Correlational Research: An overview

1. Correlational Research: An overview

2. Definition and Purpose Correlational research involves the collection of data to determine the extent to which two (or more) variables are related. If a relationship exists, we say that the two variables covary in some non-random way. The strength of the relationship is expressed as a correlation coefficient, r.

3. Purpose of Correlation Research Descriptive: Show (or describe) the associations among variables. Hypothesis testing: Test whether variables expected to be related are, in fact, related. Theory driven. Correlations often occur spuriously. Should not examine correlations, first, and then construct a theory to explain them.

4. The Correlation Coefficient, r The coefficient, r, better known as the Pearson product moment coefficient, gives a quantitative measure of the linear relationship between two variables, X and Y, say. To indicate which variables are being correlated, we sometimes write rXY. An r of -1 (or close to -1) indicates a strong negative or inverse relationship. An r of 1 (or close to 1) indicates a strong positive (or direct) relationship. An r of 0 (or close to 0) indicates a lack (or at least a weak) relationship.

5. A Table of Correlations Correlations among several variables are usually given in a correlation table.

6. A Table of Correlations Only one half of a correlation table need be displayed. The upper triangular half or��

7. A Table of Correlations The lower triangular half.

8. A Table of Correlations Often the diagonal is replaced by dashes.

9. Correlation ? Causation The more highly correlated (i.e. the closer r is to + or � 1) the more accurate are predictions based on the relationship. This, however, does not necessarily imply that one variables is the cause of the other. Implying causation from correlation is what causal comparative research is all about.

10. Correlational Research Design Collect data on two or more variables for each participant in the research study. Minimally accepted sample size is 30. If the measures have low reliability, larger sample sizes are needed. If participants are to be subdivided (say, into males and females) larges sample sizes are needed.

11. Sample Sizes Depends on the reliability of the measures. With reasonable reliability a minimum of 30 cases with bivariate measures is usually acceptable. The statistical test is a t test of the null hypothesis: H0: ?xy = 0.0

12. Interpreting Correlations Correlations close to -1 or to +1 indicate the same high degree of relationship, but in different directions. E.g., an r of -.87 between hours of TV watched and GPA indicates that higher GPSs are associated with lower hours watching TV. Question: Does this mean that more hours spent watching TV leads to lower GPSs?

13. Interpreting Correlations Correlations lower than .5 typically are not very interpretable. Correlations in the 60�s and 70�s are considered adequate for interpreting relationships among variables within groups. Correlations in the 80�s and higher are good for interpreting relationships among variables for individuals. In the end, however, the interpretability of a correlation coefficient depends upon the purpose of the study.

14. The END