### Correlation

**You will need the ****grades.sav**** file that you created from the ****grades2.dat**** file in Assignment 1.**

For this two-part assessment, you will respond to a question about interpreting correlations and use SPSS software to complete a data analysis and application report.

You will examine three fundamental inferential statistics, including correlation, *t*-tests, and analysis of variance (ANOVA). The first inferential statistic we will focus on is correlation, denoted *r*, which estimates the strength of a linear association between two variables. By contrast, *t*-tests and ANOVAs will examine group differences on some quantitative dependent variable.

By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies and assessment criteria:

- Analyze the computation, application, strengths, and limitations of various statistical tests.
- Develop a conclusion including strengths and limitations of correlation.

- Analyze the decision-making process of data analysis.
- Analyze the assumptions of correlation.

- Apply knowledge of hypothesis testing.
- Develop a research question, null hypothesis, alternative hypothesis, and alpha level.

- Interpret the results of statistical analyses.
- Interpret the correlation output.

- Apply a statistical program’s procedure to a data set.
- Apply the appropriate SPSS procedures to check assumptions and calculate the correlations.

- Apply the results of statistical analyses (your own or others) to your field of interest or career.
- Develop a context for the data set, including a definition of required variables and scales of measurement.

- Communicate in a manner that is scholarly, professional, and consistent with the expectations for members in the identified field of study.
- Communicate in a manner that is scholarly, professional, and consistent with the expectations for members in the identified field of study.

Read the Assessment 2 Context document attached for important information on the following topics:

- Interpreting correlation: Magnitude and sign.
- Assumptions of correlation.
- Hypothesis testing of correlation.
- Effect size in correlation.
- Alternative correlation coefficients.
- Correlationapplication.
- Proper reporting of correlations.
*r*, degrees of freedom, and correlation coefficient.- Probability values.
- Effect size.

As you prepare to complete this assessment, you may want to think about other related issues to deepen your understanding or broaden your viewpoint. You are encouraged to consider the questions below and discuss them with a fellow learner, a work associate, an interested friend, or a member of your professional community. Note that these questions are for your own development and exploration and do not need to be completed or submitted as part of your assessment.

- Correlation versus causation:
- If correlation does not imply causation, what does it imply?
- Are there ever any circumstances when a correlation can be interpreted as evidence for a causal connection between two variables?
- If yes, what circumstances?

- Application of correlation:
- Is there a research question from your professional life or career specialization that can be addressed by a correlation?
- Why would a correlation be the appropriate analysis for this research question?
- What are the variables and their scale of measurement?
- What is the expected outcome (positive, negative, no relationship)?

In addition, you will need the **grades.sav** file that you created from the **grades2.dat** file in Assessment 1.

SPSS Software

The following statistical analysis software is required to complete your assessments in this course:

- IBM SPSS Statistics (recent version for PC or Mac).

This course requires the following as a minimum:

- IBM SPSS Statistics
**Standard**GradPack. (The**Base**GradPack is not acceptable for use in this course.)

**Versioning:** This software is routinely updated. While it is recommended that you use the latest version of the software available, you may use an older version if you already own it or have access to it, but it **must** be version 22 or higher. Be sure to use the version that is compatible with your operating system (PC or Mac).

#### Suggested Resources

The resources provided here are optional. You may use other resources of your choice to prepare for this assessment; however, you will need to ensure that they are appropriate, credible, and valid. TheXX-FP7864 Quantitative Design and Analysis Library Guidecan help direct your research, and the Supplemental Resources and Research Resources, both linked from the left navigation menu in your courseroom, provide additional resources to help support you.

##### Resources

- George, D., & Mallery, P. (2016).
*IBM SPSS statistics 23 step by step: A simple guide and reference*(14th ed.). New York, NY: Routledge.

##### Internet Resources

- Lane, D. M. (2013).
*HyperStat online: An introductory statistics textbook and online tutorial for help in statistics courses*. Retrieved from http://davidmlane.com/hyperstat - StatSoft, Inc. (2013).
*Electronic statistics textbook*. Tulsa, OK: StatSoft. Retrieved from http://www.statsoft.com/textbook *Sophia*. (2014). Retrieved from http://www.sophia.org/- Browse Sophia for tutorials that explore statistical topics.

- StatisticsLectures.com. (2012).
*Free statistic lectures*. Retrieved from http://statisticslectures.com/ - Khan Academy. (2013). Retrieved from https://www.khanacademy.org
- This Web site offers resources covering a range of subjects, including statistics

- Hall, R. (1998). Between subjects one-way ANOVA example.
*Psychology World*. Retrieved from http://web.mst.edu/~psyworld/anovaexample.htm - Elliot, A. C. (2012). ANOVA using Microsoft Excel: One-way analysis of variance.
*Excel Tutorials for Statistical Data Analysis*. Retrieved from http://www.stattutorials.com/EXCEL/EXCEL_ANOVA.htm… - Onwuegbuzie, T. (Producer). (2009).
*Mixed methods research*[Video] | Transcript. Available from http://videolectures.net/ssmt09_onwuegbuzie_mmr

Suggested Readings

*PSY Learners*

**Note:**For the first article, focus on interpreting Table 1.

- Jia, Y., Konold, T. R., & Cornell, D. (2015). Authoritative school climate and high school dropout rates.
*School Psychology Quarterly*,*31*(2), 289303. - Anderson, C. A., & Bushman, B. J. (2001). Effects of violent video games on aggressive behavior, aggressive cognition, aggressive affect, physiological arousal, and prosocial behavior: A meta-analytic review of the scientific literature.
*Psychological Science, 12*(5), 353359.

*SOE Learners*

- Walk, M., & Rupp, A. (2010). Pearson product-moment correlation coefficient. In N. J. Salkind (Ed.),
*Encyclopedia of research design*(pp. 10231026). Thousand Oaks, CA: Sage.- Chapter 10, “Bivariate Correlation.”

##### Resources

##### George, D., & Mallery, P. (2016).*IBM SPSS statistics 23 step by step: A simple guide and reference*(14th ed.). New York, NY: Routledge.

- Field, A. (2013).
*Discovering statistics using IBM SPSS*(4th ed.). Thousand Oaks, CA: Sage. - Warner, R. M. (2013).
*Applied statistics: From bivariate through multivariate techniques*(2nd ed.). Thousand Oaks, CA: Sage.- Chapter 7, “Bivariate Pearson Correlation.”
- Chapter 8, “Alternative Correlation Coefficients.”

- American Psychological Association. (2010).
*Publication manual of the American Psychological Association*(6th ed.). Washington, DC: Author.

**Preparation**

Read the Assessment 2 Context document (linked in the Resources, under the Required Resources heading) to learn about the concepts used in this assessment. This assessment contains two parts. Follow the instructions provided for each part. Submit both parts of your assessment as Word documents.

#### Part 1: Interpreting Correlations

A meta-analysis (Anderson & Bushman, 2001) reported that the average correlation between time spent playing video games (X) and engaging in aggressive behavior (Y) in a set of 21 well-controlled experimental studies was*r*+ = .19. This correlation was judged to be statistically significant. In your own words, what can you say about the nature of the relationship? Write a one-page response to this question.

#### Part 2: Correlations

You will use the following resources for this assessment. They are linked in the Resources, under the Required Resources heading.

- Complete this part of the assessment using the
**DAA Template.** - Read the
**SPSS Data Analysis Report Guidelines**for a more complete understanding of the DAA Template and how to format and organize your assessment. - Refer to
**IBM SPSS Step-By-Step Instructions: Correlations**for additional information on using SPSS for this assessment. - If necessary, review the
**Copy/Export Output Instructions**to refresh your memory on how to perform these tasks. As with your previous two assessments, your submission should be narrative with supporting statistical output (table and graphs) integrated into the narrative in the appropriate place (not all at the end of the document).

You will analyze the following variables in the**grades.sav**data set:

- gender.
- gpa.
- total.
- final.

##### Step 1: Write Section 1 of the DAA

Provide a context of the**grades.sav**data set. Include a definition of the specified variables and corresponding scales of measurement. Indicate the type of correlation for each X, Y pair (for example, Pearson’s*r*, Spearman’s*r*, point-biserial*r*, et cetera). Specify the sample size of the data set.

##### Step 2: Write Section 2 of the DAA

Test the assumptions of correlation for**gpa**and**final**. Paste the SPSS histogram output for each variable and discuss your visual interpretations. Paste SPSS descriptives output showing skewness and kurtosis values and interpret them. Paste SPSS scatter plot output with gpa set to the horizontal axis and final set to the vertical axis. Conduct a visual inspection of the scatter plot to analyze other assumptions of correlation. Summarize whether or not the assumptions of correlation are met.

##### Step 3: Write Section 3 of the DAA

Specify a research question related to**gpa**and**final**. Articulate the null hypothesis and alternative hypothesis. Specify your alpha level.

##### Step 4: Write Section 4 of the DAA

Paste the SPSS output of the intercorrelation matrix for all specified variables.

- First, report the
**lowest magnitude**correlation in the intercorrelation matrix, including degrees of freedom, correlation coefficient,*p*value, and effect size. Interpret the effect size. Specify whether or not to reject the null hypothesis for this correlation. - Second, report the
**highest magnitude**correlation in the intercorrelation matrix, including degrees of freedom, correlation coefficient,*p*value, and effect size. Interpret the effect size. Specify whether or not to reject the null hypothesis for this correlation. - Third, report the correlation between
**gpa**and**final**, including degrees of freedom, correlation coefficient,*p*value, and effect size. Interpret the effect size. Analyze the correlation in terms of the null hypothesis.

##### Step 5: Write Section 5 of the DAA

Discuss the implications of this correlation as it relates to the research question. Conclude with an analysis of the strengths and limitations of correlational analysis.

##### Reference

Anderson, C. A., & Bushman, B. J. (2001). Effects of violent video games on aggressive behavior, aggressive cognition, aggressive affect, physiological arousal, and prosocial behavior: A meta-analytic review of the scientific literature.*Psychological Science*,*12*(5), 353359.

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