An analysis published last week in the Journal of the American Medical Association examined more than 228,000 clinical trials and found that about 9 percent of them had “very large” findings — showing that a particular treatment was five times or 500 percent more likely to help someone or hurt them compared with a placebo.

These were mostly from small studies with very few measured outcomes such as heart attacks or deaths. If 10 heart attacks occurred in one group and five heart attacks in another, for example, the researchers would have found a five-fold difference between the two groups. But the laws of statistics dictate that smaller samples have larger margins of error.