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Application: Correlation Study: Intelligence and Self-Esteem
In Chapter 1 you read about the differences between experimental and observational research and read that correlational studies are one type of observational research. In an experiment, the researcher manipulates a variable to determine differences between two or more levels of that variable. In an observational study, the researcher looks at patterns of relationships without manipulating variables. In correlational studies, you cannot show that one variable causes a change in another variable. However, you can demonstrate that as one variable increases, another increases. You also may find that as one variable increases, the other decreases. You may even find that there is no relationship at all. Use your understanding of correlations to work through the following scenario.
Scenario:
To prepare for this Assignment, recall that in Week 1 you imagined you were a researcher interested in determining if student intelligence is related to self-esteem. Now imagine that 10 individuals participated in your study and the raw data are given here:
Participant Self-Esteem Score IQ
1 3.2 100
2 4.1 140
3 2.2 95
4 3.0 112
5 2.6 130
6 2.0 99
7 5.0 118
8 4.8 121
9 3.7 129
10 4.4 138
Assignment:
To complete this Assignment, submit by Day 7 your answers to the following. Based on the scenario, use SPSS to determine if self-esteem is related to intelligence in your sample by computing a correlation. Save and submit both the SPSS data and output files.
Before computing the correlation, state either a one-tailed or two-tailed, alternative hypothesis and the corresponding null hypothesis in words (not formulas).
Based on the hypotheses you stated, explain whether you should conduct a one-tailed or two-tailed test. Provide a rationale for your choice.
Identify what the correlation coefficient (r) is for this data set.
State the degrees of freedom and explain how it is calculated.
Identify the p value.
Explain whether you should retain or reject the null hypothesis. Provide a rationale for your decision.
Describe the direction and strength of the relationship between self-esteem and intelligence.
Submit three documents for grading: your text (Word) document with your answers and explanations to the application questions, your SPSS Data file, and your SPSS Output file.
References:
Readings
Heiman, G. (2015). Behavioral sciences STAT 2 (2nd ed). Stamford, CT: Cengage.
Chapter 10, “Describing Relationships Using Correlation and Regression” (pp.162-181)
Chapter 13, “Chi Square and Nonparametric Procedures” (pp.218-229 only)
Chapter 10 Review Card (p. 10.4)
Chapter 13 Review Card (p. 13.4)
Media
Bjorkman, S. (2014). SPSS tutorial - Chi-square. Retrieved from http://screencast.com/t/mJsqW8p7 Note: The approximate length of this media piece is 5 minutes. This video demonstrates calculating and interpreting chi-square analyses in SPSS. Ludwig, T. E. (n.d.a). Correlation [Interactive media]. Retrieved June 11, 2013, from http://bcs.worthpublishers.com/WebPub/Psychology/psychsim5/PsychSim5%20Tutorials/Correlation/Correlation.htm Note: This site offers additional information about correlations, including interactive media examples.Son, J. (2011). Statistics – Regression [Video file]. Retrieved from http://www.youtube.com/user/EducatorVids2?v=51JcydfYaTY&feature=pyvNote: The approximate length of this media piece is 5 minutes. This video explains linear regression, including predictor and response variables.StatsLectures. (2011d). SPSS - Pearson's r (+hypothesis test) [Video file]. Retrieved from http://www.youtube.com/watch?v=jexXeAoymh4Note: The approximate length of this media piece is 4 minutes. This video shows how to calculate Pearson’s r in SPSS. In addition, a hypothesis test is conducted to determine if the Pearson’s r is significant.
Optional Resources:
BBC (Producer). (2010). The joy of stats [Video series]. Retrieved from http://www.bbc.co.uk/programmes/p00cgkfk
“Hans Rosling’s 200 Countries, 200 Years, 4 Minutes”
University of South Carolina. (n.d.a). Regression applet. Retrieved June 11, 2013, from http://www.stat.sc.edu/~west/javahtml/Regression.htmlUniversity of South Carolina. (n.d.b). Understanding correlation. Retrieved June 11, 2013, from http://www.stat.tamu.edu/~west/applets/rplot.html
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