2012-4 Two-sample rank tests under complex sampling

Rank tests are widely used for exploratory and formal inference in the health and social sciences.  With the increasing use of data from complex survey samples in medical research, there is increasing demand for versions of rank tests that account for the sampling design. In the absence of design-based rank tests, naive unweighted rank tests are being used in survey analyses even by researchers who otherwise use inferential methods appropriate for the sampling design. We propose a general approach to constructing design-based rank tests when comparing groups within a complex sample and when using a national survey as a reference distribution, and illustrate both scenarios with examples.  We show that the tests have asymptotically correct level and that the relative power of different rank tests is not greatly affected by complex sampling.

Thomas Lumley, Alastair Scott

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2012-3 An empirical-process central limit theorem for complex sampling under bounds on the design effect

Uniform central limit theorems (`Donsker theorems’) have been widely useful in semiparametric statistics, both under iid sampling and for stationary sequences and random fields. Only limited results have been available under complex sampling, especially multistage sampling. In this note we derive a complex-sampling analogue of Ossiander’s bracketing-entropy conditions for a uniform central limit theorem, under the assumption that certain design effects are uniformly bounded. We discuss the plausibility of this assumption in realistic surveys.

Thomas Lumley

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