A correction factor for the impact of cluster randomized sampling and its applications.

Cluster randomized sampling is 1 method for sampling a population. It requires recruiting subgroups of participants from the population of interest (e.g., whole classes from schools) instead of individuals solicited independently. Here, we demonstrate how clusters affect the standard error of the mean. The presence of clusters influences 2 quantities, the variance of the means and the expected variance. Ignoring clustering produces spurious statistical significance and reduces statistical power when effect sizes are moderate to large. Here, we propose a correction factor. It can be used to estimate standard errors and confidence intervals of the mean under cluster randomized sampling. This correction factor is easy to integrate into regular tests of means and effect sizes. It can also be used to determine sample size needed to reach a prespecified power. Finally, this approach is an easy-to-use alternative to linear mixed modeling and hierarchical linear modeling when there are only 2 levels and no covariates.