Every medical researcher I've worked with had a biostatistician on hand to handle the stats. As a aerospace engineer, I always had interesting discussions with them on the meaningfulness of a clinical study with 15 people, but have come to appreciate the massive difficulty in progressing medical research if everybody were to wait for a clinical trial with a 1000 patients.
There's no problem with a n=15 study, the problem is that there isn't a proper effective process that aggregates these small studies and the designs and conducts n=1000 ones. What we have instead is academic peacocking. (Grant applications judged by other scientists who are also at the same time in the grant game.)
Of course this is somewhat a necessary consequence of having academic freedom.
