Here are a couple of statements about the justification of the sample size from reports of clinical trials in high-impact journals (I think one is from JAMA and the other from NEJM):
We estimated that a sample size of 3000 … would provide 90% power to detect an absolute difference of 6.3 percentage points in the rate of [outcome] between the [intervention] group and the placebo group.
The study was planned to detect a difference of 1.1 points in the [outcome score] between the 2 interventions with a significance level of .05 and a power level of 90%.
There is nothing remarkable about these at all; they were just the first two that I came across in rummaging through my files. Statements like this are almost always found in clinical trial reports.
A translation, of the first one:
“We estimated that if we recruited 3000 participants and the true absolute difference between intervention and placebo is 6.3 percentage points, then if we assumed that there was no difference between the groups, the probability (under this assumption of no difference) of getting data that were as unusual or more unusual than those we actually obtained would be less than 0.05 in 90% of a long series of replications of the trial.”
That’s what it actually means but I guess most clinicians and researchers would find that pretty impenetrable. An awful lot is hidden by the simple word “detect” in the sample size justification statements. I suspect the language (“detect a difference”) feeds into the misunderstandings of ”significant” results – it’s a real difference, not due to chance, etc.
Original post 5 March 2017, http://blogs.warwick.ac.uk/simongates/entry/sample_size_statement/