# Choosing bins for chi-square testing distributional fits for distribution similar to normal/heavy-tailed

Chi-squared test can be used to check the hypothesis, that given sample is from the given theoretical distribution. If the distribution is continuous then we should properly choose bins.

Question 1 : What are the suggestions to choose bins ?

SubQuestion 1.1 : If we are testing normal distribution or something similar, is there some particular suggestion?

SubQuestion 1.2 : If we are testing "bell-shaped", heavy tailed is there some particular suggestion?

Question 2: Is it corrected that we should choose such bins that $E_i$ (expected frequecies) are greater than 5, (if less, Yates correction should be introduced).

PS

There is similar question, but with the focus on Poisson distribution (it is unanswered): How Do You Choose The Number of Bins To Use For A Chi-Squared GOF Test?

• Unless the observations are already interval-censored, then why not use a goodness-of-fit test suitable for continuous variables? If you do use Pearson's test, avoid making the mistake described here - it's rather common. – Scortchi - Reinstate Monica Jun 26 '18 at 10:21
• @Scortchi Thank you for your comment ! May be indeed I should use other tests. Would you be so kind to look at: stats.stackexchange.com/questions/353230/… – Alexander Chervov Jun 26 '18 at 10:50
• stats.stackexchange.com/questions/114146/… (which includes the usual advice to use bins that would be expected to have about the same proportion of observations under the null and the advice that this will still be pretty low powered). There's lots of posts on site about testing goodness of fit. – Glen_b -Reinstate Monica Jun 26 '18 at 13:02
• @Glen_b thank you for advice. May I ask you about "Question 2" above - is my understanding correct ? i.e. NOT use bins with E_i < 5 - I have seen such rule for chi-squared "Testing for statistical independence" for exampe in SPSS and some other places. I guess it should be similar for goodness-of-fit test, but I cannot find a reference, so I am worried. – Alexander Chervov Jun 27 '18 at 5:58
• It's certainly the case that the chi-squared approximation to the discrete distribution of the test statistic can be poor when the expected count is low, particularly if the expected counts are not close to equal. The rule about $E_i<5$ is often too strict, particularly if the expected counts are similar in each category. – Glen_b -Reinstate Monica Jun 27 '18 at 9:00