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A test (typically of distribution, independence, or goodness of fit), for the family of distributions use [chi-squared-distribution].
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chi-squared test for non-iid binomial data
Simple case: Suppose we have $N$ observations of $X_i$ that we believe are theoretically iid binomial random variable $\text{Binomial}(k, p)$. Well, one way we could test to see if this is true is usi …