The Ratio Bias in Surveys

原文摘要

Sample survey data are commonly expressed by the ratio mean r = y/x, where both y and x are random variables, each the sum of a survey variable. Most commonly, x is simply the sample size and r the sample mean. Simplicity of computing and presenting this mean gives it considerable advantages, particularly in multi-purpose surveys. Though consistent, it is not an unbiased estimator. Our empirical investigations, set in a theoretical framework, show that the bias in most practical surveys is usually negligible; the ratio of bias to standard error (B/σ) was small in every test, even those based on small subclasses. This bias ratio (B/σ) is necessarily less than Cx, the coefficient of variation of the sample size, which appears as a useful criterion for judging the adequacy of survey samples. It can usually be controlled with practical procedures of stratification and selection with probabilities proportional to size. The difference (r – r′) of two ratio means is used frequently either to measure change between two surveys, or to compare two subclasses of the same survey. A useful limit is found for the bias ratio when the two means are independent. For the important practical cases of correlated means a reasonable and empirical “limit” is found in the greater of the two involved coefficients of variation, Cx and Cx′; this “limit” is borne out in a large variety of empirical results.

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