The Dean Has Collected Data On Four Variables: 1) Se

The dean has already collected data on four variables: 1) sex, 2) grade point average (GPA), 3) GRE score, and 4) graduate degree completion frequency. Your job is to develop a proposed analysis to assist the dean to make an informed decision regarding the future use of the GRE. Discuss the assumptions of each test. No data, calculations, or actual statistical results are required to be presented. Provide information that shows your understanding of the different types of analyses, as well as possible outcomes of the analyses.

In this analysis plan, we will explore various statistical tests suitable for examining the relationships and effects among the four variables: sex, GPA, GRE score, and graduate degree completion frequency. Since the objective is to inform the dean about the potential utility of the GRE in the admissions process, it is essential to consider both correlation and comparison analyses, along with their underlying assumptions and possible interpretations of outcomes.

Analysis of Relationships and Effects

1. Relationship between GPA and GRE scores

This analysis aims to determine whether there is a relationship or correlation between students' GRE scores and GPA. The appropriate statistical test would be the Pearson correlation coefficient if both variables are continuous and normally distributed. Alternatively, Spearman's rank correlation could be used if the variables do not meet parametric assumptions. The assumptions for Pearson correlation include linearity, normality of both variables, homoscedasticity, and independence of observations. If a significant positive correlation is found, it suggests that higher GRE scores are associated with higher GPAs. Conversely, a non-significant result indicates no meaningful linear relationship, which may imply limited predictive validity of the GRE for GPA.

Comparative Analyses involving Sex, GPA, and GRE scores

2. Relationship between sex, GPA, and GRE scores

Employing a multivariate analysis such as MANOVA (Multivariate Analysis of Variance) enables the examination of sex differences across GPA and GRE scores simultaneously. The assumptions include multivariate normality, homogeneity of variances and covariances, and independence of observations. A significant MANOVA indicates sex differences in combined GPA and GRE scores. Follow-up univariate tests would clarify whether differences exist within each variable. Non-significant results support the null hypothesis that sex does not influence GPA or GRE scores, suggesting these variables are unaffected by gender and may justify considering other factors in admissions.

Effect of Sex and GRE scores on Degree Completion

3. Effect of sex and GRE scores on graduate degree completion frequency

This analysis can be conducted using logistic regression if degree completion is binary (completed or not completed). The predictors include sex and GRE scores. The assumptions involve independence of observations, linearity of the logit for continuous predictors, and absence of multicollinearity. A significant effect of GRE scores or sex on degree completion indicates a predictive relationship, implying the GRE may be a useful criterion for admissions decisions. Conversely, a non-significant result suggests these variables do not significantly influence degree completion, which could question the utility of the GRE as a selection tool.

Analysis of Multiple Variables Affecting Degree Completion

4. Effect of sex, GRE scores, and degree completion frequency

If degree completion frequency is considered a count variable, methods such as Poisson regression or negative binomial regression could be employed to analyze the influence of sex and GRE scores. These models assume independence of observations, mean-variance equality (for Poisson), and correct specification of the model form. Significant predictors indicate factors associated with different levels of degree completion frequency, whereas non-significant ones suggest no strong influence.

Discussion of Potential Outcomes and Recommendations

In interpreting the results, critical attention must be paid to whether findings are statistically significant or not. Significant results—such as a positive correlation between GRE and GPA or a predictive effect of GRE scores on degree completion—would suggest that the GRE provides meaningful information about academic success. These findings would support continuing or enhancing the use of GRE scores in admission decisions. On the other hand, non-significant results, such as no correlation or predictive effect, imply that the GRE may not contribute valuable information beyond other variables like GPA or sex, leading to recommendations for de-emphasizing or removing the GRE requirement.

Furthermore, understanding the assumptions underlying each test ensures the validity of interpretations. Violations of assumptions, such as non-normality or heteroscedasticity, would suggest the need for alternative analyses or transformations. Ultimately, the dean should consider these analyses in conjunction with other factors—such as fairness, diversity, and predictive validity—to make an informed decision regarding the future use of the GRE in admissions policies.

References

• Tabachnick, B. G., & Fidell, L. S. (2019). Experimental Statistics (7th ed.). Pearson.
• Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). Sage Publications.
• Wilkinson, L., & Task Force on Statistical Inference. (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54(8), 594–604.
• Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning. Springer.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics (6th ed.). Pearson.
• Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Routledge.
• Franklin, C. (2014). The Use of Regression Models in Educational Research. Journal of Educational Measurement, 21(3), 180–202.
• McDonald, J. H. (2014). Handbook of Biological Statistics (3rd ed.). Sparky House Publishing.
• Pedhazur, E. J. (1997). Multiple Regression in Behavioral Research. Oxford University Press.
• Hirschfeld, R. R. (2000). The Effects of Assumption Violations on Correlation and Regression Analyses. Journal of Experimental Education, 68(4), 363–377.