The random group method of variance estimation amounts to selecting two or more samples from the population, usually using the same sampling design for each sample; constructing a separate estimate of the population parameter of interest from each sample and an estimate from the combination of all samples; and computing the sample variance among the several estimates. Historically, this was one of the first techniques developed to simplify variance estimation for complex sample surveys. It was introduced in jute acreage surveys in Bengal by Mahalanobis (1939, 1946), who called the various samples interpenetrating samples. Deming (1956), the United Nations Subcommission on Statistical Sampling (1949), and others proposed the alternative term replicated samples. Hansen, Hurwitz, and Madow (1953) referred to the ultimate cluster technique in multistage surveys and to the random group method in general survey applications. Beginning in the 1990s, various writers have referred to the resampling technique. All of these terms have been used in the literature by various authors, and all refer to the same basic method. We will employ the term random group when referring to this general method of variance estimation.
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