A firm is concerned with variability in hourly output at several factories and shifts. Here are the results of an ANOVA using output per hour as the dependent variable (some information is missing). $$\begin{array} { | l | c | c | c | c | c | }
\hline \text { Source } & \text { Sum of Squares } & d f & \text { Mean Square } & \text { FRatio } & P \text {-value } \
\hline \text { Factory } & 19012.5 & 1 & 19012.5 & 26.427 & 0.000 \
\hline \text { Shift } & 258.333 & 2 & 129.167 & 0.180 & 0.838 \
\hline \text { Factory* Shift } & 80908.333 & 2 & 40454.167 & 56.230 & \
\hline \text { Error } & 8633.333 & 12 & 719.444 & & \
\hline \text { Total } & 108812.5 & 17 & 6400.735 & & \
\hline
\end{array}$$ The p-value for the interaction effect is going to be:
A)very small (near 0).
B)very large (near 1).
C)impossible to know-could be either large or small.

Question

A firm is concerned with variability in hourly output at several factories and shifts. Here are the results of an ANOVA using output per hour as the dependent variable (some information is missing). $$\begin{array} { | l | c | c | c | c | c | } 
\hline \text { Source } & \text { Sum of Squares } & d f & \text { Mean Square } & \text { FRatio } & P \text {-value } \
\hline \text { Factory } & 19012.5 & 1 & 19012.5 & 26.427 & 0.000 \
\hline \text { Shift } & 258.333 & 2 & 129.167 & 0.180 & 0.838 \
\hline \text { Factory* Shift } & 80908.333 & 2 & 40454.167 & 56.230 & \
\hline \text { Error } & 8633.333 & 12 & 719.444 & & \
\hline \text { Total } & 108812.5 & 17 & 6400.735 & & \
\hline
\end{array}$$ The p-value for the interaction effect is going to be:
A)very small (near 0).
B)very large (near 1).
C)impossible to know-could be either large or small.

Quizplus · Accepted Answer

The p-value for the interaction effect is not provided in the table. However, we can infer from the very small p-value (near 0) for the Factory effect and the non-significant p-value (near 1) for the Shift effect that there is a significant difference between the factories, but not between the shifts. This suggests that there may be an interaction effect between the factory and shift variables, which is confirmed by the very high F-ratio and small p-value for the Factory*Shift effect. Therefore, it is likely that the p-value for the interaction effect is very small (near 0), indicating a significant interaction between the factory and shift variables.

A Firm Is Concerned with Variability in Hourly Output at Several