ACT Science: Control Groups

A control group is a concept that appears semi-frequently on the ACT Science Test. In an experiment, a control group is used to compare results by providing a baseline. The control group participants are typically given a placebo or placed under neutral controlled conditions so that any changes in the experimental group can be judged based on the control group. Control groups can appear in any of the three passage-types, but is usually found in Conflicting Viewpoints passages. Let’s look at an example passage and a couple of questions!
 

A study of patients who have been taking the prescription drug rosiglitazone has raised doubts about this medicine’s safety.  Of the 6,241 patients who had taken the medicine for more than one year, 93 suffered heart attacks and 102 suffered heart failure.  By comparison, only 84 cases of heart attacks and 62 cases of heart failure were reported among the 7,870 patients in the control group (who had the same illness but did not receive rosiglitazone).
Scientist 1:
Based on the above results, the medicine appears to raise the risk of heart disease: 1 out of every 66 patients taking the medicine suffered heart attacks, versus only 1 in every 95 patients who were not taking the medicine.  The risk of heart failure increased even more.
The best course of action would therefore be to stop the sale of this medicine while a larger follow-up study is performed to confirm the results.
Scientist 2:
I agree that the results of the study are worrisome.  As Scientist 1 noted, approximately 1.5% of the patients taking rosiglitazone experienced heart attacks, compared to approximately 1.1% of the patients not taking this medicine.  However, such studies provide only an estimate of the true risks – and when the number of patients reporting a particular side effect is small, the estimates are likely to contain significant errors.
In this case, the differences between the two groups could be due to errors in the estimates.  For example, consider the fraction of patients taking rosiglitazone who suffer heart attacks, which is estimated to be 93 out of every 6,241. According to the laws of statistics, the uncertainty in this risk estimate can be estimated simply by taking the square root of 93, which is approximately 10.  There is actually 1 chance in 3 that the risk estimate is in error by more than this amount, so the true value could well be less than 83 out of every 6,241 (rather than 93).  It is equally possible that the correct number in the other group is more than 93 out of 7,870 (rather than 84).
A larger follow-up study should be performed as soon as possible, but I would not advise banning use of rosiglitazone in the meantime.  This medicine has been shown to be effective at preventing a dangerous illness, and patients would be harmed if they switch to a medicine that turns out to be less effective.

According to Scientist 2, the accuracy of the risk estimates in such a study will:
A. depend on the square of the number of patients
B. depend on the number of patients
C. depend on the square root of the number of patients
D. not depend on the number of patients
In this passage, Scientist 2 emphasizes that large errors in the risk estimates can occur when the sample size is small (“when the number of patients…is small, the estimates are likely to contain significant error.) Scientist 2 then uses one estimate from the study as an example (paragraph 2), and explains that the square root of the number of patients (“can be estimated simply by taking the square root of 93….”) will indicate the possible error in the estimate. The answer is C.

Assume that another study reported the following results: 62 of 6,550 patients taking rosiglitazone suffered heart attacks, and 107 suffered heart failure. 80 of 7,500 patients in the control group suffered heart attacks, and 59 suffered heart failure. Which of these results is least consistent with the results of the previous study?
A. heart attacks among patients taking the medicine
B. heart failure among patients taking the medicine
C. heart attacks among patients not taking the medicine
D. heart failure among patients not taking the medicine
The number of patients taking the medicine is 6,550, only a tiny amount more than the 6,241 patients taking the medicine in the original study. Similarly, the number of patients in the control group changed minimally, from 7,870 to 7,500. Therefore, the number of patients in a particular group who experience a particular side effect should be similar to the number in the original study. Only the number of heart attacks in the group taking the medicine changed by more than a few percent. This number was 62 in the new study, but it had been 93 – one and a half times as many – in the original study. The answer is A.