Bootstrapping

Bootstrapping: Origins and Execution

Although bootstrapping can be used to recover an estimate of any parameter (such as a sample mean), bootstrap methods are most commonly used to calculate measures of the “spread” around a given statistic that can be used in hypothesis testing. The term bootstrapping has its origins in the phrase “to pull oneself up by one’s bootstrap.” This phrase is commonly uttered in reference to an impossible task—something that simulation-based approaches to statistical inference certainly were prior to the advent of computers that were capable of handling such demands. The process of “booting up” a computer is similarly derived from this phrase, and refers to the early days of computing when starting a machine sometimes involved an iterative process of feeding it progressively more complex lines of code.

In understanding how bootstrap methods differ from more traditional, parametric approaches to statistical inference it is perhaps best to begin with reference to a simple example. Suppose that a professor wants to know whether the students in an upper-division communication course that she taught in the spring semester performed better, on average, than students in the same course the previous fall. Because it is an upper-division course, the final grades in both courses exhibited a negative skew, meaning that more students received an A or a B rather than either a D or an F. While this situation is good for the students, and might net the professor higher teaching evaluations, it creates something of a dilemma for her. If the grade distribution in both classes approximated a normal (symmetrical with equal area under the curve on either side of the mean), then testing the null hypothesis that the grade averages for the two classes are not statistically different from one another would be a straightforward matter, as the known properties of the normal distribution allow the professor to calculate measures of variance around the averages from each class. Because the distribution of grades in each class is skewed, [Page 107]however, standard errors around the average grade in each class that are calculated under the assumption that the sampling distributions are normally distributed (and therefore symmetric) are likely wrong.

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