Chapter 14 - Bootstrap Methods and Permutation Tests - WH Freeman

14-40 CHAPTER 14 Bootstrap Methods and Permutation Tests
CAUTION
because the details of producing the confidence intervals are quite technical. 10
The BCa method requires more than 1000 resamples for high accuracy. Use
5000 or more resamples if the accuracy of inference is very important. Tilting
is more efficient, so that 1000 resamples are generally enough. Don’t forget
that even BCa and tilting confidence intervals should be used cautiously when
sample sizes are small, because there are not enough data to accurately determine
the necessary corrections for bias and skewness.
The 2002 Seattle real estate sales data are strongly skewed (Figure
14.6). Figure 14.17 shows the bootstrap distribution of the
EXAMPLE 14.10
sample mean x. We see that the skewness persists in the bootstrap distribution and
therefore in the sampling distribution. Inference based on a normal sampling distribution
is not appropriate.
We generally prefer resistant measures of center such as the median or trimmed
mean for skewed data. Accordingly, in Example 14.5 (page 14-18) we bootstrapped
the 25% trimmed mean. However, the mean is easily understood by the public and is
needed for some purposes, such as projecting taxes based on total sales value.
The bootstrap t and percentile intervals aren’t reliable when the sampling distribution
of the statistic is skewed. Figure 14.18 shows software output that includes all four
of the confidence intervals we have mentioned, along with the traditional one-sample
t interval. The BCa interval is
(329.3 − 62.2, 329.3 + 127.0) = (267.1, 456.3)
Observed
Mean
200 300 400 500
Resample means, $1000s
FIGURE 14.17 The bootstrap distribution of the sample means of 5000 resamples from
the data in Table 14.1, for Example 14.10. The bootstrap distribution is right-skewed, so we
conclude that the sampling distribution of x is right-skewed as well.