Complete the following ANOVA summary table for a two-factor model, where there are two levels of factor A (fixed program effect) and five levels of factor B (random school effect). Each cell of the design includes seven students ($\alpha$ = .05).

$\begin{array}{ccccccc}
\hline \text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \mathrm{A} & 100 & - & - & - & - & - \
\mathrm{B} & 210 & - & - & - & - & - \
\mathrm{AB} & - & - & 20 & - & - & - \
\text { Within } & - & - & - & & & \
\text { Total } & 690 & - & & & & \
\hline
\end{array}$

Question

Complete the following ANOVA summary table for a two-factor model, where there are two levels of factor A (fixed program effect) and five levels of factor B (random school effect). Each cell of the design includes seven students ($\alpha$ = .05).

$\begin{array}{ccccccc}
\hline \text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \mathrm{A} & 100 & - & - & - & - & - \
\mathrm{B} & 210 & - & - & - & - & - \
\mathrm{AB} & - & - & 20 & - & - & - \
\text { Within } & - & - & - & & & \
\text { Total } & 690 & - & & & & \
\hline
\end{array}$

Quizplus · Accepted Answer

The Answer is There are 2 levels of the fixed factor A, so J = 2.
There are 5 levels of the random factor B, so K = 5.
Each cell has 7 students, so n = 7. N = 2*5*7 = 70.

df_A= J- 1 = 2 - 1 = 1, df_B = K - 1 = 5 - 1 = 4, df_A_B = (J -1)(K- 1) = 1*4 = 4, df_with = N - JK = 70 - 2*5 = 60, df_total = N - 1 = 70 - 1 = 69.

SS_AB = MS_AB*df_A_B = 20*4 = 80;
SS_with = SS_total - SS_A - SS_B - SS_AB = 690 100 210 80 = 300.

MS_A = SS_A/df_A = 100/1 = 100; MS_B = SS_B/df_B = 210/4 = 52.5;
MS_with = SS_with/df_with = 300/60 = 5.

F_A = MS_A/MS_AB = 100/20 = 5; critical value for A = _.0₅F_1,4 = 7.71 > F_A, fail to reject H₀.

F_B = MS_B/MS_with = 52.5/5 = 10.5; critical value for B = _.0₅F_4,60 = 2.53 < F_B, reject H₀.

F_AB = MS_AB/MS_with = 20/5 = 4; critical value for AB = _.0₅F_4,60 = 2.53 < 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 } & 100 & 1 & 100 & 5 & 05 F_{1,4}=7.71 & ext { fail to reject } H_{0} \\mathrm{~B} & 210 & 4 & 52.5 & 10.5 & 05 F_{4,00}=2.53 & ext { reject } H_{0} \\mathrm{AB} & 80 & 4 & 20 & 4 & 05 F_{4, \infty 0}=2.53 & ext { reject } H_{0} \ ext { Within } & 300 & 60 & 5 & & & \ ext { Total } & 690 & 69 & & & & \\hline\end{array}

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

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