# Why does Chi-square formula have two different ones?

1. Oct 3, 2011

### EigenCake

One is:
http://en.wikipedia.org/wiki/Chi-squared_distribution

where at the bottom of the page, chi-square = sum of something devided by variance.

However, here:
http://www.napce.org/documents/research-design-yount/23_chisq_4th.pdf [Broken]

where the chi-square formula is that the sum of the same thing devided by expectation value.

Which formula is right then?

Last edited by a moderator: May 5, 2017
2. Oct 4, 2011

### uart

The first reference is the definition of Chi-squared :- the distribution of a RV formed from the sum of squared standard-normal random variables.

The second reference is an application of the above distribution to the case of expect versus observed frequencies, where (O-E)/sqrt(E) is asymptotically standard-normal and hence (O-E)^2/E is asymptotically Chi-squared.

3. Oct 4, 2011

### EigenCake

Thanks!

It seems that for goodness of fit I should use the second formula to either reject or accept the null hypothesis, rather than use the first formula.