Restricted Range

Consider a study that investigated the correlation between arm strength and grip strength for 147 people working in physically-demanding jobs. Do you think the correlation was higher for all 147 workers tested, or for the workers who were above the median in grip strength? The upper portion of the figure below shows that the scatterplot for the entire sample of 147 workers. The lower portion of the figure shows the scatterplot for the 73 workers who scored highest on grip strength. The correlation is 0.63 for the sample of 147 but only 0.47 for the sample of 73. Notice that the scales of the X-axes are different.

Whenever a sample has a restricted range of scores, the correlation will be reduced. To take the most extreme example, consider what the correlation between high-school GPA and college GPA would be in a sample where every student had the same high-school GPA. The correlation would necessarily be 0.0.

Click here for an interactive demonstration of the effect of restriction of range and here for a related demonstration.