12.38 Grade-point average, fraternities, sororities, and two-way between-groups ANOVA: A sample of students from our statistics classes reported their grade-point averages (GPAs), indicated their genders, and stated whether they were in the university’s Greek system (i.e., in a fraternity or sorority). Following are the GPAs for the different groups of students: Men in a fraternity: 2.6, 2.4, 2.9, 3.0 Men not in a fraternity: 3.0, 2.9, 3.4, 3.7, 3.0 Women in a sorority: 3.1, 3.0, 3.2, 2.9 Women not in a sorority: 3.4, 3.0, 3.1, 3.1

a. What are the independent variables and their levels? What is the dependent variable?

b. Create a table that lists the cells of the study design. Include the cell means.

c. Conduct all six steps of hypothesis testing.

d. Draw a bar graph for all statistically significant effects.

e. Is there a significant interaction? If yes, describe it in words and indicate whether it is a qualitative or a quantitative interaction. Explain.

f. Compute the effect sizes, R2 , for the main effects and interaction. Using Cohen’s conventions, interpret the effectsize values.