4.3.2—Goodness-of-fit test

The chi-squared goodness-of-fit statistic is Σ(O−E)²/E. Under H₀ the proposed distribution is adequate, subject to model and expected-count conditions.

Combine tail classes when expected counts are too small, subtract parameters estimated from the data when determining degrees of freedom, and state the conclusion in context.

A large statistic relative to the critical value gives evidence against the fitted distribution; it does not identify which class caused the mismatch without inspecting contributions.

Rejecting H₀ does not prove every observation is wrong, and a small statistic cannot prove the model true.