \\mathrm{AB} & 10.4 & 2 & 5.2 & 4 & .05 F_{2,30}=3.32 & ext { Reject } H_{0} \ ext { Within } & 39.0 & 30 & 1.3 & & & \ ext { Total } & 65.0 & 35 & & & & \\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 $\alpha$