The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. What value for the missing mean would result in NO interaction between A and B? $\quad $$\quad $$\quad $$\quad $$\text {B1 }$$\quad $$\quad $$\quad $$\text {B2 }$
$\begin{array}{c}
\begin{array}{lll}
\text { A1 } \
\
\text {A2 }
\end{array}
\begin{array}{ | l | l| }
\hline \
40\quad \quad&60\quad\quad \
\
20 & 40 \
\hline
\end{array}
\end{array}$

A) 0
B) 10
C) 20
D) 40

Question

The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. What value for the missing mean would result in NO interaction between A and B? $\quad $$\quad $$\quad $$\quad $$\text {B1 }$$\quad $$\quad $$\quad $$\text {B2 }$
$\begin{array}{c}
\begin{array}{lll}
\text { A1 } \
\
\text {A2 } 
\end{array}
\begin{array}{  | l | l| } 
\hline \
40\quad \quad&60\quad\quad \
\
20 & 40 \
\hline
\end{array}
\end{array}$

A) 0
B) 10
C) 20
D) 40

Quizplus · Accepted Answer

For there to be no interaction between factors A and B, the effects of A at each level of B must be consistent. The difference between A1 and A2 under B1 is 20 (40 - 20 = 20). To have no interaction, the difference under B2 should also be 20. Since A2 under B2 is 40, subtracting 20 gives us 20. However, since 20 is already the value for A2 under B2, to maintain no interaction, the missing value for A1 under B2 must maintain the pattern of differences seen in B1. Thus, the difference between A1 and A2 under B2 should also be 20, making A1 under B2 equal to 60 (40 + 20 = 60), not 20. This maintains the pattern of interaction (or lack thereof) across both levels of B, indicating a consistent effect of A across levels of B.

The Following Data Represent the Means for Each Treatment Condition \quad

The Following Data Represent the Means for Each Treatment Condition $\quad$