# & Data Analysis

The following module includes a discussion of basic types of correlational studies and common statistical techniques used to analyze data from these studies.

Learning Objectives:

• Describe the three basic types of correlational studies.
• Explain statistical techniques used for correlational data including bivariate correlations, multivariate correlations and regression analysis.

Types of Correlational Studies

There are several ways to collect data in an effort to show a correlation between variables.  The three most common types of correlation studies are described below:

• Naturalistic Observation is when a researcher collects data by observing subjects in their natural environment without interfering or interacting with them in any way. This type of observation is commonly used when lab experimentation is not possible, feasible or ethical.  An example may be that a researcher wants to see if there if there is correlation between class participation and grades by observing the amount of participation by subjects in a classroom.  This method can be time-consuming but offers the advantage of being assured that the subjects are behaving normally.
• Survey Research is done by gathering information from a random selection of subjects through the use of mail surveys, email or internet surveys, or interviews. Survey research is relatively simple to perform once the survey questions have been developed and the researcher can reach a large number of potential subjects quickly.  The drawbacks are that the response rate can be low and there is no guarantee that the subjects are being honest.  An example of survey research that is testing for a correlation could be a researcher who is looking for a correlation between home ownership and education level by surveying home owners and asking about their education level.
• Archival Research involves analyzing data that has previously been collected by others and looking for correlations. The researcher does not have control over the data or how it was gathered, however, the researcher may have access to large amounts of data with relatively little effort and often the data is free.  For example, a researcher may examine the crime statistics of several neighborhoods to see if there is any correlation with crime and a sluggish housing market in particular areas.

Statistical Techniques

Researchers use several statistical techniques to look for correlations in the data collected through these types of studies.  While this module does not allow for an in-depth discussion of all of the various statistical techniques used in correlational studies, following is a list of the commonly used analyses:

• The most common statistical test is the calculation of the correlation coefficient (r), as discussed in the previous module in this series. This is a bivariate correlation analysis that is a measure of the strength of the relationship between two variables. There are several different correlation coefficient calculations and the types of calculation used depends on the data type.  The Pearson Correlation Coefficient is the most common, but the following link offers a key that helps determine which calculation is appropriate:  Choosing a Correlation Test.   Refer to the previous module and the Resource Links on this page for more information about the correlation coefficient.
• Regression analysis allows for the analysis of more than just two variables. It used to examine one or more independent variables (multiple variables) to predict a single dependent variable or outcome.  For example, a researcher may be looking at a the monthly discretionary spending of families (dependent variable) and looking for correlations with other variables such as the number of children, income, college education, and size of home (the independent variables).   The regression analysis is commonly used to look for linear relationships (linear regression analysis), but there are other forms as well.  The regression analysis is used to develop predictions.
• Path Analysis is an extension of regression analysis for more than a single dependent variable or outcome. This allows for testing of more complex theoretical models
• Canonical correlation analysis is used to examine the possible correlation between two different linear sets of variables. For example, the researcher may examine the presence of two variables – diagnosis of clinical depression and recent traumatic life events – on those that attempted suicide.

The following video summarizes the statistical techniques covered in this module using graphical representations and specific examples.  This module provided an introduction to these topics and the video reviews the material well. For more detailed information about correlational statistical techniques, please see the Resource Links on this page.

• Bordens, K. S., & Abbott, B. B. (2002). Research design and methods: A process approach. McGraw-Hill.
• Gall, M. D., Borg, W. R., & Gall, J. P. (1996). Educational research: An introduction. Longman Publishing.
• Feldman, C. F., & Hass, W. A. (1970). Controls, conceptualization, and the interrelation between experimental and correlational research. American Psychologist, 25(7), 633.
• Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (1993). How to design and evaluate research in education (Vol. 7). New York: McGraw-Hill.
• Keppel, G., & Zedeck, S. (1989). Data analysis for research designs. Macmillan.
• Lee Rodgers, J., & Nicewander, W. A. (1988). Thirteen ways to look at the correlation coefficient. The American Statistician, 42(1), 59-66.
• Slavin, R. E. (1992). Research methods in education. Allyn & Bacon.
• Wilkinson, L. (1999). Statistical methods in psychology journals: guidelines and explanations. American psychologist, 54(8), 594.