Hypotheses Testing from Complex Survey Data Using Bootstrap Weights: A Unified Approach

Abstract

Standard statistical methods without taking proper account of the complexity of a survey design can lead to erroneous inferences when applied to survey data due to unequal selection probabilities, clustering, and other design features. In particular, the Type I error rates of hypotheses tests using standard methods can be much larger than the nominal significance level. Methods incorporating design features in testing hypotheses have been proposed, including Wald tests and quasi-score tests that involve estimated covariance matrices of parameter estimates. In this article, we present a unified approach to hypothesis testing without requiring estimated covariance matrices or design effects, by constructing bootstrap approximations to quasi-likelihood ratio statistics and quasi-score statistics and establishing its asymptotic validity. The proposed method can be easily implemented without a specific software designed for complex survey sampling. We also consider hypothesis testing for categorical data and present a bootstrap procedure for testing simple goodness of fit and independence in a two-way table. In simulation studies, the Type I error rates of the proposed approach are much closer to their nominal significance level compared with the naive likelihood ratio test and quasi-score test. An application to an educational survey under a logistic regression model is also presented. Supplementary materials for this article are available online.