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Correcting a Significance Test for Clustering

Northwestern University

A common mistake in analysis of cluster randomized trials is to ignore the effect of clustering and analyze the data as if each treatment group were a simple random sample. This typically leads to an overstatement of the precision of results and anticonservative conclusions about precision and statistical significance of treatment effects. This article gives a simple correction to the t statistic that would be computed if clustering were (incorrectly) ignored. The correction is a multiplicative factor depending on the total sample size, the cluster size, and the intraclass correlation . The corrected t statistic has Student’s t distribution with reduced degrees of freedom. The corrected statistic reduces to the t statistic computed by ignoring clustering when = 0. It reduces to the t statistic computed using cluster means when = 1. If 0 < < 1, it lies between these two, and the degrees of freedom are in between those corresponding to these two extremes.

Key Words: cluster-randomized trials • significance tests • intraclass correlations • multilevel models

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