Plain record › Study 1

Is our standard test's lopsided false-alarm rate on stock splits a general effect of skew?

Study 1 · Inconclusive · recorded 26 September 2026 · answer: Not settled · full paper with figures

The question

An earlier methods study on stock splits found that our standard test raised too many false alarms in the tail opposite the sample's skew, and that a bootstrap remedy kept both tails on target. We repeat the check on shares that never split, to tell a general effect of skew from an effect of splits, chance or heavy tails.

Rules fixed before the result

Before any case ran we fixed six simulated cases: low-priced shares, higher-priced shares and a random-sign copy of the low-priced values, each at 221 and 548 values, with 4,000 draws. Skew was blamed if the low-priced shares showed the imbalance and the copy did not, heavy tails if both of the copy's tails were off target in the same direction, and splits or chance if the low-priced shares did not show it. Any other combination reads as cannot say.

Data and method

This is a methods study on simulated samples with a true mean of zero, so every rejection is a false alarm. The values are five-day returns after randomly chosen days in shares that never split and share no company with the stock split events, grouped by share price. The measure is the lower-tail false-alarm rate minus the upper-tail rate, for the standard test and the bootstrap remedy.

The answer

On low-priced shares that never split, whose returns are strongly skewed, the standard test again raised false alarms in its lower tail well above the 2.5% target, as on stock splits. The control meant to tell skew from heavy tails did not work: we gave each value a random sign to remove the skew, but the signs happened to leave the largest values positive, so the copy stayed strongly skewed. By the rules set in advance this combination cannot be read, so the cause is not settled. The bootstrap remedy kept both tails on target only on higher-priced shares at the larger sample size, and failed in the other cases.

What it changes

Nothing changed. The planning rules drawn from the stock split studies, including the choice of the bootstrap remedy, stay limited to stock split studies, and a drafted rule using a bootstrap interval stays on hold.

What remains uncertain

The design could not tell skew from heavy tails, because the copy meant to remove the skew kept it. The low-priced sample was small and carried by its largest values, and the larger cases drew more values than it holds, so they reuse the same values. Only the five-day horizon was tested, there was no sample skewed the other way, and randomly chosen days are not real events.