Pearson Correlation Coefficient
How is the degree of correlation expressed? The strength and direc- tion of a relationship can be expressed as a coefficient of correla- tion. This can be calculated as a number falling somewhere between -1.00 and +1.00. Drawing graphs of relationships can also help clarify their nature (see • Figure 1.9). If the number is zero or close to zero, the association between two measures is weak or nonexistent. For example, the correlation between shoe size and intelligence is zero. (Sorry, size 12 readers.) If the correlation is 1.00, a perfect positive relationship exists (see • Figure 1.9e); if it is -1.00, a perfect negative relationship has been discovered.
The correlation coefficient tells how strongly two measures are related. These graphs show a range of rela- tionships between two measures, X and Y. If a correlation is negative (a), increases in one measure are associated with decreases in the other. (As Y gets larger, X gets smaller.) In a positive correlation (e), increases in one measure are associated with increases in the other. (As Y gets larger, X gets larger.) The center-left graph (b “moderate negative relationship”) might result from comparing time spent playing computer games (Y) with grades (X): More time spent playing computer games is associated with lower grades. The center graph (c “no relationship”) would result from plotting a person’s shoe size (Y) and his or her IQ (X). The center-right graph (d “moderate positive relationship”) could be a plot of grades in high school (Y) and grades in college (X) for a group of students: Higher grades in high school are associated with higher grades in college.
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