Placebo

A placebo is an inactive version of the treatment: a sugar pill, a saline injection, a sham procedure. It is given rather than withheld, so the placebo group is receiving a treatment in the design, one that does nothing on its own. The placebo effect has a definition worth stating exactly, because it is a difference between two averages: it is the average response to a placebo minus the average response to no treatment at all.

Three arms make that visible. Suppose 150 chronic pain patients are randomly assigned in equal groups, 50 taking the drug, 50 taking an identical inactive pill, 50 taking nothing. Mean pain reduction comes out 3.6 points for the drug, 2.1 for the placebo, and 0.9 for no treatment. The placebo effect is $2.1 - 0.9 = 1.2$ points. The drug's own effect is $3.6 - 2.1 = 1.5$ points. Had the trial compared the drug against no treatment, it would have credited the active ingredient with $3.6 - 0.9 = 2.7$ points, nearly double what it did.

The sentence to correct is "the control group gets a placebo." Sometimes. A control group is defined by supplying the baseline, not by what it swallows, and plenty of sound experiments have one with no placebo in sight. The error that runs the other way is "we used a placebo, so the study was double-blind." A placebo makes it possible to keep subjects unaware of their assignment; it does not do the keeping. If the labels differ, or the nurse handing out the bottles knows which is which, somebody is not blind.

Placebos are unavailable more often than not. There is no inactive version of a twelve-week exercise program or a smaller class size, and a sham surgery raises an ethical problem a sugar pill does not. They also do nothing for units that cannot form expectations, which is why plant and machine experiments never use them.