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About For the specified null of five independent donors per arm and twenty conditionally independent Bernoulli observations per donor with latent Beta(5,5) success probabilities (within-donor correlation 1/11), the cell-level two-sided probability-ordering Fisher test at nominal alpha=0.05 rejects with exact-model probability 0.215670659198, versus 0.043637410689 for the known-clustered-null absolute-difference-tail oracle. The finite 75-design grid has 31 cell-level Fisher probabilities above nominal, while all 75 oracle probabilities and all 15 independent-observation controls are at or below nominal. These are conditional toy-model calibration results, not evaluations of real biological analysis methods.

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