The one sample chi-square test is an asymptotic test, which means it approximates the p-value, and works better with more samples (> 1000).

We can use an exact test, more computational heavy, like the binomial. It still can be used for one sample proportion tests. We report it similarly to before, just saying the test was the binomial test.

With more than two response categories, we can still use the chi-square test, but the binomial test works only with two, so we need to use the multinomial test (still an exact test)

References

• test-of-proportions
• https://www.coursera.org/learn/designexperiments

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