Studies with small sample sizes I'm asking myself the question of why studies with small sample sizes are not as convincing as those with larger sample sizes, and when this becomes a statistical issue. A complaint I've heard a lot with studies is while they show a certain "desired" result (e.g. the treatment group had lower cholesterol than the placebo group), the sample size was small.
Statistically, if you have the sample size to detect an effect, then the sample size was large enough in that sense. So at that point, on what grounds could you claim a higher sample size would be better? To get more exact confidence intervals if they are asymptotic?
Personally I would feel more convinced with a sample of 1000 rather than 500, but I can't identify technically where this makes a difference aside from precision.

Let's use reductio ad absurdum to see how the "if you have the sample size to detect an effect, then the sample size was large enough in that sense" logic doesn't hold. Imagine that you had a sample of size $N=1$. In such a sample, you can either observe a result that confirms or disagrees with your hypothesis. Unless you can make a strong hypothesis like "it should never happen" (but then, you don't need statistics, just logical reasoning), there will always be some chance to observe either of the results, even if unlikely. In such a case, your single sample does not "prove" anything, as it could be pure luck. However, if you repeated the experiment many times and saw the same result repeated, it gets less likely that it was luck.
