What is the relationship between GPA and mandated GRE scores? (correlation)


This study is meant to gauge the relevance ofthe Graduate Record Exam (GRE) as predictor of graduate school performance. The controversy is due to the belief among educators that the exam is a poor evaluator of undergraduate performance and therefore should be eliminated from the graduate school admissions process.

In order to analyze the data and define the relationship between the GRE and student degree completion the researcher will explore relationships between variables to determine the predictive relationship of the exam and make recommendation to the dean as to proceed with use of the GRE as a part of the graduate school admissions requirement because it is a significant indicator of graduate degree completion.

Analysis of the Effect of Graduate Record Exam (GRE) on Undergraduate Performance

The main objective of this study is to determine the relevance of Graduate Record Exam (GRE) as a determinant of undergraduate performance and graduate completion. This study will analyze the statistical relationship between gender, grade point average, GRE scores and frequency of graduate degree completion. 

For the study to be valid, the data the Dean has collected should have been collected in a statistically valid manner and should be large enough to approximate the true distribution of the population of graduate students. Parametric tests will be used; comparison testing, regression testing and correlation testing will be used. Further, we assume that the variables are not related, and is comparable among all groups in the study. This is normality and homogeneity necessary for nonparametric statistical testing.


  1. What is the relationship between GPA and mandated GRE scores? (correlation)

Ho: There a non-significant relationship between GPA and GRE scores.

Ha: There is significant relationship between GPA scores and GRE scores.

The relationship between GPA & GRE scores compares two continuous variables. You would use the Pearson correlation and determine statistically the size of the correlation, its direction, and its level of statistical significance. For small, medium, and large correlations as r = |.20|, |.30|, and |.50|, respectively (the vertical bar is used to  “|” show an absolute value, which can be positive or negative). The Pearson correlation is a measure of the linear relationship. This fact does not imply that no other relationship exists between the two variables of GPA & GRE.

  • What is the effect of gender on GPA? (t-test)

Ho: There is a non-significant effect of gender on GPA..

      Ha: There is significant effect of gender on GPA.

      Gender and GPA are independent samples.

  • What is the relationship between gender, GPA and GRE scores? (linear regression)

Ho: There is a non-significant relationship between gender, GPA and GRE scores.

Ha: There is a significant relationship between gender, GPA and GRE scores.

  • What is the effect of gender, GPA and GRE scores on the frequency of degree completion?

Ho: Gender, GPA and GRE scores will have no significant effect on the frequency of graduate degree completion.

Ha: Gender GPA and GRE scores will have a significant effect on the frequency of graduate degree completion.



A paired t-test will be used to compare the relationships between subsets of data. The t test tells you how significant the differences between groups are meaning, if those differences (measured in means) could have happened by chance. A t test compares the means of the two groups and lets  you know the probability of those results happening by chance. The relation betweenGRE scores and GPA scores will be tested using t-test test to determine whether the results have a significant or non-significant relationships. If the p value is greater than 0.05, we fail to reject HO and conclude that the GRE scores and GPA scores are similar.

Chi-Square Test

The Chi-Square test will show if the null hypothesis tests of  the data is as expected. The basic idea behind the test is to compare the observed values in your data to the expected values that you would see if the null hypothesis is true. The chi-square test will be used to support the notion that of whether there is a significant relationship between the sets of values. It assumes the data is random and independent. A low value for chisquare means there is a high correlation between the two sets of data.


The bivariate Pearson Correlation test will produce a sample correlation coefficient, r, which will measure the strength and direction of linear relationships between pairs of continuous variables. This test will evaluate whether there is statistical evidence for a linear relationship among the same pairs of variables in the population which is represented by a population correlation coefficient, ρ (“rho”). The Pearson Correlation is a parametric measure which will be used to analyze the relationships and effects between the variables of GPA and GRE, gender and GPA, and gender and GRE.  The bivariate Pearson Correlation is commonly used to measure correlations among pairs of variables and within sets of variables. It indicates whether, a) a statistically significant linear relationship exists between two continuous variables, b) the strength of a linear relationship (i.e., how close the relationship is to being a perfectly straight line), and c) the direction of a linear relationship (increasing or decreasing) A calculated p value of less that .01 will indicate that the correlation is insignificant at 5%.  A calculated p value of -.500 indicates a moderate negative correlation, and a calculated p value of .006 or greater indicates a significant correlation at 1%.


An MANOVA linear regression analysis can be used to show persistence and effect between all variables. MANOVA can detect patterns between multiple dependent variables.  ANOVA statistically tests the differences between three or more group means. The analysis assumes a 2-way measure of relationships between the variables, the relationships are linear and the variables are drawn from normal population.  If the p value in the MANOVA is greater than 0.05, it will indicate that the regression coefficient is significant at 5%.  GPA, GRE and gender means will be measured to determine if each value has a significant effect on degree completion.

Test of Equality of Error Variance

The Laverne’s test of equality of error variance will test the assumption of homogeneity of variance between the variables and will test the null hypothesis between all mean scores.


If the results indicate that there isweak and insignificant positive correlation between gender and GRE, a less than significant correlation between degree completion and GRE  and a non-significant positive correlation  between degree completion and GPA we can assume that the regression coefficient is insignificant.

The results of this study  would then  indicate that gender does not influence GRE scores, there is no difference between GRE scores and GPA scores and degree completion is not influence by GRE scores.


The study which agrees with the null hypothesis for each research question with non-significant results would lead to a recommendation to the dean of eliminating the Graduate Record Exam (GRE) as a measure for admission . Should the study agree with the alternative hypothesis, the recommendation would be that the GRE remain a tool used in the admissions process as a  predictor of the success of students.