Correlation

Does high school grade point average (GPA) predict college performance? Does reading to a child help future school performance? Researchers, legislators, business people, teachers, and parents are all interested in how variables are related. This relationship is the general way in which different values of one variable are associated with different values of a second variable. The degree of relation permits us to predict future behavior and performance. Correlation can refer to either the statistic used to represent the degree of relation between two variables or to the correlational level of interpretation in research methods.

The correlation coefficient, often denoted as r, is a statistic that describes how strongly variables are related. The correlation coefficient ranges from −1.00 to +1.00. It provides two important pieces of information about the relationship between two variables. The strength describes the degree of relation in numerical terms. The closer to 1.00, the stronger the degree of relation. When describing the strength of the correlation, the sign, either positive or negative, is ignored. Zero indicates that the two variables are not related. In other words, knowing variable A does not tell you anything about variable B. Knowing a person’s shoe size tells you nothing about his intelligence. In contrast, a correlation of 1.00, either positive or negative, would allow you to perfectly predict changes in variable B from  changes  in  variable A.  Most  correlations  fall somewhere  between  zero  and  1.00. The  correlation between high school GPA and first year college success is about +.5. This means that about 25% of the variability in first year college success can be explained by high school performance. The percentage of variability explained is obtained by squaring the correlation.

The sign of the correlation provides information about the direction of the relationship between the two variables. A positive correlation indicates that the variables change in the same direction. In other words, when the values of one variable increase/decrease, the values of the second variable increase/decrease in the same direction. For example, on average, the more a person studies for a test the better their grade tends to be. Both variables change in the same direction.

A negative correlation indicates that the variables changed in opposite directions. In other words, when the values of one variable increase/decrease, the values  of  the  second  variable  increase/decrease  in the opposite direction. For example, there is less hot chocolate consumed in the summer than in the winter. Therefore, the relation between amount of hot chocolate consumed and outside temperature is negative.

Correlational designs, nonexperimental designs that seek to describe relationships between variables without directly manipulating the variables, are useful for prediction. The major problem with the use of findings from correlational designs is that they are often interpreted in a causal manner. Correlations can be used in research involving both experimental and nonexperimental methods. It is important to note that causality cannot be inferred from correlational analysis when working with the nonexperimental methods. Without proper experimental control, researchers cannot determine the direction of cause and effect. For example, in a bivariate relationship, the change in variable X could cause the change in variable Y. However, it is also conceivable that variable Y is causing the change in variable X. When a nonexperimental method is used, there is also the danger that no direct causal relationship exists between the two variables. Instead there may be a relationship between the two variables because some other variable causes them both. This third variable limits the ability of the researcher to identify the cause of changes in the variables.

References:

  1. Cozby, P. (2001). Methods in behavioral research (7th ed.). Palo Alto, CA: Mayfield.
  2. Everitt, S. (2001). Statistics for psychologists. Mahwah, NJ: Erlbaum.
  3. StatSoft, (n.d.). Basic statistics: Correlations. Retrieved from http://www.statsoft.com/textbook/stbasic.html
  4. Trochim, W. (2001). The research methods knowledge base (2nd ). Cincinnati, OH: Atomic Dog.