Chi-Square Test Calculator

This calculator runs a chi-square goodness-of-fit test across four fixed categories, summing (observed − expected)² / expected for each (lines 20-23) and converting the total into an approximate p-value via a Wilson-Hilferty chi-square-to-normal transformation (lines 29-37) rather than an exact chi-square table lookup. Degrees of Freedom is always 3 — the category count minus one (line 25) — regardless of what you type into any observed or expected field, because it comes purely from the four-cell structure of this test, not from the data. At the defaults, Chi-Square = 6.25 with a p-value near 0.098, which the calculator reports as not significant at either α=0.05 or α=0.01, despite a fairly large-looking statistic.

Each Expected Count field falls back to 1 via a boolean-OR default (lines 8-11), so typing a literal 0 does not zero it out — it becomes 1 instead, the same as leaving the field blank. That fallback also makes an internal safety check dead code: the summation guards against a zero expected value with `if (e === 0) return sum` (line 21), but e can never actually be 0 by the time it reaches that line, since the boolean-OR fallback already replaced any 0 upstream. What this does not account for: a negative Expected Count is not blocked or clamped anywhere in the engine itself (only the input's UI minimum of 0.01 discourages it), and a negative expected value flips that cell's contribution to the sum negative, which can artificially shrink Chi-Square below what a valid goodness-of-fit test would ever produce.