kaal:claim:7598518-038

Claim. A positive reading on substrate G needs nine superior labels, and if the ten percent arm's retention exceeds 0.90 in a family the pool cannot be labeled superior to it there and no positive reading is possible.

Type. design · Support. stated

Holds when

• The power calculation assumes a normal approximation and a planning alternative fixed before the runs.
• The stated power covers the labels only and not the gates.

Source quote

A positive reading on substrate G needs nine superior labels. For a contrast with paired seed-level standard deviation sd over S seeds, se = sd/ S. Under a normal approximation and a true effect δalt, the label power is ( Φ​ δalt−max(δ, z1−0.05/24 se) se ), z1−0.05/24 ≈ 2. 865, where z1−0.05/24 is the critical value at the most demanding Holm step and Φ is the standard normal distribution function. The design takes the product of the nine single-test powers as the conjunction power. At S = 200 and δalt = 0. 15, the break-even sd for a conjunction power of 0. 80 is about 0. 36, a figure that holds only when the comparator's retention is at most 0. 85. If the ten percent arm's retention exceeds 0.90 in a family, the pool cannot be labeled superior to it there, and no positive reading is possible.

From. Wulf A. Kaal, Can Reputation Prevent Model Collapse? A Preregistered Test of Reputation-Weighted Data Filtering (2026). Full text.

Cite as. Wulf A. Kaal, Can Reputation Prevent Model Collapse? A Preregistered Test of Reputation-Weighted Data Filtering (2026). SSRN: https://ssrn.com/abstract=7598518

Verify. sha256 of source PDF cd22d148b2b55c2e27f087dcaa61cdf44ad7022b400b355c31a9cd7e43a31749 at https://wulfkaal.com/papers/7598518.pdf

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