In the design of experiments, treatments are applied to experimental units in the treatment group(s). In comparative experiments, members of the complementary group, the control group, receive either no treatment or a standard treatment.
A placebo control group can be used to support a double-blind study, where a portion of patients are given a placebo medication (typically, sugar pill), in order to observe the patients are taking their medications in the manner as proscribed, with no major procedural differences between the treatment group(s) versus the placebo control group(s). In such cases, a 3rd, nontreatment control group can be used to measure the placebo effect, as the difference between placebo subjects and the non-treatment subjects, perhaps paired by age group, twin/triplet or other related factors.
For the conclusions drawn from the results of an experiment to have validity, it is essential that the items or patients assigned to treatment and control groups be representative of the same population. In some experiments, such as many in agriculture or psychology, this can be achieved by randomly assigning items from a common population to one of the treatment and control groups. In studies of twins involving just one treatment group and a control group, it is statistically efficient to do this random assignment separately for each pair of twins, so that one is in the treatment group and one in the control group.
In some medical studies, where it may be unethical not to treat patients who present with symptoms, controls may be given a standard treatment, rather than no treatment at all. An alternative is to select controls from a wider population, provided that this population is well-defined and that those presenting with symptoms at the clinic are representative of those in the wider population. Another method to reduce ethical concerns would be to test early-onset symptoms, with enough time later to offer real treatments to the control subjects, and let those subjects know the first treatments are "experimental" and might not be as effective as later treatments, again with the understanding there would be ample time to try other remedies.