Busting bootstrap myths

There are two very prevalent myths regarding the bootstrap that we will briefly address in this section.

The first is that the bootstrap is a panacea for small sample sizes. I think at least part of this myth is due to the name the bootstrap, which conjures of images of some rugged person pulling themselves up by the bootstraps and making something from nothing. Unfortunately, the bootstrap does not make something from nothing, nor does it even make more out of less. The important thing to remember is that the accuracy of your bootstrap distribution is completely dependent on the representativeness of your original sample. Refer back to Figure 8.1. Notice that, although the bootstrap distribution and the sampling distribution of sample means have the same shape, the bootstrap distribution was shifted slightly to the left because, by chance, the sample we got had a mean slightly less than the population mean. This will happen. And, of course, the smaller the sample...