Confounding Two types of confounding 1 A cofounding

Confounding

Two types of confounding 1. A cofounding variable hides a non-apparent relationship between two variables 2. A cofounding variable (at least partly) explains away an apparent relationship between two variables Note that there alternative strict definitions of confounding variables which would not accord with what follows Note also that although we speak of “effects”, this does not necessarily presuppose some causal relationship between the independent and dependent variables (as you should know by now)

Confounding as hiding Consider this regression analysis of the division. sav data According to the Beta coefficient, the median total household income across electorates has a trivial, positive and statistically non-significant effect on preference for the Coalition

Confounding as hiding Preference for the Coalition Suppose, then, that we have a (simplified) scatter plot and regression line that looks like this Regression line Income

Confounding as hiding But now let’s look at the effect of income when controlling for population density

What is going on here?

Confounding as hiding Preference for the Coalition Consider our scatterplot again Regression line Income

Confounding as hiding Preference for the Coalition Suppose the highlighted data points are rural electorates with low population densities Regression line Income

Confounding as hiding Let us now compare the effect of income among those groups with similar population densities Income Preference for the Coalition We can see that income does have some effect when controlling for density line n o i ess r g e R Income

Confounding as hiding There you have it

Two types of confounding 1. A cofounding variable hides a non-apparent relationship between two variables 2. A cofounding variable (at least partly) explains away an apparent relationship between two variables

Confounding as explaining away Consider this regression analysis from the WVS data set Here, we see that income has a small, positive and statistically significant effect on happiness

Confounding as explaining away Now let’s control for health, effectively examining the effect of income among people with similar states of health

A possible theoretical explanation? So we see that, when controlling for health, income has a negligible and statistically non-significant effect on happiness. Positive effect Income Happiness Positive effect Income Health Happiness

Side note: Some would not consider either of these instances of confounding variables to be truly confounding variables. Some define confounding to only consist of “explaining away” relationships, not hiding them. Health is technically a “mediator variable” (or perhaps a “moderator variable”), and some would not consider this to be confounding. But this is a definitional issue that we are not too fussed about here. Nevertheless, note that there alternative definitions!