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University of Michigan - Ann Arbor

Chi-square test is the degree of deviation between the actual observed value and the predicted value of samples. The degree of deviation determines the size of the chi-square value. The larger the chi-square value, the greater the deviation. On the contrary, the deviation between them is smaller; If the two values are completely equal, the chi-square value is 0, indicating that the theoretical value is completely consistent.

Contingency table test is a special case of chi-square test, and it is one of the common methods of independence hypothesis test. 
$$ \chi^2 = \sum_{i=1}^{2} \sum_{j=1}^{2} \frac{(n_{ij} - \hat{\mu_{ij}})^2}{\hat{\mu_{ij}}} $$


Chi-square

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