In the center of this figure you can see the sampling distribution of r. To the left is the
obtained correlation (–.268) and upper and lower confidence limits. These are –.43 and –.11.
Because they are both on the same side of 0.00, we also know that our correlation is signif-
icant. The confidence interval may strike you as surprisingly wide, but confidence intervals
on correlation coefficients often are.
The example from Macauley involved a fairly low correlation coefficient that, because it
was only –.268, was nearly symmetrically distributed around 0.00. If we run the same analy-
sis on the beta-endorphin data that we used earlier, we can easily see the skewed nature of the
sampling distribution for large correlations. This result is shown in Figure 18.9.
Figure 18.9 presents two interesting results. In the first place, notice that, because the
correlation is fairly large (r 5 .699), the sampling distribution is very negatively skewed.
In addition, notice how asymmetrical the confidence limits are. The upper limit is .91,
which is a bit more than 20 points higher than r. However, the lower limit is .11, which is
approximately 59 points lower. Whenever we have large correlations the sampling distribu-
tion will be skewed and our confidence limits will be asymmetrical.672 Chapter 18 Resampling and Nonparametric Approaches to Data
Figure 18.9 Sampling distribution of rfor beta-endorphin data for 10,000 resamples