# Bootstrap Percentile Method Test

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## Chapter: Biostatistics for the Health Sciences: Tests of Hypotheses

Here we will demonstrate bootstrap confidence intervals for the bootstrap percentile method.

BOOTSTRAP PERCENTILE METHOD TEST

Previously, we considered one of the simplest forms for approximate bootstrap con-fidence intervals, namely, Efron’s percentile method. Although there are many oth-er ways to generate bootstrap type confidence intervals, such methods are beyond the scope of this text. Some methods have better properties than the percentile method. To learn more about them, see Chernick (1999), Efron and Tibshirani (1993), or Carpenter and Bithell (2000). However, the relationship given in the previous section tells us that for any such confidence interval we can construct a hy-pothesis test through the one-to-one correspondence principle. Here we will demonstrate bootstrap confidence intervals for the bootstrap percentile method.

Recall that in Section 8.9 we had the following ten values for blood loss for the pigs in the treatment group: 543, 666, 455, 823, 1716, 797, 2828, 1251, 702, and 1078. The sample mean was 1085.9. Using the Resampling Stats software, we found (based on 10,000 bootstrap samples) that an approximate two-sided per centile method 95% confidence interval for the population mean μ was [727.1, 1558.9].

From this information, we can construct a bootstrap hypothesis test of the null hypothesis that the mean μ = μ0, versus the two-sided alternative that μ μ0. The test rejects the null hypothesis if the hypothesized μ0 < 727.1 or if the hypothesized μ0 > 1558.9. We will know μ0 and the result depends on whether or not μ0 is in the confidence interval. Recall we reject H0 if μ0 is outside the interval.