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

Abstract

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.

Correlation-adjusted standard errors and confidence intervals for within-subject designs: A simple multiplicative approach

“…I provided code to perform the Winer test in R; we are also finishing a graphing module in R to plot descriptive statistics and corresponding error bars under any of the methods outlined here (Cousineau, Goulet, & Harding, submitted). It also includes the effect of sampling method (Cousineau & Laurencelle, 2015) and extends to other descriptive statistics (Harding, Tremblay, & Cousineau, 2014, The Quantitative Methods for Psychology Coverage of the various 95% confidence interval methods under 2 covariance matrix structures. Between parentheses is the standard deviation of the coverage estimates across 1000 random covariance matrices.…”

Varieties of Confidence Intervals

“…Regarding cluster randomized sampling, Cousineau and Laurencelle (2015) provided a cluster-adjusted CI M . It requires an estimate of the intraclass correlation.…”

“…The intra-class correlation, noted by ρ, must be estimated first (Shrout and Fleiss, 1979). The adjustment factor is given by λ$\lambda =false\frac{1+(n-1)\rho }{1-{\displaystyle \frac{n-1}{kn-1}}\rho }$Multiply L by λ (A9)The value of λ is always larger than 1, reflecting the well-known fact that cluster randomized samples have less precision than simple randomized samples (Kish, 1965; Cousineau & Laurencelle, 2015). …”

“…The value of λ is always larger than 1, reflecting the well-known fact that cluster randomized samples have less precision than simple randomized samples (Kish, 1965; Cousineau & Laurencelle, 2015). …”

A Replication of Waugh and Norman (1965) Primary Memory study

“…The APA (Van-denBos, 2010) recommends that there are always at least 20 participants per group. It is meant to minimize the risk that a homogeneous -but unrepresentative-sample biases the results under cluster sampling (Cousineau & Laurencelle, 2015).…”