Hypothesis Testing With Complex Survey Data: The Use of Classical Quadratic Test Statistics With Particular Reference to Regression Problems

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Abstract
Sample surveys often have complex sample designs with multistage cluster sampling, stratification, and differential selection probabilities. This article is concerned with testing the null hypothesis H 0: θ = θ, where the p-dimensional parameter θ = g( μ ) and μ is a q-dimensional vector of means. The asymptotic framework that consists of a sequence of increasing finite populations is used to define μ as the limit of finite population means. As part of the inference, we use replicated estimates of variances that take into account the complex sample design. The Wald statistic can be used to test H 0. But inference for θ based on the Wald statistic can have low power. Thus an alternative to using a Wald test is pursued in this article. First, define a classical quadratic test statistic that would be used if one had a simple random sample of the population. Second, treating this quadratic form as a population parameter, use design-based methods to estimate it from the observed survey data. Last, use...

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