In a clinical study of treatments for rheumatoid arthritis, patients were randomly allocated to receive either a standard medication or a newly designed medication. After a suitable period of observation, statistical analysis showed that there was no significant difference in the therapeutic response of the two groups, but that the incidence of undesirable side effects was significantly lower in the group receiving the new medication. The researchers concluded that the new medication should be regarded as clearly preferable to the standard medication, because it had been shown to be equally effective therapeutically and to produce fewer side effects. In what respect is the researchers' reasoning faulty? (Assume that the term "significant" refers to rejection of H0 at α = 0.05.)