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I will rephrase your question:: Is the chi-square positively or negatively skewed? It has to be positively skewed, as the mean > median > mode, and skewness is positive. The degrees of freedom, k, must be greater than zero, therefore: skewness = square root of 8/k, is also positive. Mean of the distribution is k, median is k- 2/3 and mode is k-2 for k > 2, therefore in all cases the mean > median > mode condition holds. You may like to view the following link for additioal info: http://www.scaweb.org/assets/papers/2004_papers/SCA2004-01.pdf

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Q: Why is a chi-square test for independence always right-tailed?
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