data reflect the relationship in the population, and then to obtain confidence limits simply
by taking the cutoffs for the a/2 percent of each end of the distribution.
As an example, we can look at the data from Macauley on the mental status scores of
older adults. Macauley’s data included 123 adults between the ages of 60 and 97, and we
can look at the relationship between memory performance and age. We would probably
expect to see a negative correlation between the two variables, but the significance of the
correlation is not as useful as confidence limits on this correlation, which give us a better
sense of how strong the relationship really is.
The bootstrap approach to obtaining these confidence limits would involve sampling
123 cases, with replacement, from the XY pairs in the sample, computing the correlation
between the variables, and repeating this a large number of times. We then find the 2.5 and
97.5 percentile of the sampling distribution, and that gives us our 95% confidence limits.
I have written a Windows program, which is available at http://www.uvm.edu/~dhowell/
StatPages/ that will carry out this procedure. (It will also calculate a number of other
resampling procedures.) The results of drawing 2000 resamples with replacement from the
pseudo-population of pairs of scores are shown in Figure 18.8.Section 18.5 Bootstrapping Confidence Limits on a Correlation Coefficient 671Figure 18.8 Sampling distribution and confidence limits on correlation between age and memory
performance in older adults