5. Correlation

 

When to use correlation

 

Correlation is a technique that summarizes the relationship between 2 paired variables. The technique gives one number, the correlation coefficient, that expresses whether “higher” numbers in one variable tend to be paired with “higher” numbers in the other variable (a positive correlation), or whether “higher” numbers in one variable are associated with “lower” numbers in the second variable (a negative correlation).

 

Because the paired t-test and correlation use the same type of data (i.e., paired numbers), it is easy to confuse the two techniques. The paired t-test is used to test for differences in the mean values of each variable, while correlation shows associations between the pairs of values. Both tests can be valuable, but answer completely different questions. The important point to remember is that correlation describes whether the individual values within each pair tend to move in the same direction (a positive correlation) or opposite directions (a negative correlation).

 

Example 5.1

 

In the example below, we correlate two scores taken from the same persons. We want to see if clinical measures of Anxiety and Depression are related. Is an anxious person also likely to be depressed and/or is a depressed person likely to be anxious? The Anxiety and Depression test scores for 5 randomly selected Psychiatric hospital patients are illustrated in columns 1 and 2 below: