Two types of confounding 1 A cofounding variable hides a nonapparent relationship between two variables 2 A cofounding variable at least partly explains away an apparent ID: 532743
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Slide1
ConfoundingSlide2
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 are 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)Slide3
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 CoalitionSlide4
Confounding as hiding
Suppose, then, that we have a (simplified) scatter plot and regression line that looks like this
Income
Preference for the Coalition
Regression lineSlide5
But now let’s look at the effect of income
when controlling for population density
Confounding as hidingSlide6
What is going on here
?Slide7
Confounding as hiding
Consider our scatterplot again
Income
Preference for the Coalition
Regression lineSlide8
Confounding as hiding
Suppose the highlighted data points are
rural electorates with low population densities
Income
Preference for the Coalition
Regression lineSlide9
Confounding as hiding
Let us now compare the effect of income among those groups with similar population densities
We can see that income does have some effect when controlling for density
Income
Preference for the Coalition
Income
Preference for the Coalition
Regression lineSlide10
Confounding as hiding
There you have itSlide11
Two types of confounding
1. A cofounding variable
hides
a non-apparent relationship between two variables2
. A cofounding variable (at least partly)
explains away
an
apparent relationship between two variablesSlide12
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 happinessSlide13
Confounding as explaining away
Now let’s control for health, effectively examining the effect of income among people with similar states of health Slide14
A possible theoretical explanation?
Happiness
Income
Happiness
Income
Health
Positive effect
Positive effect
Positive effect
So we see that, when controlling for health, income has a negligible and
statistically non-significant effect on happiness.Slide15
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 are alternative definitions!Slide16
… Fin…