Overview
Our data set contains many variables related to course-specific performance and overall GPA. In looking at the grades for the course, the teacher sees that students in one section performed much better on the third quiz than the students in the other two sections of the course. The teacher is concerned about why students taking identical quizzes in each section are performing so differently. She hypothesizes that one section might comprise students with higher overall GPAs and therefore are stronger students than those in the other two sections. To see if removing the variance in quiz 3 that is explained by the GPA of the students, you will perform a one-way ANCOVA using the variables quiz 3, GPA, and section.
Please use the DAA Template [DOCX] to complete this assignment.
See the Data Set Instructions [PDF] file for information on the data set.
Instructions
Briefly describe the goal of your analysis.
Specify the variables used in this analysis (independent, covariate, and dependent) and the scale of measurement of each variable.
State the sample size (N) and the alpha level you will use (.05 unless otherwise specified).
Explain why the analysis is a good choice based on the nature of your variables.
Specify a research question and articulate a null hypothesis and alternative hypothesis. Specify the alpha level.
Articulate and test the assumptions of ANCOVA.
Paste the histogram output for Quiz 3 and discuss your visual interpretations.
Paste descriptives output showing skewness and kurtosis values for Quiz 3 and interpret them.
Paste the output for the Shapiro–Wilk test of Quiz 3 and interpret the results.
Report the results of the Levene test and interpret it.
Present the results of the test of homogeneity of regression slopes.
Explain whether the assumptions of ANCOVA are met. If assumptions are not met, discuss how to ameliorate violations of the assumptions.
Paste the output of the means plot and provide an interpretation.
Also, report the means and standard deviations of Quiz 3 and GPA for each level of the section variable.
Paste the ANOVA output and report the results of the F test. Include the following:
Degrees of freedom.
F values.
p values.
Interpretation of the effect size.
Interpret statistical results against the null hypothesis and state whether it is accepted or rejected.
Provide a brief summary of your analysis and the conclusions drawn.
Discuss whether the removal of the variance in Quiz 3 that was explained by GPA influences the relationship between Quiz 3 and section.
Analyze the strengths and limitations of the statistical test.
Provide any possible alternate explanations for the findings and potential areas for future exploration.
Additional Requirements
Written communication: Should be free of errors that detract from the overall message.
APA formatting: References and citations are formatted according to current APA style guidelines. Refer to Evidence and APALinks to an external site. for more information on how to cite your sources.
Length: 8–10 double-spaced pages, in addition to the title page and references page.
Competencies Measured
By successfully completing this assignment, you will demonstrate your proficiency in the following course competencies and rubric criteria:
Competency 1: Given a research question, select the appropriate statistical analysis.
Provide context for the data set, including a definition of independent, covariate, and dependent variables and scales of measurement.
For the ANCOVA, articulate a research question, null hypotheses, and alternative hypotheses. Specify alpha level.
Competency 2: Apply statistical analysis.
Analyze the assumptions of the ANCOVA.
Competency 3: Analyze data using statistical software.
Apply the appropriate statistical software procedures to check the assumptions and generate required output for the ANCOVA.
Competency 4: Apply the results of statistical analyses (your own or those of others) to your field of interest or career.
Generate a conclusion including strengths and limitations of the ANCOVA.
Competency 5: Interpret the results of statistical software analysis.
Interpret the output of the ANCOVA.
Competency 6: Communicate in a manner that is scholarly, professional, and consistent with expectations for members of the psychological professions.
Demonstrate an academic writing style through well-organized prose that follows assignment guidelines.
Demonstrate compliance with current APA style, citation, and referencing guidelines in written text and statistical reporting.
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