Distribution
The null distribution of the Pearson statistic with j rows and k columns is approximated by the chi-squared distribution with (k − 1)(j − 1) degrees of freedom.
This approximation arises as the true distribution, under the null hypothesis, if the expected value is given by a multinomial distribution. For large sample sizes, the central limit theorem says this distribution tends toward a certain multivariate normal distribution.
Read more about this topic: Pearson's Chi-squared Test
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