Correlation

A correlation gives you a number, called r, which can range from 0.0 to 1.00 (or -1.00). Zero correlation means there is no relation between two variables. If the correlation between SAT and GPA were zero, then knowing SAT does not let you predict GPA better than just guessing at random. A correlation of 1.00 (either + or -) means perfect correlation. If the correlation between SAT and GPA were 1.00, you could predict a person's GPA exactly from his/her SAT.

The correlation between SAT and GRE is about 0.3 to 0.4, very reasonable values, because correlations between two traits individuals have don't often go as high as 0.5. This means that the predictive relation between most psychological variables is nowhere near perfect.

The sign of the correlation (+ or -) depends only on how you set up the two variables. Suppose, for example, you had the SAT and GPA scores for each person in this class. The SAT is given as the number of points a person got (maximum = 1600). The GPA is usually given on a scale where 4.0 is the maximum. Say that the correlation between SAT and GPA for this class is 0.34.

But the SAT could be changed to the number of points a person missed (instead of the points s/he got). Then two people who had SAT's of 540 and 490 would have scores of 800 - 540 = 260 and 800 - 490 = 310. In this way of reporting SAT's, the lower the score, the better the performance.

If you calculated the class correlation using this reversed system of reporting SAT, then the correlation would be -.34. The only change in the correlation is its sign. The sign (+ or -) of a correlation tells only which direction a relation goes, not how strong it is. In the example, the correlation of .34 is just as strong as the correlation of -.34. Only the direction of the relation has changed. In the original correlation of .34, as SAT increases, on the average the GPA increases. In the correlation of -.34 with the reversed SAT, as the SAT decreases, on the average the GPA increases.

In golf, the lower the score, the better the performance. So if you correlate the year's total winnings for each member on the PGA tour with their total scores for the the year, the correlation would be negative and probably quite high. It's negative and high because lower scores are required to win tournaments and prize money.