Design Effects of Two-Stage Sampling.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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In sampe surveys, the design effect of a statistic is usually defined as the ratio of its true variance under the given sample design to its variance had the sample been obtained by simple random sampling. Empirical work suggests certain patterns for design effects of different types of statistics under different designs but theoretical work explaining these patterns is limited. This paper obtains general theoretical results on the sructure of design effects for a broad class of statistical inference under a two-stage sampling design. In particular, it discusses the relation between design effects of multivariate and of univariate statistics. This relation is of practical interest because it is of relevance to the imputation of standard errors for multivariate statistics such as correlation coefficients or regression coefficients using design effects of univariate statistics. The latter quantities are often routinely derived on completion of the survey. The former may be difficult to compute by standard procedures, either because of the absence of the necessary design information or because of software or degrees of freedom limitations.
- Statistics and Probability