Lesson 5 of 6 · 14 min

Contingency tables and the chi-square test of independence

For categorical data, compare the count in each cell with the count you would expect if the two classifications had nothing to do with each other.

In short

A contingency table (two-way table) counts observations classified by two categorical variables.
$H_0$ : the classifications are independent (not related); $H_a$ : they are not independent (related).
Expected frequency: $E_{ij}$ = (row i total × column j total) / overall total.
$\chi^2 = \sum (O_{ij}-E_{ij})^2/E_{ij}$ over all m = r × c cells, with (r − 1)(c − 1) degrees of freedom.
The test is non-parametric and right-tailed: squared gaps make $\chi^2 \ge 0$ , so only large values reject.

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