The coefficient of correlation is a quantitative value of the relationship between two or more variables. The correlation coefficient can range from .00 to 1.00 in either a positive or negative direction. Thus, perfect correlation is 1.00 (either +1.00 or –1.00), and no relationship at all is .00 (see the sidebar for examples of perfect correlations and examples of no correlation).
Positive Correlation
A positive correlation exists when a small value for one variable is associated with a small value for another variable and a large value for one variable is associated with a large value for another. Strength and body weight are positively correlated: Heavier people are generally stronger than lighter people. (The correlation is not perfect because some lighter people are stronger than some heavier people and weaker than some who weigh even less.)
Figure 8.1 is a graphic illustration of a perfect positive correlation involving boys. Notice that Bill’s body weight is 70 lb (32 kg) and his strength measure is 150 lb (68 kg). Dick’s data are weight = 80 lb (36 kg) and strength = 175 lb (79 kg); the increase continues through Tom’s data where weight = 110 lb (50 kg) and strength = 250 lb (113 kg). Thus, when the scores are plotted, they form a perfectly straight diagonal line. This is perfect correlation (r = 1.00). The relative positions of the boys’ pairs of scores are identical in the two distributions. In other words, each boy is the same relative distance from the mean of each set of scores. Common sense tells us that perfect correlation does not exist in human traits, abilities, and performances because of so-called people variability and other influences.
Figure 8.2 illustrates a more realistic relationship using the PGA data presented at the end of chapter 6. The data are from 30 PGA players (2008 year), and the correlation is between the percentage of greens hit in regulation (x axis) and number of putts per round (y axis). The correlation is r = .549, which is significant at p = .002 with 28 degrees of freedom (number of participants, N – 2, called df). As can be observed, the data points (each point represents one person—read to the x axis for the percentage of greens in regulation and to the y axis for putts per round) generally progress from the lower left to the upper right representing a relationship but not a perfect one.
Negative Correlation
In figure 8.3, we have plotted the PGA data for driving distance versus driving accuracy. The correlation is r = –.594, p < .001, dfs = 28. This means that the correlation is negative—driving the ball a greater distance is negatively related to driving the ball into the fairway. This relationship is shown in figure 8.3 in which the general pattern of the data points is from upper left to lower right. This is a negative correlation. A perfect negative correlation would be a straight diagonal line at a 45° angle (the upper left corner of the graph to the lower right corner). Figure 8.3 depicts a negative correlation of a moderate degree (r = –.594), but an upper-left-to-lower-right pattern is still apparent.
