Correlation

1. Correlation Advanced Research Methods in Psychology - lecture - Matthew Rockloff

2. 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 “higher” numbers in one variable are associated with “lower” numbers in the second variable (a negative correlation).

3. When to use correlation (cont.) • 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 differencesin the mean values of each variable, while correlation shows associations between the pairs of values.

4. Paired t-test OR correlation ? • 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).

5. Depressed Duck Example 5.1 • In the next example, 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 vise versa? • The Anxiety and Depression test scores for 5 randomly selected Psychiatric hospital patients are illustrated in columns 1 and 2 on the next slide

6. Column 1 Column 2 Example5.1 (cont.)

7. Example 5.1 (cont.) • Calculating a correlation coefficient requires a relatively simple transformation of both sets of values. • In order to compare these two sets of values, the Anxiety and Depression scores must first be measured on comparable scales. • The average of Anxiety scores is 50, and the average of Depression scores is 40. To begin our comparison, we must eliminate these mean differences.

8. Example 5.1 (cont.) • A simple way to do this is to subtract the average for each set. • This will leave each set of values with a mean of “0.” • The next way in which we need to make these values comparable is to make the variance, and likewise standard deviation of the two sets the same.

9. Example 5.1 (cont.) • This is easily accomplished by dividing by the standard deviation of each set. • The 2 sets of transformed scores for Anxiety and Depression both have a mean of “0” and a standard deviation of “1.” • These are so-called z-scores, or standard normal deviates.

10. Example 5.1 (cont.) • A correlation coefficient summarizes whether the scores … • move in the same direction, = positive correlation, • move in the opposite direction, = negative correlation, • or are not linearly related = zero correlation.

11. Example 5.1 (cont.) • To accomplish this goal, multiply the 2 sets of z-scores. • Summing this final column and dividing it by the number of observations (n=5) yields the correlation coefficient (=.60). • Since we expected that Anxiety and Depression would be positively correlated, this is a 1-tailed test. • In some Statistics textbooks you can find a “Table of Critical Values for Pearson Correlation.” • The critical correlation for n=5 is r = .805. • Since our calculated value is less than the critical value, we cannot conclude that this correlation is significant.

12. Example 5.1 - Conclusion There was a non-significant positive correlation between Anxiety and Depression scores, r(3) = .60, p > .05, ns. • Notice that there is no need to include “mean” values, because unlike previous techniques, the correlation coefficient does not answer a question regarding the means of each variable, but rather the association between 2 variables.

13. Example 5.1 Using SPSS • First, we must setup each variable in the SPSS variable view. Although not strictly necessary, we add a variable for “personid.”

14. Example 5.1 Using SPSS (cont.) • Next, we enter the data into the SPSS data view:

15. Example 5.1 Using SPSS (cont.) • The syntax for a correlation is as follows: correlation Variable1 Variable2. • In our example, the following syntax is entered:

16. Row 1 Row 2 Example 5.1 Using SPSS (cont.) • The results appear in the SPSS output viewer:

17. Example 5.1 Using SPSS (cont.) • The correlation syntax allows 2 or more variables to be entered in one command. • The SPSS output shows all pairs of correlations in a matrix format. • As is shown in the output, on the previous slide, it is possible to correlate both Anxiety with Depression (row 1), and separately, Depression with Anxiety (row 2). • Both answers, however, are the same.

18. Example 5.1 Using SPSS (cont.) • In other words, it doesn’t matter which variable comes first in either the hand calculations, or when entered as syntax in SPSS. • In our example, the answer for the correlation coefficient is always: r = .60. • Notice that SPSS calls the correlation coefficient the “pearson correlation.”

19. Example 5.1 Using SPSS (cont.) • Unlike the tables in the back of a statistics textbook, which give a “critical value” for the correlation coefficient, SPSS provides a p-value, or significance, associated with the correlation (i.e., p = .285). As usual, when this p-value is below “.05” we can declare a significant correlation between our 2 paired variables.

20. Example 5.1 Using SPSS (Conclusion) • In our example, however, the correlation was not significant, thus we conclude: There was a non-significant positive correlation between Anxiety and Depression scores, r(3) = .60, p = .29, ns.

21. Thus concludes Correlation Advanced Research Methods in Psychology Week 4 lecture Matthew Rockloff