During the 1980s, findings from the National Assessment of Educational Progress have shown that the size of average achievement differences between White and Black students has been steadily decreasing. In Jones, L. V. (1984). White-black achievement differences: The narrowing gap. American Psychologist, 39, 1207-1213, national data are reported suggesting that some of the existing difference between Blacks’ and Whites’ average mathematics achievement test scores may be due to differences in enrollment patterns in high school math courses. The following hypothetical data are modeled after the data reported by Jones (1984). Suppose that a group of high school seniors who have taken zero, one, two, or three high school math courses have received the following scores on a standardized math achievement test: a. Find the mean achievement test score for all Black students, irrespective of number of courses. Find the comparable mean for White students. How large is the difference between the means? b. Find the unweighted marginal mean for Black students in the two-way design. Find the comparable mean for White students. How large is the difference between the means? c. Why is the difference in part b much smaller than the difference in part a? d. Test the significance of the race main effect allowing for a “number-of-courses” main effect and a “number of courses” by race interaction.
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