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One-sample location tests for multilevel data. (English) Zbl 1182.62102

Summary: We consider testing the location parameter with multilevel (or hierarchical) data. A general family of weighted test statistics is introduced. This family includes extensions to the case of multilevel data of familiar procedures like the \(t\), the sign and the Wilcoxon signed-rank tests. Under mild assumptions, the test statistics have a null limiting normal distribution which facilitates their use. An investigation of the relative merits of selected members of the family of tests is achieved theoretically by deriving their asymptotic relative efficiency (ARE) and empirically via a simulation study. It is shown that the performance of a test depends on the clusters configurations and on the intracluster correlations. Explicit formulas for optimal weights and a discussion of the impact of omitting a level are provided for 2 and 3-level data. It is shown that using appropriate weights can greatly improve the performance of the tests. Finally, the use of the new tests is illustrated with a real data example.

MSC:

62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
65C60 Computational problems in statistics (MSC2010)
62F03 Parametric hypothesis testing
62E20 Asymptotic distribution theory in statistics

Software:

Ox
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Full Text: DOI

References:

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