Lurking Variables

Consider this situation: Students who take AP math courses have a relatively high performance in the first year at university. Some school officials and advisors have concluded that all high school students should be strongly encouraged to take AP math so that they will do better at university. The alleged causative variable is taking an AP math course. The response variable is performance in the first year at university. Does taking an AP math course cause better performance at university?

What school officials are concluding is that we have causation. Let x be the taking of an AP math course, and y be academic performance at university. If x causes y we have this: CAUSATION

This suggests that for better academic performance, students should take AP math. Is this the only possible interpretation? As much as I am in favor of having all students take AP math, I’m not sure that this will make all students successful at university. Is there another possible explanation to the observed association? Consider: COMMON RESPONSE

Here a third variable is causing the effects on both x and y. What could that third variable be? I’m sure that you can think of several possible lurking variables. Higher academic ability among AP math students is one. High motivation is another. This phenomenon is called common response.

But we do believe that better preparation in high school leads to success at university…. And there is considerable evidence that having some exposure to university level expectations prior to going to university is beneficial….so we now consider a third possibility. In this case there is some effect on y by x, but there are also effects on y by a third variable, z, a lurking variable. CONFOUNDING The lurking variable, z, is said to confound the results.

We cannot separate the effect of x and z. Both variables act on y. CONFOUNDING With the example of taking an AP math course and achievement at university, we could also have confounding. What possible lurking variable could we have? Note that in this case the lurking variable does not act on x. Could another aspect of preparation for high school, other than taking an AP math, be the lurking variable?

Taking a strong English course in high school is known to help at university. The taking of such a course is one possible example of a lurking variable that confounds the interpretation of the AP math and university achievement results. This example shows that there may be both common response and confounding in the same situation.

What lurking variables might be acting here?

In summary, be sure that you understand and can distinguish these three effects: Causation Common Response Confounding