ࡱ> #` `bbjbjmm 0Y>Hvavava8aLa8opbb" c c c c c cnnnnnnn$phsrn /e c cMeae n c cnkkkme c cnk/enkkk cb p5vvaShkko08oks1jsksf$k( chtcJkc<c5 c c cnnIkj c c c8o/e/e/e/e-r5,r5 Here is an example of a well-written major project for PSYC 6431 (which is now PSYC 7431). This paper was prepared by Phillip Braddy in the Spring of 2002 and is posted here with his permission.  Abstract The current study employed a multiple regression analysis to develop a model that best predicts college grade point average. The variables in this model included high school GPA, SAT verbal scores, and SAT quantitative scores. That data analyzed for this study were simulated using SAS. The results indicated that all predictor variables were significantly correlated with college GPA. However, high school GPA accounted for a large proportion of the variance in the criterion measure.  Predicting College Grade Point Average from A Combination of High School Grade Point Average, SAT Verbal Scores, and SAT Mathematical Scores How should colleges and universities determine which applicants to admit? Should they use high school GPA, SAT Scores, or some combination of these two predictor variables? Should colleges and universities develop new criteria for selecting applicants? The previous questions have repeatedly been asked by many individuals, including students, parents, professors, administrators, and numerous others. Unfortunately, there may not be any clear-cut answers, but, in an attempt to address these questions, a review of the literature on college admissions is necessary. A plethora of research studies have attempted to answer the questions posed in the previous paragraph. Specifically, many studies have been conducted to ascertain if high school GPA and SAT scores are valid predictors of success in college. For example, Chissom and Lanier (1975) examined the relationship among SAT scores (both verbal and math), high school grade point average, and college grade point average. For this study, data were collected on three predictor variables and the criterion variable from 669 college students. The results from this study indicated that college grade point average was significantly predicted from all predictor variables (R = 57). Additionally, the results indicated that the criterion variable was best predicted from high school grade point average (r = .46), then by SAT Math (r = .39) and finally by SAT Verbal (r = .37). Similarly, Larson and Scontrino (1976) examined the relationship among high school grade point average, SAT scores (verbal and quantitative), and college success for the duration of eight years. The researchers determined that, each year, all predictor variables were significantly correlated with the college GPA. Similar to the previous study, the results from this study indicated that high school GPA had the highest correlation with the criterion variable. Additionally, the results indicated that SAT math and verbal scores were significantly correlated with the criterion, even though adding these variables only explained an additional 4.7% of the variance. As indicated previously, various criteria (e.g., SAT scores and GPA) have been investigated in an attempt to ascertain if, in general, these are good predictors of success. Additionally, these criteria have been examined to determine if they are equally predictive for both black and white students. For example, Lawlor, Richman, and Richman (1997) examined the relationship among six predictor variables and college GPA. Participants in this study were black and white students from Wake Forest University. The results from this study indicated that high school GPA was a valid predictor of college GPA for both blacks and whites. On the other hand, however, SAT scores did not correlate equally well with college GPA. In fact, for white students, the correlation coefficient was .61, whereas the correlation coefficient for black students was .33. Consequently, as pointed out by Lawlor et al. (1997), a disproportionate advantage would be given to white relative to black students (p. 509 510). In short, based on the review of the literature, it seems that high school GPA is unquestionably the single best predictor of college performance. However, it appears that SAT scores tend not to improve ones model for predicting college GPA by much, even though they have a statistically significant relationship with college performance. Consequently, the purpose of the current study was to examine the relationship among high school GPA, SAT scores, and college GPA in an attempt to provide more support for the contention that high school GPA is the single best predictor of success, whereas SAT scores may not be contributing adequately. Hypotheses H1: High school GPA should be the best predictor of freshman GPA. H2: SAT Math should be the second best predictor of freshman GPA. Method The current study employed a multiple regression analysis to predict college grade point average from a linear combination of three variables (high school GPA, SATV, and SATQ). The data that were analyzed for this study were simulated using SAS. The process began by writing a SAS program (see Appendix A) that included data obtained from a correlation matrix, which was retrieved from a study in the published literature (Chissom & Lanier, 1975). A sequential procedure was then used to determine what weights to use in the simulation program. College GPA was predicted from high school GPA, SAT Verbal, and SAT Math, high school GPA was predicted from SAT Math and Verbal, and, finally, SAT Math was predicted from SAT Verbal. From the output obtained from the previous program, slopes, intercepts, and standard errors of estimate were then used to actually simulate the data on the basis of the sequential model (see Appendix B). The ROUND function was used to round the data for the following variables: SAT Verbal and SAT Math. The data obtained from the simulation were then entered into a word document to create a data file. Finally, Microsoft Access was used to assign identification numbers, and then a program for multiple regression analysis was written to analyze the data in an attempt to ascertain which variables were better predictors of college GPA (see Appendix C and D). Results A multiple regression analysis was employed to develop a model for predicting college grade point average from SAT scores (both verbal and quantitative) and from high school grade point average. Basic descriptive statistics and regression coefficients are provided in Table 1. Each of the predictor variables had a significant (p < .001) zero-order correlation with college grade point average. The three predictor model accounted for 30.5% of the variance in college grade point average, F(3, 640) = 93.65, p < .001. Table 1 College Grade Point Averages Related to Criteria Used When Making Admission Decisions (N = 644)Zero-Order r(sr2bVariableCGPASAT_VSAT_MHSGPASAT_V.341*.161*.020.001SAT_M.373*.479*.248*.047.002HSGPA.428*.166*.131*.368*.131.539 Intercept = -.952*Mean2.29424.33457.262.70SD.7774.7881.73.52R2 = .305**p < .05 Discussion The current study employed a multiple regression analysis to develop a model that would best predict college grade point average. The results from this analysis indicated that the model accounted for 30.5 percent of the variance in college GPA and that all three predictor variables were significantly correlated with the criterion measure. Of the three predictor variables, however, high school grade point average was the best predictor variable, explaining approximately 13 percent of the variance which could not be accounted for by the other two predictor variables. It is important to note that these results are congruent with other studies. For example, Chissom and Lanier (1975) also found that high school GPA was the best predictor of college GPA. In fact, their study indicated that high school GPA accounted for 20 percent of the variance in the dependent measure. The current study also revealed that SAT scores were significant predictors of the criterion measure, even though these variables only explained an additional 6.7 percent of the variance which was not explained by high school GPA. Once again, these results were congruent with previous findings. For example, Larson and Scontrino (1976) found that SAT scores, both verbal and quantitative, were significant predictors of college GPA. However, they also reported that the mean proportion of variance accounted for in the eight combined samples by using all three predictor variables in combination was only 4.7% greater than the mean proportion of variance accounted for by the high school GPA as a single predictor (p. 441). Given the results from this study and previous studies, it is apparent that SAT scores do not contribute much in terms of explaining overall variance in college GPA. Thus, as illustrated in a review of the literature by Mouw and Khanna (1993), many universities and colleges will inadvertently have many false positives and negatives when making admission decisions, primarily because of the heavy emphasis on SAT scores. In an attempt to reduce these errors, it may be important in the future to decrease reliance on such criteria and perhaps focus more attention on finding criteria that have more predictive validity.  References Chissom, Brad S., & Lanier, Doris (1975). Prediction of the first quarter freshman GPA using SAT scores and high school grades. Educational and Psychological Measurement, 35, 461-463. Larson, James R., & Scontrino, Peter M. (1976). The consistency of high school grade point average and of the verbal and mathematical portions of the scholastic aptitude test of the college entrance. Educational and Psychological Measurement, 39, 439-443. Lawlor, Sarah, Richman, Susan, & Richman, Charles L. (1997). The validity of using the SAT as a criterion for black and white students admission to college. College-Student-Journal, 31, 507-515. Mouw, John T., & Khanna, Ritu K. (1993). Prediction of academic success: a review of the literature and recommendations. College-Student-Journal, 27, 328-336.  Appendix A Obtaining Simulation Parameters From Input Corr Matrix options pageno=min nodate formdlim='-'; Data Braddy(TYPE=CORR); LENGTH _NAME_$ 5; INPUT _TYPE_ $ _Name_ $ SAT_V SAT_M HSGPA CGPA; cards; CORR SAT_V 1.00 .49 .21 .37 CORR SAT_M .49 1.00 .17 .39 CORR HSGPA .21 .17 1.00 .46 CORR CGPA .37 .39 .46 1.00 MEAN . 421.55 458.01 2.81 2.35 STD . 76.05 82.78 .55 .80 PROC REG; A: MODEL CGPA = SAT_V SAT_M HSGPA; B: MODEL HSGPA = SAT_V SAT_M; C: MODEL SAT_M = SAT_V; run; The SAS System 1 The REG Procedure Model: A Dependent Variable: CGPA Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 2134.77783 711.59261 1667.94 <.0001 Error 9996 4264.58217 0.42663 Corrected Total 9999 6399.36000 Root MSE 0.65317 R-Square 0.3336 Dependent Mean 2.35000 Adj R-Sq 0.3334 Coeff Var 27.79440 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 -1.04228 0.04912 -21.22 <.0001 SAT_V 1 0.00180 0.00009962 18.12 <.0001 SAT_M 1 0.00233 0.00009080 25.63 <.0001 HSGPA 1 0.55714 0.01219 45.72 <.0001 ------------------------------------------------------------------------------------------------- The SAS System 2 The REG Procedure Model: B Dependent Variable: HSGPA Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 151.31050 75.65525 263.22 <.0001 Error 9997 2873.38700 0.28742 Corrected Total 9999 3024.69750 Root MSE 0.53612 R-Square 0.0500 Dependent Mean 2.81000 Adj R-Sq 0.0498 Coeff Var 19.07901 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 2.03298 0.03482 58.39 <.0001 SAT_V 1 0.00121 0.00008087 14.91 <.0001 SAT_M 1 0.00058668 0.00007430 7.90 <.0001 ------------------------------------------------------------------------------------------------- The SAS System 3 The REG Procedure Model: C Dependent Variable: SAT_M Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 16451275 16451275 3158.99 <.0001 Error 9998 52067156 5207.75716 Corrected Total 9999 68518431 Root MSE 72.16479 R-Square 0.2401 Dependent Mean 458.01000 Adj R-Sq 0.2400 Coeff Var 15.75616 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 233.17114 4.06491 57.36 <.0001 SAT_V 1 0.53336 0.00949 5  Appendix B Data Simulation Program options pageno=min nodate formdlim='-'; Data Phillip; do s=1 to 669; SAT_V=round(421.55 + 76.05*normal(0)); SAT_M=round(233.17 + .53*SAT_V+72.16*normal (0)); HSGPA=(2.03 + .001*SAT_V+.0006*SAT_M+.54*normal (0)); CGPA=(-1.042 + .0018*SAT_V+.0023*SAT_M+.557*HSGPA+.653*normal (0)); OUTPUT; FILE 'A:\Timbibo.dat'; PUT SAT_V--CGPA; END; Proc Reg corr; model CGPA = SAT_V SAT_M HSGPA / stb scorr2 tol; run;  Appendix C Multiple Regression Program options pageno=min nodate formdlim='-'; title 'Multiple Regression Analysis'; run; data psyc; infile 'A:\Timbibo.dat'; input SAT_V SAT_M HSGPA CGPA; Proc Corr; Proc Reg; Model CGPA = SAT_V SAT_M HSGPA / scorr2 pcorr2 tol stb; run;  Appendix D Multiple Regression Output The CORR Procedure 4 Variables: SAT_V SAT_M HSGPA CGPA Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum SAT_V 644 424.33075 74.78322 273269 221.00000 702.00000 SAT_M 644 457.26398 81.73444 294478 236.00000 709.00000 HSGPA 644 2.70437 0.52830 1742 0.96795 4.44588 CGPA 644 2.28541 0.77311 1472 0 4.44008 Pearson Correlation Coefficients, N = 644 Prob > |r| under H0: Rho=0 SAT_V SAT_M HSGPA CGPA SAT_V 1.00000 0.47872 0.16631 0.34104 <.0001 <.0001 <.0001 SAT_M 0.47872 1.00000 0.13058 0.37335 <.0001 0.0009 <.0001 HSGPA 0.16631 0.13058 1.00000 0.42755 <.0001 0.0009 <.0001 CGPA 0.34104 0.37335 0.42755 1.00000 <.0001 <.0001 <.0001 ------------------------------------------------------------------------------------------------- Multiple Regression Analysis 2 The REG Procedure Model: MODEL1 Dependent Variable: CGPA Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 117.23776 39.07925 93.65 <.0001 Error 640 267.08007 0.41731 Corrected Total 643 384.31784 Root MSE 0.64600 R-Square 0.3051 Dependent Mean 2.28541 Adj R-Sq 0.3018 Coeff Var 28.26618 Parameter Estimates Squared Parameter Standard Standardized Semi-partial Variable DF Estimate Error t Value Pr > |t| Estimate Corr Type II Intercept 1 -0.95200 0.19788 -4.81 <.0001 0 . SAT_V 1 0.00166 0.00039080 4.26 <.0001 0.16096 0.01969 SAT_M 1 0.00235 0.00035563 6.60 <.0001 0.24820 0.04732 HSGPA 1 0.53906 0.04899 11.00 <.0001 0.36837 0.13148 Parameter Estimates Squared Partial Variable DF Corr Type II Tolerance Intercept 1 . . SAT_V 1 0.02755 0.75986 SAT_M 1 0.06375 0.76815 HSGPA 1 0.15910 0.96897     PAGE  PAGE 1 Predicting College Grades  Phillip should also have described the procedure which would be used if he had actually gathered the data rather than simulated them.  Phillip did not report a confidence interval for R-squared because the program for doing so was not available at the time. @Y I SV" µ’’’’¬vv¬e¬ jhGhG0JU\^JhGhH*OJQJ^JhGhH*OJQJ^JhGh6OJQJ^JhGh5\^JhGh^JjhGhU^JhGhOJQJ^J'jhGh56OJQJU^JhF56OJQJ^JhGh56OJQJ^J! 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