The following four-year public and private Iowa colleges and universities were included in the analysis:

Transcription

1 Explaining the Variance in Graduation Rates among Iowa Four-Year Colleges and Universities Michael C. Morrison President February

2 Explaining the Variance in Graduation Rates among Iowa Four-Year Colleges and Universities Purpose This study exams graduation rates at Iowa s public and private four-year colleges and universities. Its major purpose is to account for the variance in graduation rates taking into account several predictor variables. Data and Sample Data was obtained from The Education Trust: The following four-year public and private Iowa colleges and universities were included in the analysis: Colleges and Universities Grinnell College Luther College Wartburg College Coe College Drake University Central College Cornell College Clarke College Iowa State University University of Northern Iowa University of Iowa Dordt College Loras College Simpson College Northwestern College Morningside College Saint Ambrose University Briar Cliff College Buena Vista University Allen College Graceland University Upper Iowa University Maharishi University of Management Grand View College University of Dubuque Iowa Wesleyan College William Penn University Sample size equals 27. Data was collected for the college year. 2

3 Variables in the analysis: Variable Type Label Description Observed, endogenous Graduation rate in six years GRAD_RATE (dependent) variable: (1997 to 2003) Observed, exogenous (independent) variables: PCT_PELL Percent Pell grants (Based on the percentage of undergraduates receiving Pell Grants in ) SAT EXP_FTE PCT_UR_MIN SIZE Estimated median SAT score Expenditure per fulltime equivalent (FTE) student (This includes instructional, student services, and academic support expenditures.) Percent underrepresented minority (Calculated as the percent of FTE undergraduates who are Black, Latino, or Native American.) Size of the college (FTE undergraduates) Hypotheses: This analysis tests the following null hypotheses: 1. Ho: Graduation Rate is not related to Percent Pell 2. Ho: Graduation Rate is not related to SAT scores 3. Ho: Graduation Rate is not related to Expenditure per FTE 4. Ho: Graduation Rate is not related to Percent Underrepresented Minority 5. Ho: Graduation Rate is not related to Size Statistical Technique Multiple regression employing maximum likelihood estimation and path analysis techniques were utilized to: Test the hypotheses; Determine the amount of variance in graduation rate explained by the combined influence of the independent variables; and Develop a parsimonious model of graduation rates among Iowa four-year public and private colleges and universities. Path Analysis Model A recursive path analysis model was constructed to provide a means to test the hypotheses and to visually interpret the results. The following path model depicted below directs the initial analysis: 3

4 Graduation Rates in Iowa Four Year Colleges SAT Percent Pell FTE Student Expenditure Graduation Rate 1 e1 Size Percent Underrepresented Minority Analysis The maximum likelihood estimates for the initial model are depicted below: Graduation Rates in Iowa Four Year Colleges -.70 SAT Percent Pell FTE Student Expenditure Graduation Rate.80 e Size Percent Underrepresented Minority The full model has zero degrees of freedom and therefore is a saturated or just identified model. The maximum likelihood regression weights with their associated probabilities are revealed in Table 1: 4

5 Maximum Likelihood Regression Weights: Table 1 Estimate S.E. C.R. P GRAD_RATE <--- PCT_PELL GRAD_RATE <--- SIZE GRAD_RATE <--- EXP_FTE GRAD_RATE <--- PCT_UR_MIN GRAD_RATE <--- SAT Standardized Regression Weights: Table 2 Estimate GRAD_RATE <--- PCT_PELL GRAD_RATE <--- SIZE GRAD_RATE <--- EXP_FTE.059 GRAD_RATE <--- PCT_UR_MIN GRAD_RATE <--- SAT.499 Squared Multiple Correlation Table 3 Estimate GRAD_RATE.774 While the amount of explained graduation rate variance is large, three exogenous variables, EXP_FTE, SIZE and PCT_UR_MIN must be removed from the model as they are not statistically significant. Estimates for the new parsimonious model, which deletes the EXP_FTE, SIZE and PCT_UR_MIN paths to GRAD_RATE, are depicted below: 5

6 Graduation Rates in Iowa Four Year Colleges SAT Graduation Rate e1 Percent Pell -.30 Regression Weights: Table 4 Estimate S.E. C.R. P Label GRAD_RATE <--- SAT *** GRAD_RATE <--- PCT_PELL Standardized Regression Weights: Table 5 Estimate GRAD_RATE <--- SAT.640 GRAD_RATE <--- PCT_PELL Squared Multiple Correlation: Table 6 Estimate GRAD_RATE.774 The model s F-Ratio equals with p<.001. We, therefore, accept the model. In addition, both SAT and PCT_PELL are statistically significant and explain a large amount (77%) of the variance in graduation rates among Iowa four-year colleges and universities. SAT has twice the direct impact (.64) on graduation rates than PCT_PELL (-.30). 1 In addition, it is noteworthy, albeit not surprising, that there is a very strong negative correlation (-.77) among the exogenous variables, 6

7 PCT_PELL and SAT. Achievement as measured by the SAT is negatively correlated with student financial assets. Conclusion The input characteristics that students bring to Iowa four-year colleges, specifically academic achievement (SAT) and financial status (PCT_PELL), explain a large amount (77 percent) of the variance in graduation rates among Iowa four-year colleges. Iowa four-year public and private college graduation rates are primarily a reflection of their entering student characteristics. This conclusion agrees with major research findings across this country for several years. (See References.) Scatterplots also reveal the strong relationships between graduation rates and SAT and PCT_PELL. 2 Conceptually important variables --- Expenditure per FTE, Percent Underrepresented Minority, and Size --- are not related to graduation rates among Iowa s public and private four-year colleges and universities. 7

8 Footnotes: 1 An outlier, William Penn University with a studentized residual of , was revealed in the analysis. This case was deleted and regression estimates were derived with a sample size of 26. No significant differences were discovered in the smaller sample size analysis. R 2 still equals.770 with an F-Ratio of and p<.001. Beta weights for PCT_PELL and SAT were.615 and -.347, respectively. Both beta weights were statistically significant. The plot of residuals against predicted values graphically reveals a homoskedastic distribution. Plot of residuals against predicted values RESIDUAL ESTIMATE 2 Scatterplot: Graduation Rate vs SAT r =.85 Graduation Rate SAT 8

9 2 Scatterplot: Graduation Rate vs Percent Pell Graduation Rate r = Percent Pell 9

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