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TABLE 3.2 Power Estimates
Sample Size
Test Mean < 6
a
Power
3
0.23
0.84
4
0.04
0.80
5
0.06
0.89
3.3's. Most were a mixture. Table 3.2 illustrates the results; for example,
in our trials, 23% of the bootstrap samples of size 3 from our starting
sample of test results had medians less than 6. If, instead, we drew our
bootstrap samples from the hypothetical “worst-case” population, then
84% had medians less than 6.
If you want to try your hand at duplicating these results, simply take the
test values in the proportions observed, stick them in a hat, draw out
bootstrap samples with replacement several hundred times, compute the
sample means, and record the results. Or you could use the Stata TM boot-
strap procedure as we did. 1
Prepare for Missing Data
The relative ease with which a program like Stata or StatXact can produce
a sample size may blind us to the fact that the number of subjects with
which we begin a study may bear little or no relation to the number with
which we conclude it.
A midsummer hailstorm, an early frost, or an insect infestation can lay
waste to all or part of an agricultural experiment. In the National Institute
of Aging's first years of existence, a virus wiped out the entire primate
colony destroying a multitude of experiments in progress.
Large-scale clinical trials and surveys have a further burden, namely, the
subjects themselves. Potential subjects can and do refuse to participate.
(Don't forget to budget for a follow-up study, bound to be expensive, of
responders versus nonresponders.) Worse, they agree to participate initially,
then drop out at the last minute (see Figure 3.1).
They move without a forwarding address before a scheduled follow-up.
Or simply don't bother to show up for an appointment. We lost 30% of
the patients in the follow-ups to a lifesaving cardiac procedure. (We can't
imagine not going in to see our surgeon, but then we guess we're not
typical.)
The key to a successful research program is to plan for such dropouts in
advance and to start the trials with some multiple of the number required
to achieve a given power and significance level.
1
Chapters 4-7 have more information on the use of the bootstrap and its limitations.
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