Chi-Square Goodness-of-Fit

Understand the chi-square goodness-of-fit result

Use Chi-Square Goodness-of-Fit when you are checking a two-category goodness-of-fit calculation before consulting a chi-square table. It asks for observed category 1, expected category 1, observed category 2, expected category 2 and reports chi-square and degrees of freedom. Each squared observed-minus-expected difference is divided by its expected count and the category terms are summed. Larger statistics indicate greater disagreement between the observed and expected pattern. By exposing chi-square and degrees of freedom, Chi-Square Goodness-of-Fit makes this specific arithmetic inspectable instead of presenting an unexplained number.

With the page defaults of Observed category 1 20, Expected category 1 25, Observed category 2 30, Expected category 2 25, the verified output is Chi-square 2, Degrees of freedom 1. Expected counts are model counts, not percentages unless converted to counts first. In Chi-Square Goodness-of-Fit, each labeled default remains visible while you edit, so you can change one assumption at a time and trace how chi-square responds.

Method, limits, and private processing

This two-category page does not calculate a p-value and expected counts should be sufficiently large. Chi-Square Goodness-of-Fit evaluates the entered values entirely in your browser, without sending the inputs to a server. When using its chi-square and degrees of freedom, retain the stated method and input units because this result is bounded by the assumptions of each squared observed-minus-expected difference is divided by its expected count and the category terms are summed.