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Analysis of Variance comparing brains

One possible explanation for why some birds migrate and others maintain year round residency in a single location is intelligence. Specifically, birds with small brains relative to their body size are simply not smart enough to find food during the winter and must migrate to warmer climates where food is easily available (Sol, Lefebvre, & Rodriguez-Teijeiro, 2005).

Birds with bigger brains, on the other hand, are more creative and can find food even when the weather turns harsh. Following are hypothesis data similar to the actual research results. The numbers represent relative brain size for the individual birds in each sample.

Non-Migrating
18, 13, 19, 12, 16, 12

N= 8
Short-Distance Migrants G=180

6, 11, 7, 9, 8, 13 â?'x2 = 2150

Long-Distance Migrants

4, 9,5, 6, 5, 7

M = 15 M = 9 M = 6
T = 90 T = 54 T = 36
SS= 48 SS= 34 SS= 16

a. Use an ANOVA with ? = .05 to determine whether there are any significant mean differences among the three groups of birds.

b. Compute ?2 , the percentage of variance explained by the group differences, for these data.

c. Use the Tukey HSD post-test to determine which groups are significantly different.

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