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Neyman's Conservative Variance
The true design variance versus the Neyman estimator as effect heterogeneity grows; coverage of the 95% interval.
Day 36: Neyman's Repeated-Sampling Variancetrue variance
15.378
S₁²/n₁ + S₀²/n₀ − S²τ/N
mean of Neyman V̂
17.629
≈ 17.621 (no S²τ term)
simulated variance
15.653
95% CI coverage
95.6%
≥ 95% ⇒ conservative
estimatesnormal with the true variancenormal with the average estimated variance
A fixed group of patients; only the assignment is random. The true variance of the difference in means subtracts S²τ/N, which the data cannot estimate, so Neyman's estimator is conservative: exact when effects are constant, too large when they vary.