The statistical correlation and regression analyses

Learning Outcomes

  1. Describe correlations and regression analyses.
  2. Analyze the relationship between correlations and predictions.

Introduction

In contrast to Week Three where statistical tests focusing on differences were introduced, in Week Four, you will explore relationships in statistical tests. Correlations and linear regression techniques will be utilized and results will be evaluated and interpreted.  The written assignments in Weeks One, Two, and Three prepared you for analyzing and evaluating research articles.  In the written assignment this week, you will focus less on actual research and more on the report writing process.

If you work in a social/behavioral sciences field, you will likely be asked to conduct research (i.e., conduct an experiment or study) and create a report based on your findings.  Generally speaking, people who investigate a scientific hypothesis have a responsibility to the scientific community to share those results.  This is particularly true when that investigation adds to/or contradicts previous research.  The research report outlines each step that was done during the research and summarizes the results and conclusions.  The goal is to give the reader enough information so that the methods and results can be accurately evaluated, and the conclusions can be replicated if necessary. Although the research report this week will be based on hypothetical and/or fictitious data, the process of creating a correctly formatted research report with all the necessary components will provide you with important skills as you progress through your degree and as you continue into the world of the social/behavioral sciences.

 


Required Resources

Required Text

Read from the course text, Statistics for the Behavioral & Social Sciences:

  • Chapter 8: Correlation
  • Chapter 9: Linear Regression

Recommended Resources

Articles

  1. Kirwan, J., Lounsbury, J., Gibson, L. (2010).  Self-direction in learning and personality: The Big Five and narrow personality traits in relation to learner self-directionInternational Journal of Self-Directed Learning, 7(2), 21-34.  Retrieved from http://sdlglobal.com/IJSDL/IJSDL7.2-2010.pdf#page=25
    • This is an article about personality, self-directed learning, and scale development and the major traits that may affect them.  These include: agreeableness, conscientiousness, emotional stability, and openness.   It incorporates correlation and regression procedures with tables that display the statistical results.
  2. Stark, P.B. (2013). Chapter 9: Regression. Retrieved from http://www.stat.berkeley.edu/~stark/SticiGui/Text/regression.htm
    • This website contains several video lectures and examples of how regression is used.
  3. Trochim, W. M.  (2006). Correlation. In Research Methods Knowledge Base.  Retrieved from http://www.socialresearchmethods.net/kb/statcorr.php
    • This website contains many tutorials and tools for statistical analyses and methods used in the social sciences.  This particular page is a detailed description, with examples and graphs, to help understand correlation statistics.

Websites

  1.  VassarStats: Website for Statistical Computation. (http://vassarstats.net)
    • This website includes tools to calculate many of the statistical tests we cover in this course including t-tests, ANOVA, correlation, and regression.  Each calculator includes a tutorial and/or walkthrough.
  2.  Web Center for Social Research Methods. (http://socialresearchmethods.net)
    • This website includes links to numerous tools and tutorials relating to statistical concepts, calculations, and scale development.

 


.

Correlation

In this post, you will be challenged to look at how statistical tests, such as correlation are commonly used and the possible limitations of such analyses. In addition, you will need to identify the appropriate application of course-specified statistical tests, examine assumptions and limitations of course specified statistical tests, and communicate in writing critiques of statistical tests.
Much has been written about the relationship between students’ SAT test scores and their family’s income.  Generally speaking, there is a strong positive correlation between income and SAT scores.  Consider and discuss the following questions as you respond:

·         What does this correlation tell you?

·         Is this correlation evidence that having a high family income causes one to have high SAT scores?

·         Is this correlation evidence that high SAT scores are a cause of higher income? Or, does this tell you something else?  Explain your answer.

·         Explain why correlation alone is rarely sufficient to demonstrate cause.

 

·         1 –Correlation – Looking at the Pearson Correlation, positive and negative correlations and the relationship between correlation and causation.

 

·         In a separate area with references, if applicable, answer these questions:

 

·         How strong do you feel your explanations are?

 

·          What might you do to strengthen their arguments?

When grading the Correlation paper I will be looking for your answer to contain:

Week 4 Paper 1 Board Rubric     
  Earned Weight
Content Criteria   0.5
Student identifies and defines what the concept of what a Pearson correlation means.
Student applied concept of correlation to income and SAT Scores to show working knowledge of material.   0.5
Student identifies type of data used in correlation.   0.5
Student explores why correlation does not equal causation   0.5
APA 6th Edition   1
Format   2
Student uses correct spelling, grammar and sentence structure.
Total   5

 

Intellectual Elaboration:

So far we have looked at descriptive statistics which show how data looks and inferential statistics which means you are looking to draw a conclusion beyond what the immediate data present can tell you. This week we will look at the relationship between statistical tests and why they are used to look at similarities within data.

Correlation is when we look at the relationship between two items (Tanner, 2011). When you eat spicy food you may notice that you have heartburn. This means that there could be correlation between spicy food and digestion issues. You may notice that when the moon is full dogs bark in your neighborhood which means there may be a correlation between the full moon and dogs barking.  To find out if there is a relationship between the variables of spicy food and digestion issues or dogs barking and the full moon you can collect and analyze the data. To determine the strength of these relationships (as opposed to testing the differences present such as with the z-test or t-test) you will want to test for a hypothesis of association.  When the statistics are significant this means that there is a relationship within the variables being tested.

A correlation in the hypothesis of association, meaning that there is a relationship between the variables being studied, is judged by a -1.0 or a +1.0. The closer to 1.0 that a correlation is the more perfect the correlation is in its relationship.  A positive correlation (closer to +1.0) means that as variable A increases so does variable B and as variable A decreases so does variable B.  A negative correlation (closer to -1.0) means that as variable A increases variable B decreases (Lanthier, 2002). When testing the hypothesis of a correlation the null hypothesis will mean that there is no relationship between the variables (the opposite of the null hypothesis of the t-test and ANOVA in which the null hypothesis states that there is no change between variables). The alternative hypothesis (that you take if the null hypothesis is not true) is that there is a statistically significant correlation between the two variables (Tanner, 2011).

In order to test correlation you can use different correlations such as the Pearson correlation or the Spearman Rho. With the Pearson correlation you are using interval or ratio data, while with the Spearman Rho you are using data from an ordinal scale (Tanner, 2011). An example of a ordinal scale is a Likert Scale used in research to rank preference on a scale of 1 to 5.

It is also important to recognize that correlation, a statistical significance in the relationship within groups, does not necessarily mean that one variable causes another variable (Tanner, 2011). For example let’s say that you have three foods, a pepper and onion pizza, jalapeno poppers, and an onion petal with a zesty dipping sauce. You notice after all three meals that you do not feel good.  You know there is a correlation between eating these foods; however do you know there is causation with the spiciness of the foods? What if you do not know you are lactose intolerant and the dairy in these foods is the culprit? This means there is still a correlation between your illness and these foods however other spicy foods without dairy will not have the same effect on you. Therefore the food has two variables, dairy and spice, and the variable of spicy food is not a cause.

When looking at regression we use the relationship between variables (such as a statistically significant correlation) to make a prediction that variable A will cause an effect on variable B. This type of analysis can be seen in the predictions of our economy.  If unemployment is going up what does that mean for the consumer market?  It unemployment is going down, does this mean that consumer spending will go up? It is through the use of correlations that we are able to make a prediction through the use of regression through predictor and criterion variables (Tanner, 2011).

 

Additional Resources (web links, videos, and articles):

Correlationhttp://www.nvcc.edu/home/elanthier/methods/correlation.htm

Please Watch the Video: Tests of Difference

References:

Lanthier, E. (2002). Correlation. Retrieved from http://www.nvcc.edu/home/elanthier/methods/correlation.htm

 

Tanner, D. (2011). Statistics for the behavioral & social sciences. San Diego, CA: Bridgepoint Education, Inc.

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