Institutional Research and Planning Room 306 1871 Old Main Drive Shippensburg, PA 17257 Phone: (717)-477-1154 Fax: (717)-477-4077 irp@ship.edu

High School GPA to Centile Conversion High schools are using a variety of strategies to ensure the competitiveness of the their students when they apply to college. Some high schools are no longer reporting class rank and class size information, others do not provide grade point averages, while still others, provide even less comparable data. This impacts Shippensburg University by adding to the complexity of fairly comparing students in the admission decision process. SU employs Centile and SAT score among other things to gauge the quality of the freshmen class and individual applicants. This study determines the most error free method of converting high school grade point average to Centile when class rankings are not provided. A prior study compared four strategies in terms of the prediction of decile based on HS GPA. Two strategies were based on curve fitting procedures, another utilized a discriminant analysis, and the final strategy involved a one-way analysis of variance (ANOVA) to examine differences in HSGPA among decile groups. Results showed that the first four deciles had distinct HSGPA distributions. Below the fifth decile, however, the HS GPA distributions had considerable overlap. Because of this overlap, the four methods produced very different predictions. When all ten deciles were compared, the quadratic and linear methods produced the least error. Both the discriminant function and confidence interval method produced moderate error. When only the first five deciles were compared, the confidence interval method produced the least error (by a considerable amount). While all methods tended to underestimate the actual decile ranks, the confidence interval method provided the best estimation. This study resulted in a conversion matrix that has been used by the admissions office for the past four years. The office asked that Institutional Research and Planning update the matrix. Data were compiled for the analysis by extracting applicants from the 976 and 986 admission records. To ensure accurate prediction, it was important to have all ranges of Centile represented. Twenty-five applicants from each of the ten Centile ranges (deciles) were included from each of the two years. That produced a sample of 500 applicants with 50 in each decile. The name and student IDs were give to admissions who extracted HSGPAs from the students' records. A master data file was produced that included Centile, HSGPA, and other relevant data. The first step was to again compare the errors associated with the variety of conversion methods. The results were consistent with prior analyses with the interval method producing lower overall error across deciles than the linear, quadratic, or discriminant functions. A new method was considered for this study. It was possible to develop a categorical variable comprised of 13 HSGPA intervals. Linear regressions were used to produce prediction equations for each of the 13 intervals. Using these separate equations, the cumulative error between the predicted Centile and the actual Centile was computed. These error rates were very low in all Centile ranges and, in total, were much lower than any of the prior methods. It was decided that this interval linear prediction method would be used to build a new conversion matrix. It may be useful to review the SPSS syntax used for these analyses. One problem still existed. The maximum and minimum predicted values at the ends of the intervals would overlap producing inconsistent results. One solution was to reduce the number of intervals from 13 to 6, thus reducing the number of overlap regions from 12 to 5. To solve the problem of these five overlap regions, the maximum and minimum values for each interval were analyzed. In order to align the intervals, the coefficients and constants of the regression functions were adjusted. The equations were entered into the final matrix based on each interval (see Appendix B). It was found that only one overlap existed; the predicted Centile for a HSGPA of 2.20 was 0.72 while the predicted Centiles for HSGPAs of 2.21 and 2.19 were both 0.71. The Centile for HSGPA of 2.20 was adjusted to 0.71. The final conversion matrix was forwarded to the Admissions Office to be put into service.