3.6% response rate? Shocking! For our new feasibility study, we sent over 200 invitations to primary care doctors in Ireland and the invitees sent us back a very strong signal. “We are not interested”, or “we are too busy”, or “we don’t have enough eligible patients”? Whatever the reason, the message remained the same: No, thanks.
Power in research experiments is about finding the truth. Experimenters want to know whether their drugs or treatments work. If the drug or treatment works and they give it to a group of people, some of them will improve, some won’t. There’s a lot of chance and uncertainty in any drug or treatment administration. If we want to know the truth beyond the effects of chance, we need to give the drug or treatment to the right number of people. There’s a formula for it, known to most statisticians. It depends on many things, like the size of the improvement that you want to observe in the treated group, or other confounding factors. The higher power in a study, the more likely it says true (see, e.g., Dr Paul D Ellis’, PhD site here).
A rule of thumb says that the more people are in the study, the higher the chances of finding a meaningful impact of the intervention. Common sense also tells us that the more people in the trial, the more representative they are of the whole population – the more confidence you can be that your results apply to all; except for Martians – unless you really want to study Martian citizenship.
The easiest would be to call some friends, doctors, and ask for a favor. This should work, but it’s not really scientific. Or you can shut down the study and conclude that it’s not feasible. Or you can do the study with the small number of interested participants. Or you can send another mailshot, a reminder, to all – sometimes that can help.