Hooded rats: social play times. In Exercise 29.12 you carried out two-way ANOVA for a study of the effect of social isolation on hooded rats. The response variable is the time (in seconds) that a rat devoted to social play during an observation period. Start your work in this exercise with your two-way ANOVA table from Exercise 29.12.

(a) Explain how the sums of squares from the two-way ANOVA table can be combined to obtain the one-way ANOVA sum of squares for the 4 groups (SSG). What is the value of SSG?

(b) Give the degrees of freedom, mean square (MSG), and F statistic for testing for the effect of groups.

(c) Is there a significant effect of group on the amount of time in play? Give and interpret the P-value in the context of this experiment.

(d) Use software to carry out one-way ANOVA of time on group. Verify that your results in parts (b), (c), and (d) agree with the software output.

Exercise 29.12:

Hooded rats: social play times. How does social isolation during a critical developmental period affect the behavior of hooded rats? Psychology students assigned 24 young female rats at random to either isolated or group housing, then similarly assigned 24 young male rats. This is a randomized block design with the gender of the 48 rats as the blocking variable and housing type as the treatment. Later, the students observed the rats at play in a group setting and recorded data on three types of behavior (object play, locomotor play, and social play).8 The data file records the time (in seconds) that each rat devoted to social play during the observation period.

(a) Make a plot of the 4 group means. Is there a large interaction between gender and housing type? Which main effect appears to be more important?

(b) Verify that the conditions for ANOVA inference are satisfied.

(c) Give the complete two-way ANOVA table. What are the F statistics and P-values for interaction and the two main effects? Explain why the test results confirm the tentative conclusions you drew from the plot of means.