Complete the following ANOVA summary table for a two-factor fixed-effects ANOVA, where there are four levels of factor A (grade level) and three levels of factor B (textbook). Each cell includes 11 students and $\alpha$ = .05.

$\begin{array}{ccccccc}
\hline \text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \mathrm{A} & & & 5 & & \
\mathrm{~B} & 42 & & & & \
\mathrm{AB} & & & 25 & & \
\text { Within } & 240 & & & & \
\text { Total } & & & & & & \
\text { Win }
\end{array}$

Question

Complete the following ANOVA summary table for a two-factor fixed-effects ANOVA, where there are four levels of factor A (grade level) and three levels of factor B (textbook). Each cell includes 11 students and $\alpha$ = .05.

$\begin{array}{ccccccc}
\hline \text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \mathrm{A} & & & 5 & & \
\mathrm{~B} & 42 & & & & \
\mathrm{AB} & & & 25 & & \
\text { Within } & 240 & & & & \
\text { Total } & & & & & & \
\text { Win }
\end{array}$

Quizplus · Accepted Answer

The Answer is A has 4 levels, so J = 4. B has 3 levels, so K = 3. Each cell has 11 students, so n = 11. N = 4*3*11 = 132.

df_A= J- 1 = 4 - 1 = 3, df_B = K - 1 = 3 - 1 = 2, df_A_B = (J - 1)(K - 1) = 3*2 = 6, df_with = N - JK = 132 - 4*3 = 120, df_total = N - 1 = 132 - 1 = 131.

SS_A = df_A*MS_A = 3*5 = 15, SS_AB = df_AB*MS_AB = 6*25 = 150,
SS_total = SS_A + SS_B + SS_AB + SS_with = 15 + 42 + 150 + 240 = 447.

MS_B = SS_B/df_B = 42/2 = 21; MS_with = SS_with/df_with = 240/120 = 2.

F_A =MS_A/MS_with = 5/2 = 2.5; critical value = _.05F_3,120 = 2.68 > F_A, fail to reject H₀.
F_B =MS_B/MS_with = 21/2 = 10.5; critical value = _.05F₂_,₁₂₀ = 3.07 < F_B, reject H₀.

F_AB =MS_AB/MS_with = 25/2 = 12.5; critical value = _.05F₆_,₁₂₀ = 2.18 < F_AB, reject H₀.

\begin{array}{ccccccc}\hline ext { Source } & S S & d f & M S & F & ext { Critical Value } & ext { Decision } \\hline ext { A } & 15 & 3 & 5 & 2.5 & 05 F_{3,100}=2.68 & ext { Fail to reject } H_{0} \\mathrm{~B} & 42 & 2 & 21 & 10.5 & 05 F_{2120}=3.07 & ext { Reject } H_{0} \\mathrm{AB} & 150 & 6 & 25 & 12.5 & 05 F_{6,100}=2.18 & ext { Reject } H_{0} \ ext { Within } & 240 & 120 & 2 & & & \ ext { Total } & 447 & 131 & & & & \\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 $\alpha$