median of 9.63, for example, no matter how many samples you drew. For this particular
population the medians must be an integer (or the average of two integers in the ordered
array) between 5 and 11. There are no other possibilities.
Ideally, to calculate a 95% confidence interval we would like to find those outcomes
that cut off 2.5% of the observations at each end of the distribution.^3 With the very dis-
crete distribution we have with medians, there is no point that cuts off the lowest 2.5%
of the distribution. At the extreme, 4/10,000 5 .04% lie at or below a median of 5, and
(496 1 4)/10,000 5 5.00% lie at or below a median of 6. At the other end of the distri-
bution, 4006/10,000 5 40.6% lie at or below 9, and 9997/10,000 5 99.97% lie at or
below 10. To be conservative we would choose the extremes of each of these sets, and
put the confidence interval at 5–10, which includes virtually all of the distribution. We
really have a 99.97% confidence interval, which is probably close enough for any pur-
pose to which we would be likely to put these data. If we were willing to let the lower
bound represent the 5% point, we would have an interval at 6–10. What is important664 Chapter 18 Resampling and Nonparametric Approaches to Data
Figure 18.2 Resampling Statsprogram and results bootstrapping the sample median 10,000 times(^3) This is the simplest approach to obtaining confidence limits, and relies on the 2.5 and 97.5 percentiles of the
sampling distribution of the median. There are a number of more sophisticated estimators, but the one given here
best illustrates the approach.