Data Set 13-6: The numbers in the cells are means based on samples of 5 in each cell.
$\begin{array}{c}
\begin{array}{ccc}
&{\text { Experiment X }} \
& \mathrm{B}_{1} & \mathrm{~B}_{2} \
\mathrm{~A}_{1} & 5 & 10 \
\mathrm{~A}_{2} & 10 & 5
\end{array}
\quad\begin{array}{ccc}
& {\text { Experiment } \mathrm{Y}} \
& \mathrm{B}_{1} & \mathrm{~B}_{2} \
\mathrm{~A}_{1} & 5 & 10 \
\mathrm{~A}_{2} & 5 & 10
\end{array}\
\quad\begin{array}{rlr}
{\text { Experiment } \mathrm{Z}} \
& \mathrm{B}_{1} & \mathrm{~B}_{2} \
\mathrm{~A}_{1} & 5 & 5 \
\mathrm{~A}_{2} & 5 & 10
\end{array}
\end{array}$

-The F value for the interaction in Experiment X of Data Set 13-6 would be based on degrees for freedom of _________ and _________ .
A) 1, 19
B) 2, 16
C) 3, 19
D) 1 , 16

Question

Data Set 13-6: The numbers in the cells are means based on samples of 5 in each cell.
 $\begin{array}{c}
\begin{array}{ccc} 
&{\text { Experiment X }} \
& \mathrm{B}_{1} & \mathrm{~B}_{2} \
\mathrm{~A}_{1} & 5 & 10 \
\mathrm{~A}_{2} & 10 & 5
\end{array}
\quad\begin{array}{ccc} 
& {\text { Experiment } \mathrm{Y}} \
& \mathrm{B}_{1} & \mathrm{~B}_{2} \
\mathrm{~A}_{1} & 5 & 10 \
\mathrm{~A}_{2} & 5 & 10
\end{array}\
\quad\begin{array}{rlr}
{\text { Experiment } \mathrm{Z}} \
& \mathrm{B}_{1} & \mathrm{~B}_{2} \
\mathrm{~A}_{1} & 5 & 5 \
\mathrm{~A}_{2} & 5 & 10
\end{array}
\end{array}$

-The F value for the interaction in Experiment X of Data Set 13-6 would be based on degrees for freedom of _________ and _________ .
A) 1, 19
B) 2, 16
C) 3, 19
D) 1 , 16

Quizplus · Accepted Answer

The degrees of freedom for the interaction in a two-way ANOVA are calculated based on the number of levels of each factor minus one, multiplied together for the numerator, and the total number of observations minus the number of conditions for the denominator. In Experiment X, there are 2 levels of A and 2 levels of B, so the degrees of freedom for the interaction (AxB) are (2-1)*(2-1) = 1 for the numerator. There are 4 groups with 5 observations each, totaling 20 observations. The denominator's degrees of freedom are 20 - 4 = 16.

Data Set 13-6: the Numbers in the Cells Are Means