Is it possible for someone to just look over this assignment and see if I am on the right track? I have a 4.0 in my doctoral studies right now and I have to get a 90 on this paper to get an A in this class. Stats is definitely not my thing!!!

Instructor Directions:

Scenario:

You are the new director of institutional research at a small state university, and you have been assigned the task of analyzing information for the dean of the School of Education regarding the performance of their undergraduate students on the often-controversial Graduate Record Exam (GRE). Many educators believe the GRE is a poor evaluator of undergraduate performance as well as a poor predictor of graduate school performance. The dean is considering eliminating the GRE from graduate school admissions requirements.

The dean has already collected data on four variables: 1) gender, 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.

Note:

(For this assignment, you don't have to produce any data. This assignment is asking for you to develop the analyses to answer the different questions (see below 1 - 4); relationships questions (What analyses can you use for relationship questions? What types of data (level of measurement)?), for effect questions (What analyses can you use to test for effects of independent variables on dependent variables?) Think on the levels of the independent variables. What types of data (nominal, ordinal, interval, ratio)?), and interaction effects between independent variables.

You should also discuss the assumptions of each test.No data is required to be presented.This is similar to a question that you will encounter in your Doctoral Comprehensive Exams.You should provide information that shows your understanding of the different types of analyses, as well as possible outcomes of the analyses. In addition, you have to include in your discussion the possible conclusions based on the possible results; rejecting the null, and not rejecting the null.You will then need to explain the type of statistical analysis to be employed to analyze relationships and effects between variables. Keep in mind, a statistical relationship analysis involving two variables often involves a Pearson r correlation or a simple regression while a statistical relationship analysis involving three or more variables often involves a multiplecorrelationor what is more widely known as a multiple regression. A statistical analysis of effect involving two variables often involves some form of a t-test while a statistical analysis of effect involving three or more variables often involves some form of an ANOVA.

Finally, you will need to provide fictitious results addressing each of your research questions and corresponding hypotheses. If a significant relationship or difference is determined, for example, p < .05, then reject the null hypothesis and accept the alternative hypothesis. If a non-significant relationship or difference is determined, for example, p > .05, then fail to reject the null hypothesis.

Fictitious Statistical Study

GPA and GRE Scores Examined

1.A relationship research question involving GPA and GRE scores; corresponding null and alternative hypotheses; the type of statistical analysis to be employed to determine significance; explanations of fictitious outcomes identifying both non-significant and significant relationships as related to both null and alternative hypotheses; and recommendations based on non-significant and significant findings.

Q1:What is the relationship between undergraduate GRE scores and undergraduate GPA?

Ho:A non-significant relationship will exist between undergraduate GRE scores and undergraduate GPA.

Ha:A significant relationship will exist between undergraduate GRE scores and undergraduate GPA.

Type of Statistical Analysis: When examining if there is a significant relationship between undergraduate performance (GPA) and GRE scores, a correlation test must be conducted (Pearson's Correlation Coefficient or Pearson's r). The correlation test will examine how closely the undergraduate GPAs and GRE scores are related. There can either be a negative or positive correlation, and the degree of correlation can either be weak or strong (Wall Emerson, 2015).

Dependent variable (DV) = GRE scores

Type of variable = Metric (interval level data)

Independent variable (IV)= GPA

Type of variable = Metric (interval level data)

Pearson Correlation Coefficient Test Assumptions:

a.Level of Measurement: Variables used in this test should be continuous; if either or both variables are ordinal than a Spearman correlation should be utilized (Statistics Solutions, 2015).

b.Related pairs: Each observation utilized in the correlation test should have a pair of variables (Statistics Solutions, 2015).

c.Absence of outliers: There cannot be any outliers in either variable as this can skew the correlation results (Statistics Solutions, 2015).

d.Linearity and homoscedasticity: Linearity and homoscedasticity are in references to the value shapes formed on the scatterplot (Statistics Solutions, 2015). A straight-line correlation between the variables should be seen to establish linearity (Statistics Solutions, 2015).Homoscedasticity is the distance between points on the straight line of the scatterplot (Statistics Solutions, 2015).

Decision:

If p .05, reject the null hypothesis and accept the Ha.

If p >.05, fail to reject the null hypothesis.

Conclusion:

If the Ho is rejected: There is enough evidence to conclude that there exists a relationship between undergraduate GPA and GRE scores.

Fail to reject the Ho:There is not significant evidence to conclude that there exists a relationship between undergraduate GPA and GRE scores.

Recommendations:

Ho Rejected: If the Ho is rejected, then there exists evidence of a significant correlation between undergraduate GPAs and GRE scores. Recommendations to the Dean would be to continue to employ the use of the GRE as an effective measurement of possible future performance in graduate school as it relates to the students' undergraduate GPA.

Fail to Reject the Ho: If the Ho is accepted, then there is not significant evidence of a correlation between undergraduate GPAs and GRE scores. Recommendations to the Dean would be to discontinue use of the GRE as an effective tool to predict future performance in graduate school in relation to ungraduated GPA and GRE scores.

Gender, GPA, GRE Scores Examined

2.A relationship research question involving gender, GPA, and GRE scores; corresponding null and alternative hypotheses; the type of statistical analysis to be employed to determine significance; explanations of fictitious outcomes identifying both non-significant and significant relationships as related to both null and alternative hypotheses; and recommendations based on non-significant and significant findings.

Q1:What is the relationship between gender, GPA, and GRE scores?

Ho:A non-significant relationship will exist between gender, GPA, and GRE scores.

Ha:A significant relationship will exist between gender, GPA, and GRE scores.

Type of Statistical Analysis:

When examining if there is a significant relationship between gender, GPA, and GRE scores a multiple regression analysis should be conducted as a predictive analysis (Courvoisier & Renaud, 2010).

Dependent variable, (DV) = GRE scores

Type of variable = Interval level data

Independent variable (IV)= GPA

Type of variable = Interval level data

Independent variable (IV)= Gender

Type of variable = Dichotomous Categorical (Campbell, 2016)

Multiple Linear Regression Assumptions:

a)The relationship between dependent and independent variables should be linear;

b)Predicted and observed values must be normally distributed, and

c)"Multiple linear regression assumes that there is no multicollinearity in the data" (Statistics Solutions, 2017).

Decision:

If p .05, reject the null hypothesis and accept the Ha.

If p >.05, fail to reject the null hypothesis.

Conclusion:

If the Ho is rejected: There is enough evidence to conclude that there exists a relationship between gender, undergraduate GPA, and GRE scores.

Fail to reject the Ho:There is not enough evidence to conclude that there exists a relationship between gender, undergraduate GPA, and GRE scores.

Recommendations:

Ho Rejected: If the Ho is rejected, then there exists evidence of a significant correlation between gender, undergraduate GPAs, and GRE scores. Recommendations to the Dean would be to continue to employ the use of the GRE as an effective measurement of possible future performance in graduate school as it relates to the students' undergraduate GPA and possible future graduate school performance.

Fail to Reject the Ho: If the Ho is accepted, then there is not significant evidence of a correlation between gender, undergraduate GPAs, and GRE scores. Recommendations to the Dean would be to discontinue use of the GRE as an effective tool to predict future performance in graduate school in relation to gender, ungraduated GPA, and GRE scores.

Gender and GRE Scores Examined

3.An effect research question involving gender and GRE scores; corresponding null and alternative hypotheses; the type of statistical analysis to be employed to determine significance; explanations of fictitious outcomes identifying both a non-significant and a significant effect as related to both null and alternative hypotheses; and recommendations based on non-significant and significant findings.

Q1:What is the effect of gender on GRE scores among undergraduate students?

Ho:A student's gender will result in a non-significant effect on GRE scores amongst undergraduate students.

Ho:A student's gender will result in a significant effect on GRE scores amongst undergraduate students.

Type of Statistical Analysis:

The analysis will compare the mean GRE scores for different genders, whether the mean GRE scores for both categories (male or female) is the same or different. Therefore, an independent t test will be conducted. The independent t test is utilized whenever two population groups are needing to be compared, and each group observations are independent of the observations of the other group (Feng et al., 2017; Stone, 2012). As it relates to this study, males and females would comprise two naturally occurring groups, and their GRE scores would be the dependent variable. Additional tests, Levene's Test of Equality of Error Variances and Shapiro-Wilk test of normality, will be conducted to test for assumptions (see below).

Dependent variable, (DV) = GRE scores

Type of variable = Metric (interval level data)

Independent variable, (IV) = Gender

Type of variable = Non-Metric (Nominal level data as only male or female)

Independent t Test Assumptions:

According to Stone (2012), there are three assumptions that must be met before conducting an independent-samples t-test including:

a)The observations within a study must be independent, meaning that one observation does not influence another observation.

b)The study must have equality or homogeneity of variance between the samples being tested. The Levene's Test of Equality of Error Variances will be conducted to test for this assumption. If significance is found with the Levene's test than the equality between the samples has not been achieved (Stone, 2012).

c)The third assumption is that each of the samples must be representative of a "normal distribution." This assumption is tested by the Shapiro-Wilk test of normality which is based on the correlation between the normal scores and corresponding data.

Decision:

If p .05, reject the null hypothesis and accept the Ha.

If p >.05, fail to reject the null hypothesis.

Conclusion:

Ho Rejected: There is significant evidence that mean GRE scores for males and females are statistically different.

Fail to Reject the Ho: There is not significant evidence that mean GRE scores for males and females are statistically different.

Recommendations:

Ho Rejected: If the Ho is rejected, then there exists evidence of a significant correlation between gender and GRE scores. Recommendations to the Dean would be to perform additional analysis to further explore the correlation between gender and GRE scores (i.e., undergraduate major focus, academic habits, social proclivities, socioeconomic background).

Fail to Reject the Ho: If the Ho is accepted, then there is not significant evidence of a correlation between undergraduate GPAs and GRE scores. Recommendations to the Dean would be to discontinue use of the GRE as an effective tool to predict future performance in graduate school in relation to ungraduated GPA and GRE scores.

4.An effect research question involving gender, GRE score, and degree completion frequency; corresponding null and alternative hypotheses; the type of statistical analysis to be employed to determine significance; explanations of fictitious outcomes identifying both a non-significant and a significant effect as related to both null and alternative hypotheses; and recommendations based on non-significant and significant findings.

Q1:What is the effect of degree completion frequency on GRE scores among undergraduate students by gender?

Ho:Degree completion frequency will result in a non-significant effect on GRE scores among undergraduate students by gender.

Ha:Degree completion frequency will result in a significant effect on GRE scores among undergraduate students by gender.

Type of Statistical Analysis:

When examining if there is a significant effect between degree completion frequency, gender, and GRE scores a three-way ANOVA analysis should be conducted.

Dependent variable, (DV) = GRE scores

Type of variable = Interval level data

Independent variable (IV)= Degree Completion Frequency

Type of variable = Dichotomous Categorical (Campbell, 2016) Assuming that there are only two options. (i.e., The student can either complete the degree (yes) or not complete the degree (no).)

Independent variable (IV)= Gender

Type of variable = Dichotomous Categorical (Campbell, 2016)

ANOVA Test Assumptions:

a)Observations within the group must be independent of each other;

b)the data should be randomly selected from the sample population;

c)the outcome variable should represent a normal distribution, and

d)the researcher must ensure that there is homogeneity of variance (Field, 2011).

Decision:

If p .05, reject the null hypothesis and accept the Ha.

If p >.05, fail to reject the null hypothesis.

Conclusion:

If the Ho is rejected: There is enough evidence to conclude that degree completion frequency does have an effect on GRE scores among undergraduate students by gender.

Fail to reject the Ho:There is enough evidence to conclude that there is not an effect between degree completion frequency and GRE scores among undergraduate students by gender.

Recommendations:

Ho Rejected: If the Ho is rejected, then there exists evidence that degree completion frequency does have an effect on GRE scores among undergraduate students by gender. Recommendations to the Dean would be to continue to employ the use of the GRE as an effective measurement of possible future performance in graduate school as it relates to the students' undergraduate degree completion frequency, gender, and possible future graduate school performance.

Fail to Reject the Ho: If the Ho is accepted, then there is enough evidence to conclude that there is not an effect between degree completion frequency and GRE scores among undergraduate students by gender. Recommendations to the Dean would be to discontinue use of the GRE as an effective tool to predict future performance in graduate school in relation to degree completion frequency and GRE scores.

5.Finalize your report with a written analysis of your results and recommendations for the dean based on your findings.

Dean of the School of Education:

After thorough analysis of the data, you provided concerning undergraduate GPA, gender, and degree completion frequency as it relates to GRE scores as predictive measures for undergraduate and graduate performance, I have come to the following recommendations. We must examine the relationships and effects between several combinations of variables that you provided. Please see below for my suggestions:

1.Variables for Analysis

Dependent Variable = GRE Scores, Independent Variable = GPA

Test Utilized for Analysis

Pearson's Correlation Coefficient

Research Question to be Answered by Analysis:

Q1:What is the relationship between undergraduate GRE scores and undergraduate GPA?

Hypothesis:

Ho:A non-significant relationship will exist between undergraduate GRE scores and undergraduate GPA.

Ha:A significant relationship will exist between undergraduate GRE scores and undergraduate GPA.

Recommendations:

If the data supports a rejection of the null hypothesis, then evidence suggests that there is a significant correlation between undergraduate GPAs and GRE scores. At this point, I would recommend that you continue to employ the use of the GRE as an effective measurement of possible future performance in graduate school as it relates to the students' undergraduate GPA. However, if the data fails to reject the null hypothesis, then there is not significant evidence of a correlation between undergraduate GPAs and GRE scores and I would recommend the discontinued use of the GRE as an effective tool to predict future performance in graduate school in relation to ungraduated GPA and GRE scores.

2.Variables for Analysis

Dependent Variable = GRE Scores, Independent Variable = GPA,

Independent Variable = Gender

Test Utilized for Analysis

Multiple Linear Regression

Research Question to be Answered by Analysis:

Q1:What is the relationship between gender, GPA, and GRE scores?

Hypothesis:

Ho:A non-significant relationship will exist between gender, GPA, and GRE scores.

Ha:A significant relationship will exist between gender, GPA, and GRE scores.

Recommendations:

If the data supports a rejection of the null hypothesis, then there exists evidence of a significant correlation between gender, undergraduate GPAs, and GRE scores. I would recommend continuing to employ the use of the GRE as an effective measurement of possible future performance in graduate school as it relates to the students' undergraduate GPA and possible future graduate school performance. If the data fails to reject the null hypothesis, then there is not significant evidence of a correlation between gender, undergraduate GPAs, and GRE scores. The recommendation would be to discontinue the use of the GRE as an effective tool to predict future performance in graduate school in relation to gender, ungraduated GPA, and GRE scores.

3.Variables for Analysis

Dependent Variable = GRE Scores, Independent Variable = Gender

Test Utilized for Analysis

Independent t Test

Research Question to be Answered by Analysis:

Q1:What is the effect of gender on GRE scores among undergraduate students?

Hypothesis:

Ho:A student's gender will result in a non-significant effect on GRE scores amongst undergraduate students.

Ho:A student's gender will result in a significant effect on GRE scores amongst undergraduate students.

Recommendations:

If the data supports a rejection of the null hypothesis, then there exists evidence of a significant correlation between gender and GRE scores. Recommendations would be to perform additional analysis to further explore the correlation between gender and GRE scores to fully understand the results (i.e., undergraduate major focus, academic habits, social proclivities, socioeconomic background). If the data fails to reject the null hypothesis, then there is not significant evidence of a correlation between undergraduate GPAs and GRE scores and the recommendation would be to discontinue use of the GRE as an effective tool to predict future performance in graduate school in relation to ungraduated GPA and GRE scores.

4.Variables for Analysis

Dependent Variable = GRE Scores, Independent Variable = Gender, Independent Variable = Degree Completion Frequency

Test Utilized for Analysis

Three-way ANOVA analysis

Research Question to be Answered by Analysis:

Q1:What is the effect of degree completion frequency on GRE scores among undergraduate students by gender?

Hypothesis:

Ho:Degree completion frequency will result in a non-significant effect on GRE scores among undergraduate students by gender.

Ha:Degree completion frequency will result in a significant effect on GRE scores among undergraduate students by gender.

Recommendations:

If the data supports a rejection of the null hypothesis, then there exists evidence that degree completion frequency does have an effect on GRE scores among undergraduate students by gender. Recommendations would be to continue to employ the use of the GRE as an effective measurement of possible future performance in graduate school as it relates to the students' undergraduate degree completion frequency, gender, and possible future graduate school performance. If the data fails to reject the null hypothesis, then there is enough evidence to conclude that there is not an effect between degree completion frequency and GRE scores among undergraduate students by gender. Recommendations would be to discontinue use of the GRE as an effective tool to predict future performance in graduate school in relation to degree completion frequency and GRE scores.

Once the data has been thoroughly analyzed, I recommend that we reconvene to determine the significance of the results and how they may impact the future use of the GRE at our university. At this point in the process, without having actually performed the analyses discussed above, I cannot say with confidence if the GRE is an accurate predictor of graduate school performance. Once we have completed the analyses of the data you have provided we can have further discussion on this matter. As to this, my final recommendation is that I perform the above mentioned statistical analysis of the data you provided and then develop an in-depth analysis of the results for your review.

References

Campbell, M. (2016). Getting to grips with statistics: Understanding variables. British Journal of Midwifery, 24(10), 738-741.

Courvoisier, D., & Renaud, O. (2010). Robust analysis of the central tendency, simple and multiple regression and ANOVA: A step by step tutorial. International Journal of Psychological Research, 3(1), 78-87.

Feng, C., Fralick, D., TU, X. M., Wang, B., XU, M., & Zheng, J. Z. (2017). The differences and similarities between two-sample t-test. Shanghai Archives of Psychiatry, 29(3), 184-188. doi:10.11919/j.issn.1002-0829.217070

Field, A. (2011). Analysis of variance (ANOVA). Encyclopedia of Measurement and Statistics, 33-35. doi:10.4135/9781412952644

Statistics Solutions. (2015, May 13). Pearson correlation assumptions. Retrieved from Statistics Solutions: http://www.statisticssolutions.com/pearson-correlation-assumptions/

Statistics Solutions. (2017, October 12). Assumptions of Multiple Linear Regression. Retrieved from Statistics Solutions: https://www.statisticssolutions.com/assumptions-of-multiple-linear-regression/

Stone, E. (2012). Encyclopedia of research design. Thousand Oaks, CA: SAGE Publications, Inc.

Vogt, W. (2011). Pearson's Correlation Coefficient. Dictionary of Statistics & Methodology, 233-234. doi:10.4135/9781412983907

Wall Emerson, R. (2015). Causation and pearson's correlation coefficient. Journal of Visual Impairment & Blindness, 36(3), 242-244.