Does the environment affect bird weight? Researchers measured the weight (in grams) of male and female adult finches that were either raised in an aviary or caught in the wild. This observational study does not have a balanced design, particularly because finches caught in the wild were more difficult to obtain. A total of 52 finches were studied. A partial ANOVA table is provided below, along with an interaction plot displaying the group means.

$$\begin{array}{l}
\begin{array} { l r r r }
\text { Factor } & \text { Type } & \text { Levels } & \text { Values } \
\text { malefemale } & \text { fixed } & 2 & f , m \
\text { origin } & \text { fixed } & 2 & \text { aviary, wild }
\end{array}\
\
\text { Analysis of Variance for bird weight }\
\
\begin{array} { l r r r r r }
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\text { Malefemale } & 1 & 10.844 & 10.844 & & \
\text { origin } & 1 & 19.607 & 19.607 & & \
\text { interaction } & 1 & 0.340 & 0.340 & & \
\text { Error } & 48 & 125.140 & 2.607 & &
\end{array}
\end{array}$$ S = 1.61465 R-Sq = 23.88% R-Sq(adj) = 19.12%
What is the F statistic for the main effect due to the birds' sex?

Question

Does the environment affect bird weight? Researchers measured the weight (in grams) of male and female adult finches that were either raised in an aviary or caught in the wild. This observational study does not have a balanced design, particularly because finches caught in the wild were more difficult to obtain. A total of 52 finches were studied. A partial ANOVA table is provided below, along with an interaction plot displaying the group means.
​
$$\begin{array}{l}
\begin{array} { l r r r } 
\text { Factor } & \text { Type } & \text { Levels } & \text { Values } \
\text { malefemale } & \text { fixed } & 2 & f , m \
\text { origin } & \text { fixed } & 2 & \text { aviary, wild }
\end{array}\
\
\text { Analysis of Variance for bird weight }\
\
\begin{array} { l r r r r r } 
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\text { Malefemale } & 1 & 10.844 & 10.844 & & \
\text { origin } & 1 & 19.607 & 19.607 & & \
\text { interaction } & 1 & 0.340 & 0.340 & & \
\text { Error } & 48 & 125.140 & 2.607 & &
\end{array}
\end{array}$$ S = 1.61465 R-Sq = 23.88% R-Sq(adj) = 19.12%
 What is the F statistic for the main effect due to the birds' sex?

Quizplus · Accepted Answer

The F statistic for the main effect due to the birds' sex is the MS for Malefemale divided by the MS error, which is 10.844/2.607 = 4.2. This indicates that there is a significant difference in weight between male and female finches. However, it is important to note that this main effect does not account for the influence of the birds' origin or any interaction between sex and origin on weight.

Does the Environment Affect Bird Weight? Researchers Measured the Weight