![]() Example: Reporting a chi-square test There was no significant relationship between handedness and nationality, 2 (1, N 428) 0.44, p. In the 'Pearsons chi square test' video, the degree of freedom is indeed n-1. So there isn't any contradiction here, everywhere there are $df$ independent normally distributed random variables in the background somehow, and $df$ sometimes equals $n - 1$, sometimes $k - 1$ (here $k$ is the $k$ from the Pearson's $\chi^2$ test above, not the $k$ in your question), sometimes some other formula, depends on the test. Report the chi-square alongside its degrees of freedom, sample size, and p value, following this format: 2 (degrees of freedom, N sample size) chi-square value, p p value). The degrees of freedom vary depending on the constraints on your data.
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