Statistical Methods

• Rows with missing row or column values are excluded from the active crosstab.
• Counts, row percentages, column percentages, and total percentages are computed from the filtered table.
• Expected frequencies use the standard independence model: row total times column total divided by grand total.
• Adjusted standardized residuals above +1.96 or below -1.96 are marked as above or below expected.

• Pearson chi-square tests overall association between the row and column variables.
• Yates' correction and Fisher's exact test are shown for unweighted 2x2 tables where applicable.
• Likelihood-ratio G-test is reported as an asymptotic alternative to Pearson chi-square.
• Cramer's V, phi, contingency coefficient, odds ratio, lambda, gamma, Kendall tau, Somers' d, and Theil's U are included as effect-size or association measures.

• Numeric weights can be applied to descriptive counts and percentages.
• Rows with missing, non-numeric, zero, or negative weights are excluded and reported in warnings.
• Weighted chi-square, p-values, residuals, and effect sizes are approximate unless the weights are valid frequency weights.
• Fisher's exact test is hidden for weighted tables because it requires unweighted integer counts.

Crosstabs warns on small samples, expected cell frequencies below 5, weighted inference caveats, invalid weights, and very wide tables. These warnings should be carried into reports rather than removed.