Hunter College, City University of New York, Department of Curriculum & Teaching

EDSTATS Primer

Session 8 - Correlational Research

Dr. Anthony G. Picciano, e-mail address: anthony.picciano@hunter.cuny.edu

Topics Covered in this Session

• Definition and Characteristics of Correlational Research
• Appropriateness/Limitations
• Correlation Coefficients/Regression Analysis

Correlational Research

Correlational research is used to explore co-varying relationships between two or more variables. A simple definition of a co-varying relationship is as one variable changes so does the other variable(s). The purpose of correlational research is to:

1. to identify variables that relate to one each other (i.e. is there a relationship between family income and grade point average; is there a relationship between part time employment and grade point average);
2. to make predictions of one variable from another variable (i.e. can I.Q. test scores be used to predict student achievement; can SAT scores be used to predict college grade point averages);
3. to examine possible cause and effect relationships between one variable and another.

A caution has to be advised when considering correlational research and cause and effect. Major researchers such as B.F. Skinner posit that while we can make many conclusions identifying a relationship between one or more variables, establishing cause and effect is very difficult and maybe impossible due to the myriad interactions of many variables in social science research.

In education-based correlational studies, data is frequently collected using standardized measures such as test scores. Report presentations almost always use hypotheses in the form of "No relationship exists between variable X and variable Y." Data analysis using correlation coefficients is generally quantitative. Rather than rich descriptive narrative as we might see in descriptive or ethnographic studies, correlation presentations tend to be succinct relying on statistical analyses of correlation coefficients and regression. Of the various quantitative methodologies, correlational research is among the easiest to design and apply. For this reason, it is popular and frequently used in conjunction with other research methodologies.

Data Sources

• Raw scores such as standardized test scores.
• Measures such as grade point averages.
• Dichotomous data , data which has two possibilities such as male/female or pass/fail.

Research Tools

• Standardized tests are the most common tools for doing correlational studies.
• Direct measurement techniques have also been used for specialized studies such as monitoring student pulse rates to determine stress on test performance.

Procedural Considerations

• Null hypothesis is frequently used.
• Research questions sometimes stated instead of hypotheses.
• Statistics used tend to be measures of relationship such as: Pearson Product-Moment Coefficient, Spearman Rank Order Coefficient, Phi Correlation Coefficient, Regression.

Report Presentation

• Reports are almost always quantitative rather than qualitative presentations.
• Statistical data is provided in the form of correlation coefficients as mentioned above.

Statistical Analysis in Correlational Research

1. Correlation is the relationship between two or more variables or sets of data. It is expressed in the form of a coefficient with +1.00 indicating a perfect positive correlation; -1.00 indicating a perfect inverse correlation; 0.00 indicating a complete lack of a relationship.
2. Pearson's Product Moment Coefficient (r) is the most often used and most precise coefficient; and generally used with continuous variables.
3. Spearman Rank Order Coefficient (p) is a form of the Pearson's Product Moment Coefficient which can be used with ordinal or ranked data.
4. Phi Correlation Coefficient is a form of the Pearson's Product Moment Coefficient which can be used with dichotomous variables (i.e. pass/fail, male/female).
5. Regression the use of correlation to plot a line illustrating the linear relationship of two variables X and Y. It is based on the slope of the line which is represented by the formula : Y = a + bX where
   • Y = dependent variable
   • X = independent variable
   • b = slope of the line
   • a = constant or Y intercept

   Regression is used extensively in making predictions based on finding unknown Y values from known X values. (i.e. predicting college GPA from known high school grade point averages.)

6. Multiple Regression is the same as regression except that it attempts to predict Y from two or more independent X variables (i.e. predicting college GPA from known high school grade point averages and SAT scores.) The formula for multiple regression is an extension of the linear regression formula:

   Y = a + b1 X1 + b2 X2 + ....

FOR MORE INFORMATION ON THE TOPICS COVERED IN THIS SESSION, PLEASE REFER TO CHAPTER 5 OF A.G. PICCIANO "EDUCATIONAL RESEARCH PRIMER".

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