Balanced Repeated Replications for Standard Errors

Abstract Balanced repeated replications (BRR) is a general method for computing standard errors. It is useful when mathematical distribution theory is impractical or lacking, and especially for analytical statistics based on complex samples where clustering destroys the independence of observations. Presented are results of methods used to measure standard errors of regression coefficients for several multivariate techniques. The basic designs of the several samples comprised two primary selections (PS) per stratum. Each replication was a half-sample, created by selecting one PS from each stratum. The variance of the coefficient , estimated from the entire sample, is measured by , where bj is the same estimator based on a half-sample. To increase the precision of the variance estimate, select k repeated replications and obtain the mean of the k computed variances, . Balanced repeated replications reduce the number of repetitions needed; e.g., 48 balanced replications sufficed for 47 strata in our samples. Though proofs are complete only for linear statistics, rationale and results are offered to indicate that BRR provides needed estimates of errors for nonlinear statistics. The ratios, , of actual standard errors to those of simple random sampling, (srs), are investigated for several statistics in five empirical studies. In each study the average values of exceed 1.00 and range from 1.05 for less clustered to 1.46 for more clustered samples.