Characteristics of students may influence how favorably they're perceived by their teachers. One study examined whether teachers' perceptions of students may be influenced by the student's gender (male, female) and socioeconomic status (SES) (lower class, upper class) (Auwarter \& Aruguete, 2008). They had a sample of teachers read a passage about a troubled student; in these passages, the researchers varied the student's gender and SES. After reading the passage, the teacher rated the student on his or her personal characteristics on a 1 to 5 scale; the higher the rating, the more positively the teacher viewed the student. The researchers hypothesized that male students would be rated more highly if they were of upper rather than lower SES, but the reverse was true for female students.

a. Calculate descriptive statistics \(\left(N_{\mathrm{AB}}, \bar{X}_{\mathrm{AB}}, s_{\mathrm{AB}}\right)\) for each combination of the two factors.

b. Create a figure to represent the cell means.

c. Conduct the two-way ANOVA and create an ANOVA summary table.

d. Report the decisions regarding the null hypotheses and the level of significance for the main effects and the interaction effect.

e. Calculate measures of effect size \(\left(R^{2}\right)\) for the main effects and the interaction effect.

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SES (Factor A): Lower Lower Upper Upper Gender (Factor B): Male Female Male Female 3 4 4 4 4 2 3 2 3 4 st 4 2 2 5 3 4 5 3 3 3 st 2 5 4 5 3 ~ m 2 3