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I'm trying to sort out an inconsistency in some data I have. I'm comparing a binarized cannabis use variable (yes/no within the last 60 days) between college kids in two states. 22.6% of kids in state A have smoked up recently, compared to 57.9% of kids in state B. Calculating an odds ratio from just these stats, I wind up with

(.579/.421) / (.226/.774) = 4.710

I've also run a logistic regression with cannabis use as the dv and state + demographics (age, race, ethnicity, etc.) as covarying IVs. Only my State variable has a significant effect there, but when I calculate the odds ratio from its coefficient I get

e^1.79 = 5.989

I feel like this suggests I've made some error in building my regression --- is it really possible that the presence of all these nonsignificant covariates would bias the OR this much? Or am I just wrong in assuming these two values should be very similar?

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I think there are two issues here.

First, I think you should expect the odds ratio from a logit model with additional covariates to be different from the bivariate odds ratio, even if none of the covariates are significant. Remember that "not significant" (which I assume means "not significant at the 95% level) doesn't mean that the covariates have NO relationship with the dependent variable, just that the relationship isn't strong enough to be detected at a given level of confidence. So the presence of even non-significant covariates will impact the estimate of the adjusted odds ratio for "state" by some amount.

Second, remember that odds ratios can only be meaningfully compared on a logarithmic scale. The difference between two ORs gets less important the bigger they are and any OR bigger than 3 is already so huge that the difference between an OR of 4.7 and 5.9 isn't that big of a difference. In your case the log of the odds is only going from 1.5 to 1.8 and if you check out the confidence interval around the coefficient from the logit model, it might even include 1.5 (which corresponds to the bivariate odds ratio), in which case you can't even say that the two odds ratios ARE different at the 95% level.

Anyways, both results are telling you substantively the same story. So no need to worry.

(PS: one thing to always remember when working with odds ratios is that very few people (even in the stats world) have any intuitive idea of what "the odds were 4 times as high" actually means. So if you want an intuitive sense of how "big" this effect is, in terms of changes in probability, then you will need to do some extra work to get that from the logit model - calculating average marginal effects or something)

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