Chi Sqaure and odds ratio help

#1
Hi all,

I was wondering - what's the relationship between chi square and odds ratio? To me it makes sense that these two values are fixed- i.e., if one value changes, the other will. Is it possible to observe the same odds ratio in two different tests with different sample sizes but get a different chi square value? I can't imagine it would, because getting more samples will result in different values being used in the cells for the calculation of the OR...

Many thanks if anyone can help :)
 
#2
I was also thinking, if the chi square is insignificant, this also means that the OR is insignificant, is that right? Is it possible to have a sample size that increases, with the same OR as the smaller sample, therefore indicating the same X^2 value, which in turn indicates the same P value, because of the way the X^2 distribution works?
 

Karabiner

TS Contributor
#3
I can't imagine it would, because getting more samples will result in different values being used in the cells for the calculation of the OR...
Test 1:
Men:Women in PlaceA versus PlaceB
10:20 versus 10:10

Test 2:
Men:Women in PlaceC versus PlaceD
100:200 versus 100:100

The odds ratio is perfectly the same, since independent of sample size
(while its standard error isn't). The Chi² will be very different, since
every additional case adds to the Chi² value.

HTH

K.
 

hlsmith

Not a robit
#4
Karabiner hit the big point that the OR is obviously a ratio, so as long as proportions stay the same the OR will be the same. I will add that with the standard error getting smaller (since n-value is in its denominator) the Chi**2 changes and so will the confidence intervals around the OR (they will get smaller, which is typically a good thing).