4. Explain why you should use ANOVA instead of several t- test to evaluate mean difference when an experiment consist of three or more conditions.
12. The following data were obtained in a study using three separate samples to compare three different treatments.
I II III
4 3 8 N = 12
3 1 4 G = 48
5 3 6 ∑Χ2 = 238
4 1 6
M = 4 M = 2 M = 6
T = 16 T = 8 T = 24
SS 2 SS = 4 SS = 8
a. Use an analysis of variance with α = .05 to determine whether there are significant difference among the treatments.
b. Compute the value for η2 for these data.
14. A researcher reports an F-ratio with df = 2, 24 for an independent –measures researcher study.
a. How many treatments conditions were compared in the study?
b. How many subjects participated in the entire study?
22. A developmental psychologist is examining the development of language skills from age 2 to age 5. Four different groups of children are obtained, one for each age with n = 15 children in each group. Each child is given a language skills assessments test. The resulting data were analyzed with an ANOVA to test to test for mean differences between age groups. The results of the ANOVA are presented in the following table. Fill in all missing values.
26. One possible explanation for why some birds migrate and others maintain year round residency in a singe 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, & Rodriquez- 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 actual research results. The numbers represent relative brain size for the individual birds in each sample.
Non- Short Long
Migrating Distance Distance
18 6 4 N = 18
13 11 9 G = 180
19 7 5 ∑Χ2 = 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 AVOVA with α =.05 to determine whether there are any significant mean differences among three groups of birds.
b. Compute η2, the percentage of variance explained by the group difference, for these data.
c. Use the turkey HSD posttest to determine which groups are significant different.