# Estimation/Analysis of Variance

Estimation/Analysis of Variance

1. The following data are from an experiment comparing three treatment conditions with a separate sample of n = 4 in each treatment.

a. Use an ANOVA with a = .05 to determine whether there are any significant differences among the three treatments.

b. Compute eta2 for these data

Treatment

I II III

2 3 7 N = 12

6 7 5 G = 60

2 6 4 X2 = 344

6 4 8

M = 4 M = 5 M = 6

T = 16 T = 20 T = 24

SS = 16 SS = 10 SS = 10

2. A researcher reports an F-ratio with df - 2,24 for an independent-measures research study:

a. How many treatment conditions were compared in the study?

b. How many subjects participated in the entire study?

3. The following summary table presents the results from an ANOVA comparing three treatment conditions with n = 12 participants in each condition. Complete all missing values.

Source SS Df MS

Between Treatments ? ? 9 F = ?

Within Treatments ? ? ?

Total 117 ?

4. One possible explanation for why some birds migrate and others maintain year round residency in a single location is intelligence. Specially, 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 hypothetical data similar to the actual research results. The numbers represent relative brain size for the individual birds in each sample.

Treatment

Non-Migrating Short-Distance Migrants Long-Distance Migrants

18 6 4 N = 18

13 11 9 G = 180

19 7 5 X2 = 2150

12 9 6

16 8 5

12 13 7

M = 15 M = 9 M = 6

T = 90 T = 54 T = 36

SS = 48 SS = 34 SS = 16

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

b. Compute eta2, the percentage of variance explained by the group differences, for these data.

c. Use the Tukey HSD posttest to determine which groups are significantly different.

#### Solution Summary

Complete, Neat and Step-by-step Solutions are provided in the attached file.