# Whether GRE is an ideal evaluator of students' performance

Document Type:Coursework

Subject Area:Statistics

### Document 1

First Analysis Report The first part of the analysis will involve analyzing the association between the GRE and the GPA of the students. A students’ sample will be used and the results that will be obtained from the analyzed data will be used to make inferences regarding the entire population of the students. Since the study involves taking measurements twice from each student, the ideal test to use for analysis will be Paired sample T-test. Paired sample T-test will help to evaluate whether the mean difference between GRE and the GRA is zero. Thus, the analysis will aim at testing the following hypothesis: The null hypothesis (H0): The mean difference between the GRE of the students and the GPA is equal to zero.

The p-value provides the likelihood of observing the test outcomes under the null hypothesis. The halt point for determining the statistical significance for a study is usually at a value of. 05 or less. Thus the lower the p-value the lower the chance of adopting the null hypothesis and for that reason, the researcher will recommend the alternative hypothesis (Schmidt & Hunter, 2014). Thus, if the study will have a significant value that is greater than. Second Analysis Report The next section will be a research study involving gender, GPA, and GRE scores. The study will aim at investigating the relationship among the three variables. Multiple correlation tests will be used to investigate the degree of association among gender, GPA, and the GRE scores.

The coefficient of multiple correlations is often used to evaluate how a given variable can be predicted by two or more variables in a linear relationship (Montgomery et al. The correlation coefficient ranges between 0 and 1and higher value denotes that a dependent variable can well be predicted by the set of independent variables. After the analysis, a correlation test table will be obtained. The table will contain the significance values and the correlation coefficient for the three variables. Interpretation The output of the correlation table will contain three variables gender, GRE, and GPA of the students. Within the table, there will be three rows as well as three columns that will depict the significance and Pearson correlation between the studied variables.

A correlation coefficient of 1 between the studied variables demonstrates that there is a perfect link between the variables. The results will be reported using the following format: Gender and GPA were significantly associated, r=. 54, p<. In case there is no significant relationship, the results should have the following format: There was a no significant association, r=. µ, p> α. Recommendation The researcher will evaluate the linear relationship between the variables by exploring the correlation coefficient (r) in order to determine the degree of association. Alternative hypothesis (H1): The variation in the gender among the students is related to the variation in GRE scores among the students. Since the study aims at investigating how gender is related to the GRE scores of the students, then the appropriate analysis test to use for analysis is a simple linear regression test.

Simple linear regression test enables the researcher to explore how variation in the explanatory variable affects the outcome variable (Fritz et al. Additionally, one is able to predict the outcome variable given the value of the explanatory variable. The regression-based prediction will provide intuition into how the gender of the students will affect the performance of the students in the school. On the other hand, if the calculated significance value is greater than the alpha value, then the researcher will retain null hypothesis and for that reason, conclude that the variation of gender among the students is not related to the variation in the GRE scores of among the students. The following is the format that can be used to report the results of the simple linear regression test: The coefficient of determination (R²), F value (F), the significance level (p), degrees of freedom (df) and the β in the regression equation (Cohen et al.

Recommendation It the analyzed data depicts that the findings are non-significant, then I would propose the head of the school of education not to retain the GRE scores as a measure of evaluating as well as predicting the performance of the students since there is no statistical evidence that supports that there is significant relationship between gender and the GRE scores. The score cannot be used to predict the performance of the students despite having the information pertaining the gender of the students. On the other hand, if the findings of the analysis reveal that there is a significant relationship between gender and GRE scores, then it will be wise for the administration of the school of education to retain the GRE scores as an evaluation tool of the undergraduate performance and also as a measure of predicting the performance of the school.

Interpretation The multiple regression results will have the model summary table, ANOVA table, and the coefficient table. The model summary table will contain the coefficient of determination (R²), the ANOVA table will depict the significance variable along with the F statistics value and lastly, the coefficient table will show the coefficients if the explanatory variable as well as their significant value. The coefficient table also records the y-intercept value. From the coefficient table, the researcher is able to generate the regression equation based on the value of the coefficient. The following is the regression equation that will represent the model for the three variables: y= β + β2χ1 + β3χ2 where: y= GRE scores (dependent variable) β = the y-intercept β2= coefficient for the explanatory variable (gender) the β3= coefficient for the explanatory variable (frequency of completion).

It is also important to ensure the β, as well as a corresponding t-test for the gender and frequency of completion in the regression, are reported. If the significance value for the entire model is greater than the set alpha value. 05, then I will retain the null hypothesis that states that the variation in the performance of the undergraduates is unrelated to the variation in the gender as well as the frequency completion of undergraduates. However, if the significance value is less than or equal to the set alpha value then I will adopt the alternative hypothesis. Recommendation Adoption of the null hypothesis which hold that the variation in the performance of the undergraduates is not related to the variation in gender as well as degree completion frequency necessitate the dean of the school of education to undertake the following measures: Initiate a change of the evaluation policy of the undergraduates performance since the GRE score is not a good evaluation tool that can be relied on to tell the performance of the students given their gender as well as their degree completion frequency.

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