Complete the following ANOVA summary table for a two-factor model, where there are three levels of factor A (random dosage effect) and four levels of factor B (random physician effect). Each cell of the design includes six patients ($\alpha$ = .05).

$\begin{array}{ccccccc}
\hline \text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \mathrm{A} & 25 & - & - & - & - & - \
\mathrm{B} & - & - & 15 & - & - & - \
\mathrm{AB} & - & - & - & - & - & - \
\text { Within } & - & - & 1 & & & \
\text { Total } & 160 & - & & & & \
\hline
\end{array}$

Question

Complete the following ANOVA summary table for a two-factor model, where there are three levels of factor A (random dosage effect) and four levels of factor B (random physician effect). Each cell of the design includes six patients ($\alpha$ = .05).

$\begin{array}{ccccccc}
\hline \text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \mathrm{A} & 25 & - & - & - & - & - \
\mathrm{B} & - & - & 15 & - & - & - \
\mathrm{AB} & - & - & - & - & - & - \
\text { Within } & - & - & 1 & & & \
\text { Total } & 160 & - & & & & \
\hline
\end{array}$

Quizplus · Accepted Answer

The Answer is There are 3 levels of the fixed factor A, so J = 3.
There are 4 levels of the random factor B, so K = 4.
Each cell has 6 students, so n = 6. N = 3*4*6 = 72.
df_A= J- 1 = 3 - 1 = 2, df_B = K - 1 = 4 - 1 = 3, df_A_B = (J - 1)(K - 1) = 2*3 = 6, df_with = N - JK = 72 - 3*4 = 60, df_total = N - 1 = 72 - 1 = 71.

SS_B = MS_B*df_B = 15*3 = 45; SS_with = MS_with*df_with = 1*60 = 60;
SS_AB = SS_total - SS_A - SS_B - SS_with = 160 - 25 - 45 - 60 = 30.
MS_A = SS_A/df_A = 25/2 = 12.5; MS_AB = SS_AB/df_AB = 30/6 = 5.

F_A = MS_A/MS_AB = 12.5/5 = 2.5; critical value for A = _.0₁F_2,6 = 10.93 > F_A, fail to reject H₀.

F_B = MS_B/MS_AB = 15/5 = 3; critical value for B = _.0₁F_3,6 = 9.78 < F_B, fail to reject H₀.

F_AB = MS_AB/MS_with = 5/1 = 5; critical value for AB= _.0₁F_6,60 = 3.12 < 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 } & 25 & 2 & 12.5 & 2.5 & .01 F_{2,6}=10.93 & ext { fail to reject } H_{0} \\mathrm{~B} & 45 & 3 & 15 & 3 & .01 F_{3,6}=9.78 & ext { fail to reject } H_{0} \\mathrm{AB} & 30 & 6 & 5 & 5 & .01 F_{6.00}=3.12 & ext { reject } H_{0} \ ext { Within } & 60 & 60 & 1 & & & \ ext { Total } & 160 & 71 & & & & \\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 $\alpha$