Research: Science & Education
Mathematical SAT Test Scores and College Chemistry Grades Harry E. Spencer Department of Chemistry, Oberlin College, Oberlin, OH 44074
Successful students of college-level general chemistry need certain mathematical skills, and several authors have attempted to predict general-chemistry grades earned in college by considering the correlations between those grades and student performance on standardized mathematics tests such as the mathematical SAT test,1 abbreviated here as SAT-M (1–9). The results of those studies indicate that students with high mathematical scores tend to achieve high chemistry grades, but the broad distribution of grades corresponding to any particular SAT-M score precludes reliable prediction of a grade based on that score alone. Nevertheless, mathematical scores have been used for some predictive purposes. Andrews and Andrews (4), for example, concluded that a high SAT-M score does not guarantee a good grade, but a low score is a strong indicator of a low grade, particularly if the SAT-M score is very low. Scarcely considered in these studies are the comparative performances of various segments of the student samples relative to their SAT-M scores. Do experienced college students achieve higher grades than firstyear ones? Do minority or female students perform better or worse than their majority or male colleagues with similar SAT-M scores? Are chemistry majors distinguishable from nonmajors? Characterization of relative performances of various subsets of students, the major focus of this study, required a different statistical approach. The question answered statistically is whether the relationship between SAT-M scores and grades for certain subsets of students is the same as that for the entire sample. Two samples are considered, each consisting of all students with SATM scores enrolled in one semester of a two-semester sequence of general chemistry. The data represent eight successive academic years. The various subsets of students considered are males, females, students who eventually majored in chemistry or biochemistry, first-year students, non-first-year students, Asians,2 Blacks,2 and Latinos.2 Of course, each student is a member of two or more of these groups, but if subsets are compared to each other, only disjoint subsets are considered. Determining whether a distribution of grades earned by members of a subset differs significantly from that for the entire sample can be handled by standard statistical methods, provided the expected distribution of grades can be determined. Here I have calculated this expected distribution of grades in the following way. For each group of students whose SAT-M scores lie within a given range of values, a certain percentage will earn a grade of A+, another percentage will earn A, a third percentage will earn B+, etc. I determine these percentages for the entire sample, then use them to calculate the expected grades for the various subsets of students. As an example of a calculation of expected grades, consider a hypothetical subset of 100 students, 60 with SAT-M scores within the range of 610–650 and 40 in the range of 560–600. Suppose that in the entire sample, 10%
1150
of the students with SAT-M scores in the 610–650 range earned a grade of A– and 15% a grade of B+, and that 5% of the students within the 560–600 range of SAT-M scores earned an A– and 7.5% earned a B+ grade. The 60 students in the 610–650 range of SAT-M scores would be expected, therefore, to earn 6 A– and 9 B+ grades, whereas the 40 students within the 560–600 range of SAT-M scores would be expected to earn 2 A– and 3 B+ grades. Thus the expected grades for the 100 students would be 8 A– and 12 B+ grades. I use the standard χ2 -test to determine the probability that chance alone could account for the difference between an expected distribution and the actual distribution of grades. The symbol used here for this probability is P, expressed as a percentage. If P = 5% or less, statisticians traditionally have termed the difference as statistically significant (10). Sample Information The general chemistry sequence at Oberlin College covers two semesters, the courses being designated Chemistry 101 and 102. The first course, Chemistry 101, is more qualitative than Chemistry 102, and a grade of C– or higher in Chemistry 101 is a prerequisite for registration in Chemistry 102. In both semesters students attend three 50-minute lectures and one 3-hour laboratory weekly. During the eight years surveyed, students used locally written notes in both semesters, accompanied by a standard general chemistry text for part of Chemistry 102 and during the last three years for part of Chemistry 101. Brief statements needed frequently on examinations and lab reports as explanations of answers and results constitute the only writing required. One of 10 grades (A+, A, A–, B+, B, B–, C+, C, C–, and NE) was assigned on the basis of examination grades and laboratory performance. The NE designation stands for No Entry, meaning unsatisfactory performance but with no permanent entry on the student’s official transcript. Before assigning grades, the faculty members had no knowledge of the students’ SAT-M scores. Two samples of students are analyzed. The first sample consists of 1160 students who studied Chemistry 101 during the fall semesters of the years 1987 through 1994; the second consists of 849 of those students who continued on in Chemistry 102 during the spring semesters of 1988 through 1995. A few students are not included because no SAT-M scores were available. SAT-M scores are divided into seven ranges, whereas grades are either reported individually or in groups. Because only a few students earned a grade of A+, I have combined the numbers of A+ and A grades into one grouping with a label of A. I have grouped the SAT-M scores into ranges of
