Prerequisites
Study design, intraclass correlation, variance, sampling and human-participant research ethics.
For equal cluster size m and intraclass correlation rho, a common planning approximation is DE = 1 + (m - 1)rho. Approximate effective sample size is n/DE. This is not a full analysis plan; few clusters, unequal sizes, missingness and estimand choice require more care.
Worked example
With 196 fictional participants in equal clusters of 28 and rho = 1/27, DE = 2 and approximate effective size is 98. Shared conditions within classes mean participants are not 196 independent replications of classroom assignment.
Further inquiry
Derive the equal-cluster planning design effect from the variance of a mean under a common within-cluster correlation. Discuss unequal cluster sizes, a small number of randomized classes, and what an appropriate inferential plan would need. Use only fictional data and preserve access to essential supplies in any proposed design.
Review criteria
- State the equal-size and correlation assumptions instead of treating the shortcut as universal.
- Identify the unit of assignment separately from the participant count.
- Explain uncertainty, safeguarding and privacy limits without collecting personal hygiene records.