Correcting a significance test for clustering

Larry V. Hedges*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


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 p. 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 p = 0. It reduces to the t statistic computed using cluster means when p = 1. If 0 < p < 1, it lies between these two, and the degrees of freedom are in between those corresponding to these two extremes.

Original languageEnglish (US)
Pages (from-to)151-179
Number of pages29
JournalJournal of Educational and Behavioral Statistics
Issue number2
StatePublished - Jun 2007


  • Cluster-randomized trials
  • Intraclass correlations
  • Multilevel models
  • Significance tests

ASJC Scopus subject areas

  • Education
  • Social Sciences (miscellaneous)


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