THE FOLD / CHEAT / GOD MODE / THE MISSING N
THE MISSING N
a sample size from a different experiment
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
A page advertised a sample size of 360. A grep for it across the repository the page claims to summarise returned zero hits — and the dead search was itself the finding. The figure is real, but it is the record count of the 180 + 180 comparison, while the effect size printed beside it came from the 60 + 60 one. Two experiments, three times apart in size, with the N of the larger sitting next to the result of the smaller.
LIT verified live: 360 is exactly the record count of the 180+180 comparison; the effect beside it came from a comparison of N = 120, a factor of 3 apart; the two carry very different precision — the 120-record interval spans 35.3 points against 19.4 for the 360-record one, a ratio of 1.81 against the √3 = 1.73 that sampling theory predicts; and the grep returns 0 hits.
LIT verified live: 360 is exactly the record count of the 180+180 comparison; the effect beside it came from a comparison of N = 120, a factor of 3 apart; the two carry very different precision — the 120-record interval spans 35.3 points against 19.4 for the 360-record one, a ratio of 1.81 against the √3 = 1.73 that sampling theory predicts; and the grep returns 0 hits.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) filed it under a heading that admits what it is: DEAD — but this one is a finding. A search that returns nothing is normally a failed search; here the absence was the evidence, because the number being looked for was supposed to be there. Seated at GOD MODE — a sample size borrowed from a larger study makes a smaller result look better armoured than it is.
AVAN (AI) checked whether the two comparisons differ in the way that matters, rather than only in name. They do, and by the amount theory predicts: interval widths scale as 1/√N, so tripling the records should narrow the interval by about 1.73×, and the measured ratio is 1.81. So attaching the larger N to the smaller result is not a labelling slip with no consequence — it implies a precision roughly 1.8× tighter than the data supports. Worth stating plainly: this page verifies the arithmetic of the mismatch, not anyone’s intent, and a mislabelled N is the sort of thing that happens by accident far more often than otherwise.
AVAN (AI) checked whether the two comparisons differ in the way that matters, rather than only in name. They do, and by the amount theory predicts: interval widths scale as 1/√N, so tripling the records should narrow the interval by about 1.73×, and the measured ratio is 1.81. So attaching the larger N to the smaller result is not a labelling slip with no consequence — it implies a precision roughly 1.8× tighter than the data supports. Worth stating plainly: this page verifies the arithmetic of the mismatch, not anyone’s intent, and a mislabelled N is the sort of thing that happens by accident far more often than otherwise.
3 ONE DIMENSION
Two experiments, two intervals, and the N that migrated between them.
4 TWO DIMENSIONS · INTERACTIVE
Attach the wrong N to a result and watch the implied precision tighten.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: two clouds of different size, and one label.
AVAN’s addition (the inverse-companion): the forward reading is “check that the N belongs to the result.” The inverse is that a sample size is not a property of a page, it is a property of a comparison, and pages hold many comparisons while displaying one number. The migration needs no dishonesty and usually gets none — two experiments, one summary line, and the largest available N is the one that reads best. Read backwards, this is why an N should be printed adjacent to its own interval and never in a summary header: separated from the comparison that produced it, it stops being a measurement and becomes a decoration that happens to be numeric.
LIT 360 is exactly the record count of the 180+180 comparison; the effect beside it came from a comparison of N=120, a factor of 3 apart; the two carry very different precision — the 120-record interval spans 35.3 points against 19.4 for the 360-record one, a ratio of 1.81 against the sqrt(3) = 1.73 that sampling theory predicts; and the grep returns 0 hits
FIG The mismatch has a measurable consequence rather than being a labelling slip: interval widths scale as 1/sqrt(N), so tripling the records should narrow the interval by about 1.73x and the measured ratio is 1.81 — attaching the larger N to the smaller result implies a precision roughly 1.8x tighter than the data supports. This page verifies the arithmetic of the mismatch, NOT anyone's intent; a mislabelled N happens by accident far more often than otherwise.
FIG The mismatch has a measurable consequence rather than being a labelling slip: interval widths scale as 1/sqrt(N), so tripling the records should narrow the interval by about 1.73x and the measured ratio is 1.81 — attaching the larger N to the smaller result implies a precision roughly 1.8x tighter than the data supports. This page verifies the arithmetic of the mismatch, NOT anyone's intent; a mislabelled N happens by accident far more often than otherwise.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of GOD MODE · David Lee Wise (ROOT0), with AVAN