Question

8. Explain the difference between a two- way ANOVA and a three- way ANOVA. A "two-way" ANOVA is used to analyze data from experiments in which there are two independent variables, whereas as "three- way" ANOVA is used to analyze data from experiments in which there are three independent variables (McDonald, 2014). 10. Complete each of the following ANOVA summary tables. Also, answer the following questions for each of the ANOVA summary tables (1)Source df SS MS F A 1 60 B 2 40 AxB 2 90 Error 30 Total 35 390 (2)Source df SS MS F A 2 40 B 3 60 AxB 6 150 Error 72 Total 8 400 (3)Source df SS MS F A 1 10 B 1 60 AxB 1 20 Error 36 Total 39 150

For each table:

a) What is the factorial notation?

b) How many conditions were in the study?

c) How many subjects were in the study?

d) Identify significant main effects and interaction effects?

For the tables could the math be shown as I am a bit confused on that aspect. Thanks!

Answer 1

$1.\\ \begin{matrix} Source &df &SS &MS &F&~Crical~F \\ \hline A& 1 & 60 &60 &9&F_{0.05,1,30}=4.17 \\ B& 2 & 40 &20 &3&F_{0.05,2,30}= 3.32 \\ A\times B & 2 &90 & 45&6.75&F_{0.05,2,30}= 3.32\\ Error &30 & 200&20/3 & \\ \hline Total &35 &390 & & \end{matrix}\\ A,B~are~main~effects~and~A\times B~is~a~interaction~effect.\\ A~has~two~levels~i.e.~2~conditions\\ B~has~3~levels~i.e.~3~conditions.\\ 36~subjects~are~used~for~this~study.\\ Main~effect~A~and~interaction~effect~AB~are~significant~since~(F>Critical~F).\\ Note:~SSE=SST-SSA-SSB-SS(A\times B)=390-60-40-90=200\\ MS=SS/df,~F=MS_{effect}/MSE$

$2.\\ Question~(2)~is~not~correct~since~df~of~A+df~of~B+df~of~A\times B+df~of~error\\ =Total~df\\ but~here,~2+3+6+x>8$

$1.\\ \begin{matrix} Source &df &SS &MS &F&~Crical~F \\ \hline A& 1 & 10 &10 &6&F_{0.05,1,36}=4.11 \\ B& 1 & 60 &60 &36&F_{0.05,1,36}= 4.11 \\ A\times B &1 &20 & 20&12&F_{0.05,1,36}= 4.11\\ Error &36 & 60&10/6 & \\ \hline Total &39 &150 & & \end{matrix}\\ A,B~are~main~effects~and~A\times B~is~a~interaction~effect.\\ A~has~two~levels~i.e.~2~conditions\\ B~has~2~levels~i.e.~2~conditions.\\ 40~subjects~are~used~for~this~study.\\ Main~effects~A,~B~and~interaction~effect~AB~are~significant~since~(F>Critical~F).\\ Note:~SSE=SST-SSA-SSB-SS(A\times B)=150-10-60-20=60\\ MS=SS/df,~F=MS_{effect}/MSE$