Recently, the corona pandemic showed us how extensively medications have tobe tested in clinical trials before they are made accessible for all. To investigate the effectiveness of drugs, mostly double-blind studies are conducted, i.e. half of the participants in the study receive the drug, the other half receive only ineffective tablets (placebo). 

In a double-blind trial to treat a serious disease, 80 of 160 patients receive a new drug and the remaining 80 receive a placebo. You’ll find the results of the clinical trial in the tables below. 

General Results

Male Patients

Female Patients

a) Put yourself in the position of one of three physicians and decide whether the use of the drug makes sense.  

• Physician 1: Interested in whether to prescribe the drug to any patient.
• Physician 2: Interested in whether to prescribe the drug to women.
• Physician 3: Interested in whether to prescribe the drug to men.

Form groups of at least 3 people and distribute the members among the above three cases. 

The results of the study are summarized in the following tables. Each group member calculates the success rates in his or her case and decides for himself or herself whether to use the drug.

b) Do you think the drug should be used or not? Why

c) This example called the Simpson paradox. Why is this a paradox?

d) This example study used very few subjects. Could this result also exist with 1600, 16000 or 100000 subjects?

e) Under normal circumstances, statistical results like that are not very likely. In your opinion, are there any mathematical anomalies in this statistic? 

From a purely technical point of view, this task is not particularly demanding. However, the context requires a certain degree of intellectual maturity to understand the implications of this example. Depending on the curriculum, the topic can be covered in the 9th to 12th grade. The task already structures the assignment. Subsequently, real cases in which the Simpson paradox played a role can be addressed. (see https://en.wikipedia.org/wiki/Simpson%27s_paradox ).