no relationship, r will be 0, and the points will be scattered across the graph. If the relationship is

perfect the points will lie exactly along a straight line, and r will either be:

: If the variables have a direct or positive relationship, meaning when one goes up, the other

goes up, or

: If the variables have an inverse or negative relationship, meaning when one goes up, the other

goes down

Correlation coefficients can be positive (indicating upward-sloping data) or negative (indicating

downward-sloping data). Figure 15-1 shows what several different values of r look like.

Note: The Pearson correlation coefficient measures the extent to which the points lie along a straight

line. If your data follow a curved line, the r value may be low or zero, as shown in Figure 15-2. All

three graphs in Figure 15-2 have the same amount of random scatter in the points, but they have quite

different r values. Pearson r is based on a straight-line relationship and is too small (or even zero) if

the relationship is nonlinear. So, you shouldn’t interpret

as evidence of lack of association or

independence between two variables. It could indicate only the lack of a straight-line relationship

between the two variables.

© John Wiley & Sons, Inc.

FIGURE 15-1: 100 data points, with varying degrees of correlation.

© John Wiley & Sons, Inc.

FIGURE 15-2: Pearson r is based on a straight-line relationship.

Analyzing correlation coefficients

In the following sections, we show the common kinds of statistical analyses that you can perform on

correlation coefficients.