Correction, 30 September 2026. Technical wording rewritten in shorter sentences under the readability rule; the meaning is unchanged.
Correction, 1 October 2026. The outcome label now follows the study's value record, which counts this study as having changed a rule or a plan.
Correction, 19 October 2026. This text was reviewed after the study finished, in a catch-up of the earliest studies; the result, outcome and dates are unchanged.
The question
Our resampling tests judge a result against many random rearrangements, some of which tie with it exactly. On data built to contain no effect, or a planted fall of 1.75 percentage points, we ask whether using 199 to 1,999 draws or every possible one, and either of two rules for counting ties, moves each test's false-alarm and detection rates.
Rules fixed before the result
The rules for each possible answer were written down and fixed before any result was seen.
Data and method
We ran the chosen tests on data with no effect, where every rejection is a false alarm, and with a planted fall of 1.75 percentage points in five-session returns, where a rejection is a detection. Each used 199, 499, 999 or 1,999 draws, or every sign arrangement for groups of up to 24 companies, crossed with two tie rules: ties count against rejection, or the result sits at random among them. We compared false-alarm rates per tail and detection rates.
What remains uncertain
Only the five-session window and one pool of stock split events, used by earlier methods studies, were tested. The draws stopped at 1,999, every possible arrangement was counted only for groups of up to 24 companies, and the bootstrap test was run on earlier no-effect data centred at zero, not on the main comparison. Placing the result at random among its ties makes a decision depend on an extra random draw, which a study must fix in advance.