**In this assignment, you will conduct an ANCOVA analysis**

**In this assignment, you will conduct an ANCOVA analysis, which will include:**

- Checking whether the CV is related to the DV

- Checking the homogeneity of regression assumption
- Conducting the ANCOVA to see if there is a relationship between the IV and DV after taking into account the CV
- Computing an effect size for the IV
- Examining post-hoc analyses to determine the significance of pairwise comparisons
- Providing an APA-format write-up of the analysis

This week’s dataset is similar to the dataset you used for the last assignment. You have data from 89 students and you want to see if the number of graduate school applications students submit differs based on the type of program to which they are applying [Program Type: 1 = Master’s of Business Administration (MBA), 2 = Master of Arts (MA), 3= Doctor of Philosophy (PhD)]. From previous analyses, you know that GRE quantitative scores significantly predict the number of graduate school applications that are submitted. Thus, you want to conduct this analysis as an ANCOVA in which GRE Quantitative will be used as the covariate (CV). The dataset is saved on eCourseware as “Assignment 10 ANCOVA.sav.”

- Before you use GRE Quantitative as a CV, you have to make sure it meets the criteria of a good covariate.
- First make sure the GRE Quantitative and Grad School Applications are sufficiently correlated. Go to “Analyze”, choose “Correlate” and click on “Bivariate...” Move the variables under “Variables” and press “OK” to run the correlation. Is GRE Quantitative correlated enough with your DV to be used as a CV? What information did you use to decide?

- Why is the above step important? In other words, why is it necessary to test if the CV is correlated with the DV?

- The second criterion of a good covariate is that it does not significantly predict the independent variable. In other words, there should not be a significant difference between the levels of the IV on GRE Quantitative. To check for this, run a one-way ANOVA by going to “Analyze”, “Compare Means”, and “One-Way ANOVA.” Examine your output. Does GRE Quantitative still appear to meet the criteria for a good covariate? What specific information on the output did you use to decide?

- Why is the above step important? In other words, why is it necessary to test if the CV significantly predicts the independent variable?

- Now you have to make sure your CV meets the homogeneity of regression assumption. To check this assumption, you will run a customized ANCOVA model that includes an interaction term between the CV and IV. (You have to run the custom model because the interaction term is not included by default in SPSS under the Full factorial model). To do this, click on “Analyze”, “General Linear Model,” and then click on “Univariate.” Select GradSchoolApplications as the DV, ProgramType as the Fixed Factor (i.e., IV), and GREQuant as the Covariate. Click on “Model...” to specify the customized model. In the window that opens up, click on “Custom.” Then enter put both variables under “Model” on the right and, lastly, add the ProgramType by GREQuant interaction term by simultaneously highlighting both variables on the left and then clicking on the arrow to bring the interaction term over to the model. Click on “Continue” and then on “OK” to run the customized ANCOVA.
- Examine your output. If the ProgramType by GREQuant interaction is significant, you have failed to meet the homogeneity of regression assumption. According to the results, do you meet the assumption? What specific information in the output did you use to decide?

- Why is the above step important? In other words, why is it necessary to test if there is an interaction between the independent variable and the CV?

- In one sentence, and using APA format, report the
*F*, degrees of freedom, and*p*-value that express the results of test of the homogeneity of regression assumption.

- Now that you have met the requirements and assumptions of ANCOVA, you can go ahead and conduct the (Full factorial) ANCOVA analysis. Go to “Analyze”, “General Linear Model,” and click on “Univariate.” Leave the variable selection in place; all you need to do is click on “Model...,” and then click on “Full factorial.” This lets SPSS know that you no longer wish to examine the presence of the ProgramType by GREQuant interaction term. Click on “Continue.” The last thing you need to do is select your follow-up analyses. To do this, click on “Options...,” move your IV under “Display Means for,” click “Compare main effects,” and under “Confidence interval adjustment” select “Bonferroni.” Click on “Continue” and then on “OK” to run the ANCOVA.

[Note: usually you would also select “Homogeneity tests” and report whether you meet the homogeneity of variance assumption. But, for the sake of brevity, you will not do this for this assignment.]

- Examine your output. Does Program Type have a significant effect on the number of graduate school applications that a student submits? What specific information in the output did you use to decide?

- Compute an effect size (ω
^{2}) for Program Type.

- Interpret the omega squared. What is the number specifically telling you about the relationship between the two variables?

- In one sentence, and using APA format, report the
*F*, degrees of freedom, and*p*-value, and ω^{2}for Program Type.

- Because there is an overall effect for Program Type, the last thing you need to do is examine the Pairwise Comparisons table to see which pairs of groups differ from each other. Based on information provided in the table, which groups are significantly different from each other? What specific information in the table did you use to decide?
- Provide an APA-format write-up of the analysis. See the last two lecture slides for an example of the general requirements.

**Category:**Mathematics, General Mathematics

**ProfMyk**

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