How often do our two-group decision rules report a false gap when one group's extreme values reach further?
Study 89 · Inconclusive · recorded 6 November 2026 · answer: Not settled · full paper with figures
The question
Earlier studies decided whether two groups' averages differ by rules pairing the plain average with the clipped one, which pulls each group's extreme values in. On made-up comparisons with no true difference, we ask how often each whole rule, applied step by step, reports a false gap on one side, against a limit of 3.75% per side.
Rules fixed before the result
Fixed in advance: on made-up comparisons with no true difference, a rule failed when its false-gap rate was shown above 7.5% (3.75% on either side) and held when its 95% range stayed within those limits, each read on 6,000 comparisons at its own groups. First, study 67's rule had to return its record's 68 false gaps in 2,000, or the study stopped. The advance check saw unequal extremes if its pass chance lay wholly under one half.
Data and method
We rebuilt two studies' ordinary trading days, redrew study 76's made-up comparisons with no true difference, keeping how much further one group's extreme values reach, and ran each earlier rule step by step on every comparison. Study 67's widening was set afresh on each comparison, as its record did, and the rebuilt rule first returned that record's 68 false gaps in 2,000. The period rules used blocks of whole trading days as periods.
The answer
Not settled: on made-up comparisons with no true difference, study 67's widened rule reported a false gap on one side in 3.3% of 6,000 comparisons at its own groups (95% range 2.88% to 3.78%), straddling the 3.75% limit per side. The rules averaging gaps by period were not settled either: study 57's stayed inside its limits, but for studies 58 and 59 every comparison formed too few periods. As fixed in advance, study 55's rule was not measured: its events are about 5.7 times as dispersed as the ordinary days. Where the clipped average first fails, the advance check guarding study 67's rule is passed in 0.25% of cases (range 0% to 22.8%), wholly under one half, so it sees unequal extremes. The plan expected study 67's rule inside its limits and the period rules above them.
Main estimate
0.033 fraction (95% range 0.029 to 0.038)
What it changes
This corrects study 88, which stopped before any data at a check its plan could not pass, and study 86, which stopped when its rebuilt rule missed its earlier record's count: the check now uses more comparisons, and the widening is set on each comparison. No rule or published answer changed; study 67's earlier uses stand with the unsettled rate named. A further stop would have parked the question for the owner.
What remains uncertain
These ordinary days were studied before, by studies 55, 67, 76 and 86, so this is a check within our development data, not on fresh data, and not a market finding. The comparisons match the events' spread, not their shape, and the period rules are imitated without the earlier designs' dependence across periods, so study 57's reading inside its limits is the imitation's alone. For studies 58 and 59 every comparison formed too few periods, so their rate stays unread.
How it was made
Run took 213 minutes; independent code review: approve; the recorded calculation reruns to the same result.
Fingerprints
plan ada0535eb3b7610478069ffb801ad484291962c08180120d5266c6aee7d1f89d result ecf7e4b64dfb0990cf66b8bdbcb9ed37c853601583c7a5dcd8b75dc6ac6dd997
Exploratory work on development data; not a performance claim.