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DOI: 10.3102/1076998606298040 © 2007 American Educational Research Association
Correcting a Significance Test for ClusteringNorthwestern 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
Key Words: cluster-randomized trials significance tests intraclass correlations multilevel models
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. The corrected t statistic has Students t distribution with reduced degrees of freedom. The corrected statistic reduces to the t statistic computed by ignoring clustering when 



