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Cluster randomisation design effect: Cluster size variance uses a sample divisor · case 04

Design effects for a fixed set of clusters are inflated.

Member previewVariant 4 · 3 implementations · 8 checks per implementation

Case contract

For clusters (e.g. companies) randomised as units: mean size m, population variance of sizes / m^2 = cv^2, design effect = 1 + ((cv^2 + 1) m - 1) icc. Effective sample = total units / design effect; clusters needed = ceil(n_required * design effect / m). No clusters or zero mean -> None. Return [round(deff, 6), round(effective n, 6), clusters needed].

Why this case matters

B2B experiments randomise by account; ignoring clustering makes results look far more certain.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
unequal cluster sizes inflate the design effect	`[2.741667, 29.179331, 69]`	`[2.54375, 31.449631, 64]`	Failed

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