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Tail-Feather Length in Birds Is Sometimes a Sexually Dimorphic Trait

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Tail-feather length in birds is sometimes a sexually dimorphic trait. That is, the trait differs substantially for males and for females. Researchers measured tail-feather length (the R1 central tail feather, in mm) in male and female long-tailed finches 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.

 Factor  Type  Levels  Values  Malefemale  fixed 2 f, m Origin  fixed 2 aviary, wild \begin{array}{lrrr}\text { Factor } & \text { Type } & \text { Levels } & \text { Values } \\\text { Malefemale } & \text { fixed } & 2 & \text { f, } m \\\text { Origin } & \text { fixed } & 2 & \text { aviary, wild }\end{array}

 Analysis of Variance for feather length  Source  DF  SS  MS  F  P  malefemale 12015.52015.5 origin 1251.7251.7 interaction 115.615.6 Error 484076.984.9\begin{array}{l}\text { Analysis of Variance for feather length }\\\\\begin{array}{lrrrrr}\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\\text { malefemale } & 1 & 2015.5 & 2015.5 & & \\\text { origin } & 1 & 251.7 & 251.7 & & \\\text { interaction } & 1 & 15.6 & 15.6 & & \\\text { Error } & 48 & 4076.9 & 84.9 & &\end{array}\end{array}

S = 9.21600 R-Sq = 47.32% R-Sq(adj) = 44.03%
 Tail-feather length in birds is sometimes a sexually dimorphic trait. That is, the trait differs substantially for males and for females. Researchers measured tail-feather length (the R1 central tail feather, in mm)  in male and female long-tailed finches 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}{lrrr} \text { Factor } & \text { Type } & \text { Levels } & \text { Values } \\ \text { Malefemale } & \text { fixed } & 2 & \text { f, } m \\ \text { Origin } & \text { fixed } & 2 & \text { aviary, wild } \end{array}    \begin{array}{l} \text { Analysis of Variance for feather length }\\ \\ \begin{array}{lrrrrr} \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\ \text { malefemale } & 1 & 2015.5 & 2015.5 & & \\ \text { origin } & 1 & 251.7 & 251.7 & & \\ \text { interaction } & 1 & 15.6 & 15.6 & & \\ \text { Error } & 48 & 4076.9 & 84.9 & & \end{array} \end{array}    S = 9.21600 R-Sq = 47.32% R-Sq(adj)  = 44.03%   What is the F statistic for the main effect due to the birds' origin? A) 84.9 B) 23.7 C) 3.0 D) 0.2 What is the F statistic for the main effect due to the birds' origin?


A) 84.9
B) 23.7
C) 3.0
D) 0.2

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