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Along with an associated 'degrees of freedom' these values can be used to give the probability of deviation from some model under the null hypothesis. For example, suppose the chi-square value proved to be 13.5 on df=6. Various sources give the value of the chi-square distribution function for this particular outcome. Let me use the Python (language) library scipy.

>>> chi2.cdf(13.5,6)

0.96425158157771951

This indicates that one would expect to see a value this large only about 0.036 or 3.6% of the time, given the truth of the null hypothesis. One would have some grounds for rejecting that hypothesis.

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Q: What does a calculated value of chi square refers to?
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