Hi ... I have a question regarding the Chi-squared goodness of fit test - I thought that the test-statistic is the following: X^2 = Sigma[(Actual - Expected)^2]/Expected However, in Sweeting, I see that he has the following (where Variance replaces the Expected in the denominator) as the test-statistic: X^2 = Sigma[(Actual - Expected)^2]/Variance i.e. X^2 = Sigma[(T_n - Tp_n)^2]/[Tp_n * (1 - p_n)] based on pg 156-157. I would like to understand the difference between the two test-statistics above (or if I'm wrong!). Does anyone have any insights as to the difference between these two ... or alternatively, point me to a good source that distinguishes between the two? Thanks
Chi square test I had also stumbled against that. I have been unable to understand what the denominator refers to! I am reasonably confident that this is an error. you are right to state that the test-statistic is: X^2 = Sigma[(Actual - Expected)^2]/Expected I shall compare the results from the example in the text book with those obtained from using statistical packages.
I'm afraid Sweeting's derivation of the goodness-of-fit test is way off! Use the formula you both think you should.
A Chi square variable is nothing but square of a standard normal variable. Y= (X-E(X))^2/Var(X). The Var(X) is replaced with E(X), when either we use binomial distribution with b being very small or when we use apoisson distribution. Hope this helps
I'm not sure it has a lot to do with p being small and it's quite a bit more complicated than noting that \(\chi^2\) is the square of a standard normal variable. If you really want to know why we put E(X) in the denominator check out: http://sites.stat.psu.edu/~dhunter/asymp/fall2006/lectures/ANGELchpt07.pdf Otherwise, just know that you have the right formula for a goodness-of-fit test and use it well!
