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We know that this association could be explained by a third variable: age. Women that give birth to say their third child, is of course going to be older than when they gave birth to their first child. So Age is associated with birth order.

Age of mother alone when child is born is associated with down syndrome.

So we suspect that age confounds the relationship between birth order and down syndrome.

A way to see if this is true is to fix the levels of the confounding variable, Age, and then produce groups within which the confounder does not vary. So within each stratum, the confounder Age cannot confound because it doesn't vary across the exposure outcome.

This is the statification strategy and it makes perfect sense. For the fixed Age groups, we see that birth order has no effect at each stratum of age.

Now how would this work for regression? Say I have

**y~birthorder**. This would give statistical significance.

Then I adjust for age.

**y~birthorder+age**. Here birthorder should not be significant. The interpretation is that birth order is not significant when age is constant.

So this seems like its the exact same thing as stratification right? In stratification, the strata is held constant. In regression, interpeting the output for the coefficient of birthorder, we hold age constant as well.

What if age is a continuous variable? Then would it work? Or would I have to split it into 5 strata just like in the stratification example?