Identify the single most significant flaw in each of the following experimental designs. Use statistical language to identify what’s missing.

a. In a test of the effectiveness of acupuncture in treating migraine headaches, a random sample of patients at a migraine clinic were provided with a novel acupuncture treatment daily for six months. The patients were interviewed at the start of the study and at the end to determine whether there had been any change in the severity of their migraines.

b. In a modified study, a second sample of patients were chosen after the acupuncture treatment was completed on the first set of patients. This second sample of patients received a placebo in pill form for six months. At the end of the study, perceived pain levels in the two groups were compared.

c. In a modified study, the sample of patients was divided into two groups according to gender. The women received the acupuncture treatment, and the men received the placebo medication in pill form. At the end of the experiment, perceived pain levels in the two groups were compared.

d. In a modified study, patients were randomly divided into two groups. One group received the acupuncture treatment, and the other received a fixed dose of placebo medication in pill form. At the end of the experiment, perceived pain levels in the two groups were compared.