Abstract
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 ρ. 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 ρ = 0. It reduces to the t statistic computed using cluster means when ρ = 1. If 0 < ρ < 1, it lies between these two, and the degrees of freedom are in between those corresponding to these two extremes.
Keywords
Cluster analysisStatisticsComputer scienceTest (biology)Statistical hypothesis testingEconometricsMathematics
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Publication Info
- Year
- 2007
- Type
- article
- Volume
- 32
- Issue
- 2
- Pages
- 151-179
- Citations
- 114
- Access
- Closed
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Cite This
Larry V. Hedges
(2007).
Correcting a Significance Test for Clustering.
Journal of Educational and Behavioral Statistics
, 32
(2)
, 151-179.
https://doi.org/10.3102/1076998606298040
Identifiers
- DOI
- 10.3102/1076998606298040