Medicine regularly uses the Odds Ratio for describing the difference
between two outcomes, especially when the rates are low and the Ns
are large. Your Odds Ratio of 1.2 might be interesting if it were an
expected or well-justified result in a controlled experiment. But even
a ratio of 1.5 would be shaky for observational data, which is what your
data appear to be. A value of 1.2 is about the weakest anyone would
consider as possibly-meaningful for a randomized study.
So. Conclude that your outcome is apt to be the result of uncontrolled
factors that differ between the populations. It can be worth mentioning
as a curiosity, but it is not sound to conclude that this is a meaningful
difference between the groups.
I think the magnitude is also described in some studies (mainly, European)
by using the "minimum effective N" that would result in a 5% test
--
Rich Ulrich
> Date: Wed, 22 Oct 2014 11:28:23 -0700
> From:
[hidden email]> Subject: chi square but very disparate sample sizes
> To:
[hidden email]>
> Hi everyone,
>
> I need advice. I'm working with a big dataset.
>
> If Population A is 4000 patients and there are 3.2% with the flu, and
> Population B is 53500 patients and 3.9% have the flu, is the difference in
> prevalence of the flu significant or not?
>
> The clinic managers are saying use chi square 2x2 table, and then the
> prevalences are hugely significantly different. Just in my opinion because
> of the big sample size difference.
>
> I'm being conservative and saying with such hugely different sample sizes,
> it's better to use 3.2/100 versus 3.9/100 so like a z test for proportions
> for the comparison -- and it's not significant.
>
> Any suggestions greatly appreciated.
>
> Susan
>
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