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To implement the methods of variance estimation described in this book, one needs to have computer software of known quality and capability. One can write original software for this purpose or purchase a commercially available software package. [ABSTRACT FROM AUTHOR]

Transformations find wide areas of application in the statistical sciences. It often seems advantageous to conduct an analysis on a transformed data set rather than on the original data set. Transformations are most often motivated by the need or desire to [ABSTRACT FROM AUTHOR]

Missing data due to nonresponse, edit failure, and other factors appear in all surveys of human populations. Standard methods of handling missing data can result in an inflation in the estimator variance relative to the variance that would have occurred had all data been observed. This final appendix defines the extra variability and summarizes several methods that can be used to ensure that it properly reflected in the variance estimates. [ABSTRACT FROM AUTHOR]

We shall now introduce measurement (or response) errors and look briefly at the properties of variance estimators when the data are contaminated by such errors. [ABSTRACT FROM AUTHOR]

Inferences from large, complex sample surveys usually derive from the pivotal quantity [ABSTRACT FROM AUTHOR]

In this book, we have studied several practical methods for variance estimation for complex sample surveys. And at this point we address briefly the ultimate question: which of the various methods can be recommended and under what circumstances can they be recommended? [ABSTRACT FROM AUTHOR]

The method of systematic sampling, first studied by the Madows (1944), is used widely in surveys of finite populations. When properly applied, the method picks up any obvious or hidden stratification in the population and thus can be more precise than random sampling. In addition, systematic sampling is implemented easily, thus reducing costs. [ABSTRACT FROM AUTHOR]

In this chapter, we discuss the possibility of a simple mathematical relationship connecting the variance or relative variance of a survey estimator to the expectation of the estimator. If the parameters of the model can be estimated from past data or from a small subset of the survey items, then variance estimates can be produced for all survey items simply by evaluating the model at the survey estimates rather than by direct computation. We shall call this method of variance estimation the method of generalized variance functions (GVF). [ABSTRACT FROM AUTHOR]

In sample surveys of both simple and complex designs, it is often desirable or necessary to employ estimators that are nonlinear in the observations. Ratios, differences of ratios, correlation coefficients, regression coefficients, and poststratified means are common examples of such estimators. Exact expressions for the sampling variances of nonlinear estimators are not usually available and, moreover, neither are simple, unbiased estimators of the variance. [ABSTRACT FROM AUTHOR]

In the foregoing chapters,wediscussed three replication-based methods of variance estimation. Here we close our coverage of replication methods with a presentation of Efron's (1979) bootstrap method, which has sparked a massive amount and variety of research in the past quarter century. For example, see Bickel and Freedman (1984), Booth, Butler, and Hall (1994), Chao and Lo (1985, 1994), Chernick (1999), Davison and Hinkley (1997), Davison, Hinkley, and Young (2003), Efron (1979, 1994), Efron andTibshirani (1986, 1993, 1997), Gross (1980), Hinkley (1988), Kaufman (1998), Langlet, Faucher, and Lesage (2003), Li, Lynch, Shimizu, and Kaufman (2004), McCarthy and Snowden (1984), Rao,Wu, and Yue (1992), Roy and Safiquzzaman (2003), Saigo, Shao, and Sitter (2001), Shao and Sitter (1996), Shao and Tu (1995), Sitter (1992a, 1992b), and the references cited by these authors. [ABSTRACT FROM AUTHOR]

In Chapters 2 and 3, we discussed variance estimating techniques based on random groups and balanced half-samples. Both of these methods are members of the class of variance estimators that employ the ideas of subsample replication. Another subsample replication technique, called the jackknife, has also been suggested as a broadly useful method of variance estimation. As in the case of the two previous methods, the jackknife derives estimates of the parameter of interest from each of several subsamples of the parent sample and then estimates the variance of the parent sample estimator from the variability between the subsample estimates. [ABSTRACT FROM AUTHOR]

Efficiency considerations often lead the survey designer to stratify to the point where only two primary units are selected from each stratum. In such cases, only two independent random groups (or replicates or half-samples) will be available for the estimation of variance, and confidence intervals for the population parameters of interest will necessarily be wider than desired. To overcome this problem, several techniques have been suggested. One obvious possibility is to apply the first version of rule (iv), Section 2.4.1, letting the random group method operate within the strata instead of across them. Variations on the collapsed stratum method offer the possibility of ignoring some of the stratification, thus increasing the number of available random groups. A bias is incurred, however, when the variance is estimated in this manner. Other proposed techniques, including jackknife and half-sample replication, aim to increase the precision of the variance estimator through some form of "pseudoreplication." [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The theory and applications of survey sampling have grown dramatically in the last 60 years. Hundreds of surveys are now carried out each year in the private sector, the academic community, and various governmental agencies, both in the United States and abroad. Examples include market research and public opinion surveys; surveys associated with academic research studies; and large nationwide surveys about labor force participation, health care, energy usage, and economic activity. Survey samples now impinge upon almost every field of scientific study, including agriculture, demography, education, energy, transportation, health care, economics, politics, sociology, geology, forestry, and so on. Indeed, it is not an overstatement to say that much of the data undergoing any form of statistical analysis are collected in surveys. [ABSTRACT FROM AUTHOR]

The orthogonal matrices used in defining half-sample replicates in Chapter 3 are known in mathematics as Hadamard matrices. A Hadamard matrix H is a k × k matrix all of whose elements are +1 or −1 that satisfies H′H = kI, where I is the identity matrix of order k. The order k is necessarily 1, 2, or 4t, with t a positive integer. [ABSTRACT FROM AUTHOR]