The most commonly used coefficient of correlation is the Pearson’s product-moment correlation (Pearson’s r), named for the English statistician Karl Pearson. It is a measure of the degree to which pairs of scores occupy the same relative position in each of their data sets. For example, does the person with the highest GPA have the highest high school average, does the person with the second highest GPA have the second highest high school average, etc. Recall that correlation coefficients range from –1.00 to 1.00. Results from correlational analyses are often presented in a correlation matrix such as that shown below. This matrix shows all possible correlations between pairs of a set of variables. In the matrix shown below, the correlations between the variables used in the scatter plots for Figure 5 are shown. Notice that HSAVG and PARTIES have large correlation values with GPA (r = .964 and r = -.945, respectively), whereas HEIGHT (as we expected) does not (r = -.018).

The figure below shows one of the many formulae for calculating the Pearson r. It is a formula based on z-scores that are used to convey information about the relative location of a score(s) within a set of scores. Although it is a definitional formula, and therefore requires more calculation steps than would a computational formula, it shows precisely what the Pearson r measures – consistency of relative location for pairs of scores.

Learning Check #18:
In a large study of twins, the Minnesota Twin study found a correlation of +.71 between the IQ scores of identical twins. Another study found that family income is correlated +.30 with the IQ of children. What do these correlation coefficients mean?

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