An Introduction to Bootstrap Methods with Applications to R

4

HYPOTHESIS TESTING

There are many ways to do hypothesis testing by the bootstrap. Perhaps the simplest is the inversion of a bootstrap confidence interval, which takes advantage of the 1-1 correspondence of confidence intervals and hypothesis tests. This will be discussed in Section 4.1.

We briefly review the basic ideas of the Neyman–Pearson approach to hypothesis testing. Usually, in research, we are interested in an outcome variable (in clinical trials, this is called an end point). A null hypothesis is formed with the hope of rejecting it. Often, the null hypothesis states that the endpoint parameter is zero.

For example, in a clinical trial, the end point could be the difference in response to a drug, where we are interested in the difference between the mean for the population of patients getting the drug and the population of patients on placebo. A value of zero is uninteresting since it indicates that the drug is ineffective.

It may be that a small difference is also not good as the drug may not be worth marketing if it provides little improvement over placebo. The magnitude of the difference that is large enough to market the drug is often referred to in the pharmaceutical industry as the clinically significant difference.

In general, hypothesis tests can be one sided or two sided. For a two-sided test, we are interested in knowing that there is a large difference regardless of whether the difference is positive or negative. This would be the case if the two treatments ...