Goodness of Fit and Contingency Tables

• χ² = Σ(O − E)²/E.
• Combine cells with expected frequency below 5.
• Goodness of fit: ν = number of cells − 1 − number of estimated parameters.
• Contingency table: ν = (r − 1)(c − 1); E = row total × column total / grand total.

Does the model fit?

H₀: the model fits. Compute expected frequencies from the model, combine small cells, find χ², compare with the critical value.

Are two factors associated?

H₀: the factors are independent. For a 2 × 2 table, ν = 1 and the 5% critical value is 3.841.