Unbiased Estimates of Variance Components With Bootstrap Procedures

This article provides general procedures for obtaining unbiased estimates of variance components for any random-model balanced design under any bootstrap sampling plan, with the focus on designs of the type typically used in generalizability theory. The results reported here are particularly helpful when the bootstrap is used to estimate standard errors of estimated variance components. For the p × i design, Wiley (2000) provided formulas for correcting for bias in bootstrap estimates of variance components. This article extends Wiley's results to any design and any bootstrap procedure. There are important differences in approach, however. In particular, in this article unbiased estimates of variance components are obtained directly for any bootstrap sample through the use of modified expected T-term (uncorrected sums of squares) equations.