Binomial probabilities for crisp truth-table rows checked

What does an upper-tail probability mean here?

In crisp data, a case is either in or out of a set. For each truth-table row, every included case counts as a trial, and a case belonging to the selected outcome counts as a success. The null probability is the success probability specified for the test. The upper-tail calculation asks how likely it would be to observe that many successes or more if that probability applied.

The reference must use the same integer counts, null probability and tail direction. The procedure does not correct for testing multiple rows. Fuzzy memberships describe degrees of membership, so treating them as binary trials would change the question rather than extend this comparison.

Which versions belong to these checks?

The table identifies the QuickPLS development and installer versions associated with the saved checks. The expected probabilities come from a separate calculation using exact fractions. The record also distinguishes the calculation checks from the installed report-preparation step.

On a small screen, swipe the table sideways to see every column.

Checking the probabilities with exact fractions

The reference checks 102 upper-tail examples with exact rational arithmetic, meaning calculations based on fractions rather than rounded intermediate decimals. There are also eight checks of the underlying calculation routines. The source data are binary and crisp, with cases either in or out of each set.

• The procedure reports unadjusted probabilities for binary crisp data. It does not apply a multiple-testing correction across rows.
• The original files have different line endings, so comparing their bytes gives a mismatch. After the line endings are normalised, the numerical content matches exactly for all 102 rows.
• The installed app prepared the report in this test. Saving that report was not tested.

What the exact agreement tells you

The comparison supports the upper-tail arithmetic for the stated crisp examples. A small probability means that the observed count would be unusual under the chosen null probability. It is not the probability that a causal claim is true, and a nonpassing row does not establish the absence of the outcome.

Keep the file and calculation checks separate. A line-ending difference changes how text is stored without changing the probability values. The example and routine counts describe focused checks, not independent research studies.

• This page combines exact-fraction calculations, underlying routine checks and a report-preparation step. It does not use one decimal-error limit for all of them. The unadjusted, upper-tail definition remains part of every interpretation.

How to inspect the binomial test report

The JSON summary covers the 102 probability checks, the calculation-routine checks and the separate file-format finding. It also identifies the tested versions and source documents.

A rerun requires the original crisp inputs, settings and software versions. The download reports completed tests; the original datasets and app source code are not included.

• Read how numerical and file checks differ ↗
• Find other truth-table checks ↗