逝去的青春

Bootstrapping is a resampling procedure which can be used to generate confidence intervals around a given statistic. Bootstrapping works by randomly choosing (with replacement) n stud- ies from a sample size of n, and then calculating the desired statistic. For example, if there were fifty studies in total, fifty studies would be chosen for each bootstrap iteration. However, because bootstrapping is sampling with replacement, some of the studies from the original sample would be chosen more than once, while others would not be chosen at all. This pro- cedure is repeated many times to generate a distribution of possible values. The lowest and highest 2.5% values are then chosen to represent the lower and upper 95% bootstrap confidence limits (or whatever percentiles are appropriate for the desired a value).

Confidence intervals generated in this way are called percentile bootstrap confidence inter- vals, because they are calculated by merely choosing certain percentile values (Dixon 1993). These confidence intervals assume that the distribution of bootstrap values is centered around the original value. When this is the case, the percentile bootstrap is known to produce the cor- rect confidence intervals (Efron 1982, Dixon 1993). However, when more than 50% of the bootstrap replicates are above or below the original value, the bootstrap confidence interval should be corrected for this bias (details can be found in Dixon 1993).

In meta-analysis, bootstrapping is generally used to generate confidence intervals around average effect sizes (either the global average or individual group/category averages, when appropriate). For example, in the Lepidoptera meta-analysis discussed above, the bootstrapped confidence interval for the grand mean under the fixed-effects model was 0.2252 to 0.4978, wider than the parametric confidence interval calculated before, but still excluding the ex- pected null value of zero.