THE FOLD / GLITCH / DIVIDE BY ZERO / THE TWO TESTS
THE TWO TESTS
same table, three p-values, one threshold
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
One 2×2 table. 110 of 180 against 128 of 180 — a ten-point improvement. Run a two-proportion z-test with the unpooled standard error and p = 0.0438. Run it with the textbook pooled error and p = 0.0450. Run Fisher’s exact test and p = 0.0581. Two of those are below 0.05 and one is above, and nothing in the data changed between them. “Significant” here is a statement about which test was chosen, not about the numbers.
LIT verified live: every figure in his receipts reproduces from the raw counts alone — z = 1.8527, 2.0155, 1.0131; p = 0.0639, 0.0438, 0.3110; Fisher exact = 0.0998, 0.0581, 1.0000; and all three confidence intervals; the method was recovered by testing — his z uses the unpooled standard error, the same one as his interval, and the pooled form reproduces none of his three; and the spread across tests on the same table is 0.0143.
LIT verified live: every figure in his receipts reproduces from the raw counts alone — z = 1.8527, 2.0155, 1.0131; p = 0.0639, 0.0438, 0.3110; Fisher exact = 0.0998, 0.0581, 1.0000; and all three confidence intervals; the method was recovered by testing — his z uses the unpooled standard error, the same one as his interval, and the pooled form reproduces none of his three; and the spread across tests on the same table is 0.0143.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) printed the z-test, the Fisher exact and the interval side by side in seam-pack/receipts-python.txt. That layout is the whole contribution: a receipts file quoting one p-value would have been unfalsifiable, and quoting three makes the disagreement impossible to miss. Seated at DIVIDE BY ZERO — the threshold that looks like a boundary and is an artefact of the divisor.
AVAN (AI) could not reproduce his z at first. The textbook two-proportion z-test pools the proportions for the standard error, and that gives 1.8268, 2.0043, 1.0065 — close to his figures and matching none of them. Testing the alternative recovered it: he used the unpooled error, which is the same quantity his confidence intervals use, so his z and his CI are internally consistent even though the pooled form is the more common default. Fisher and the intervals matched exactly on the first attempt. Stating the method matters more than the choice here; both are defensible, and only one of them was written down.
AVAN (AI) could not reproduce his z at first. The textbook two-proportion z-test pools the proportions for the standard error, and that gives 1.8268, 2.0043, 1.0065 — close to his figures and matching none of them. Testing the alternative recovered it: he used the unpooled error, which is the same quantity his confidence intervals use, so his z and his CI are internally consistent even though the pooled form is the more common default. Fisher and the intervals matched exactly on the first attempt. Stating the method matters more than the choice here; both are defensible, and only one of them was written down.
3 ONE DIMENSION
Three p-values from one table, and the line they straddle.
4 TWO DIMENSIONS · INTERACTIVE
Move a single success between arms and watch three verdicts disagree.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: one table, three instruments pointed at it.
AVAN’s addition (the inverse-companion): the forward reading is “report more than one test.” The inverse is that the disagreement is information and the threshold destroys it. All three numbers here describe the same evidence and they differ by 0.0143 — a spread that is itself a measurement of how much the answer depends on modelling choices rather than on data. Collapsing any of them to significant or not throws away exactly that. Read backwards, a result whose tests agree closely is telling you something a result whose tests straddle 0.05 is not, and the binary verdict is the one presentation that makes those two cases look identical.
LIT every figure in his receipts reproduces from the raw counts alone — z = 1.8527, 2.0155, 1.0131; p = 0.0639, 0.0438, 0.3110; Fisher exact = 0.0998, 0.0581, 1.0000; and all three confidence intervals; the method was recovered by testing, since his z uses the unpooled standard error (the same one as his interval) and the pooled form reproduces none of his three; and the spread across tests on one table is 0.0143
FIG AVAN could not reproduce his z at first. The textbook two-proportion z-test POOLS the proportions for the standard error, giving 1.8268, 2.0043, 1.0065 — close to his figures and matching none. Testing the alternative recovered it: he used the UNPOOLED error, the same quantity his confidence intervals use, so his z and CI are internally consistent even though pooled is the commoner default. Fisher and the intervals matched on the first attempt. Both choices are defensible; only one was written down.
FIG AVAN could not reproduce his z at first. The textbook two-proportion z-test POOLS the proportions for the standard error, giving 1.8268, 2.0043, 1.0065 — close to his figures and matching none. Testing the alternative recovered it: he used the UNPOOLED error, the same quantity his confidence intervals use, so his z and CI are internally consistent even though pooled is the commoner default. Fisher and the intervals matched on the first attempt. Both choices are defensible; only one was written down.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of DIVIDE BY ZERO · David Lee Wise (ROOT0), with AVAN