The difference between control group and control variables

This question came up in class sometime last week. Clearly, the two words relate to different ideas (A quick google search would illustrate this point). But, at it’s core, I think they are one in the same thing. Let me explain.

The central idea behind both the control group and control variable is the ‘ceteris paribus’ or the ‘other things equal’ condition. The control variable is a variable that is held equal between various observations (as is the case with regression analysis). One could add many control variables to an analysis to interpret how a dependent variable (y variable) is impacted by changes in an independent variable (x variable).

The idea behind a control group, is an extension of the control variable idea. In a sense, the control group ensures that all possible control variables are constant between it and the treatment group. This objective is achieved by means of random assignment.

A useful way to think about this would be to use less commonly cited words from Frost’s very commonly cited poem, The road not taken. “Two roads diverged in a yellow wood,
And sorry I could not travel both”, Frost says. Should you be able to think of (1) useful control variables or (2) a find a good control group, then except for Frost (who happens to be standing for very long at this point) choosing one of the two roads, everything should turn out to be the same.

In a sense, both the control group and control variables are used to achieve similar objectives by empiricists bases on what data is available to them.