Question about Chi-Square Test Regarding Normal Distribution

[songoku]

TL;DR

Let say I have 50 raw data of height of students. I want to do goodness of fit test to check whether normal distribution is appropriate model for the data at a certain significance level

The first step is to group the data and make a table so I can get the observed frequency for each data interval. I did two different groupings (something like 150 - 160 , 160 - 170 , etc and the other is 150 - 170, 170 - 190, etc) and found out that the conclusion of the hypothesis is different, one resulting in accepting null hypothesis and the other rejecting the null hypothesis.

Is it possible different grouping resulting in different conclusion? Or there should be mistake in my working?

Thanks

 

[BWV]

The test is sensitive to the bin size

you might try Shapiro-Wilk, which is probably the best test for normality

https://en.wikipedia.org/wiki/Shapiro–Wilk_test

 

[BvU]

You suffer from low statistics -- 50 events isn't much to confirm a distribution.

 

[BWV]

In reality, as everyone knows the height of individuals has finite variance, you can just rely on the CLT with n=50 to assume normality

 

[FactChecker]

It certainly is possible to get different results. Your first grouping would show more detail than your second grouping. It would also have twice the degrees of freedom, so the Chi-Squared distribution is different.

 

[songoku]

Thank you very much for the help and explanation BWV, BvU, FactChecker