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Pearson chi-squared test of independence

For an

r

by

c

contingency table, the statistic

X^{2} = \sum_{i, j} \frac{( O _{ij} - E _{ij} ) ^{2}}{E _{ij}}

has asymptotically a chi-squared distribution with

(r - 1) (c - 1)

degrees of freedom under independence.

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