6.9 Bootstrap Tests 810.80, at an alternative mean difference. Then pick the fi rst value of n
that achieves that desired power. Just as with the confi dence intervals,
we can sometimes construct a formula for the sample size. However,
when things get more complicated, the sample size can still be deter-
mined numerically by computer and software packages, such as SAS,
STATA, Minitab, Power and Precision, PASS 2000, and nQuery
Advisor, all have capabilities to do sample size determination.
In the Tendril DX trial, one of the steroid - eluting pacing lead trials
that I was involved in, an unpaired t - test (as well as a bootstrap test)
were carried out. For the t - test, I assumed a common standard deviation
for the capture thresholds for the steroid and the control leads. I used
δ = 0.5 V and consider the equal sample size case and the case where
the treatment group gets three times the number of patients that the
control group gets. The test was done at the 0.10 signifi cance level for
a two - sided test (even though a one - sided test is appropriate). The result
was that 99 patients were need for the treatment group and 33 for the
control, with a total sample size of 132.
On the other hand, if we were able to recruit equal numbers in both
groups, we would only have need 49 in each group for a total of 98,
saving 34 patients. Choosing equal sample sizes is the optimal choice
if there were no practical constraints and both groups had distributions
with the same variance. It would not, however, be optimal if the vari-
ances were known to be very different. Detailed output from nQuery
Advisor 4.0 can be found on page 202 of Chernick and Friis ( 2003 ).
6.9 BOOTSTRAP TESTS
We shall demonstrate the use of Efron ’ s percentile method bootstrap
for testing. We will illustrate the approach with a numerical example,
the pig blood loss data. Recall that previously, we listed the 10 blood
loss values for the treatment group. They were 543, 666, 455, 823,
1716, 797, 2828, 1251, 702, and 1078. This gives a sample mean of
1085.9.
We found, using Resampling Stats software, that a two - sided
approximate percentile method 95% confi dence interval for the popula-
tion mean μ (based on 10,000 bootstrap samples would be [727.1,
1558.9]. Now, consider the test where we have a null hypothesis that
μ = μ 0 versus the alternative that μ ≠ μ 0. Then recalling the relationship