Studies of this sort are quite likely to have too small a sample size. Studies with too large a sample size are seldom an issue. However, if a study is too small we might conclude that the results are due to chance when a larger study might show the drug to be effective. Apart from the consequences of failing to find a useful drug the small study raises a critical ethical problem. The participants who give their informed consent to participate in a study are defrauded if the study is too small to yield useful results.
Statistics can be helpful in determining the correct sample size.
In order for statistics to be helpful however, the investigator must have a working idea of the magnitude of difference between the new treatment and the usual treatment. Once the investigator makes a commitment to the magnitude of difference, the statistician can easily calculate the sample size for the study. Recap Statistics quantifies variability and aids the researcher in distinguishing between chance and cause. Observational studies suggest questions. Planned experimental studies answer questions.