Obtaining Residuals in Chi Square Goodness of Fit

[Fred]

Another question re: goodness of fit testing,

Is the procedure for obtaining standardized residuals the same ?

The PhD student who leads the module labs provided me with answers to a practice problem for goodness of fit :


Observed Expected Residual (O-E)_ (O-E)_/E
2965.814 2472.822 222.992 49725.43 20.10878

then in the next column I see:

(O-E)_ ---- whatever the heck that means - I thought we needed standardized residuals ? which are obtained by = Residual/SQRT(Expected)

Wouldn't I want to = 222.922/SQRT(2472.822)

I don't see where the 49725.43 is coming from.

That is what would be done in a independent / "normal" chi square. Am I off ? Or is the GTA being thick ?

If needed, I can gladly provide the rest of the data series.

Thanks!

[Rounds]

This 2965.814 looks like it should be 2695.814 then you get the appropriate residual.


Now having the appropriate residual (O-E)_ should refer to (O-E)^2.

O-E is the residual. On all that square root stuff your doing. Your confusing test. Your making rows to do this first summation you see:
http://en.wikipedia.org/wiki/Goodness_of_fit

[Fred]

Thank you for the reply.

I spoke with the professor yesterday.

The algorithm I posted was used by the GTA . - - he was first obtaining the squared residual then converting it to a squared standardized residual

I wasn't sure what the "_" meant -- apparently it meant squared. That was what was throwing me off. He was using a different algorithm and I could not pick up on this because I could not deduce what the "_" was.



What I do is :

Residual -- Standardized Residual --> then square --> obtain totals = chi stat

To me, the way I do it is easier - - but that is just because it didn't occur to me that was another way to do it. Regardless, I will still continue to do it "my way" (like Sinatra).

Thanks !

[Rounds]

Oh I see what your doing. You are square rooting to find a term to square in its entirety. Yeah alright--I think it might be inefficient, but sorry for accusing you of confusing test.

[Fred]

No worries - I'm certainly no expert . Given that once I find a method that works I stay with it. Maybe one day I will "see it" like all of you do. Still have some ways to go though.