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The Stata Journal
Volume 4 Number 2: pp. 142-153

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Sample size and power calculations using the noncentral t–distribution

David A. Harrison
ICNARC, London, UK
Anthony R. Brady
ICNARC, London, UK
Abstract.   The standard formulas for sample size and power calculation, as implemented in the command sampsi, make use of a normal approximation to the t-distribution. When the sample sizes are small, this approximation is poor, resulting in overestimating power (or underestimating sample size). One particular situation in which this is likely to be important is the field of cluster randomized trials. Although the total number of individuals in a cluster randomized trial may be large, the number of clusters will often be small. We present a simulation study from the design of a cluster randomized crossover trial that motivated this work and a command to perform more accurate sample size and power calculations based on the noncentral t-distribution.
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