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.

A comment made by "Josh" under this Andrew Gelman's blog post:
https://statmodeling.stat.columbia.edu/2022/01/24/how-large-a-sample-size-does-he-actually-need-he-got-statistical-significance-twice-isnt-that-enough/
helped me (finally!) understand this issue. I copied the comment here, hope that's OK:
"Let’s say we take 100 samples under the null distribution and 100 samples under the alternative distribution. We expect ~5 samples under the null to be significant. If we have power of 80 percent, we’d expect ~80 significant results under the alternative. Here only 5/85 of our results are false positives.
However, what if we have statistical power of only 10 percent. Then we expect ~10 samples under the alternative to be significant. Here 5/15 of our significant results would be false positives.
Decreasing power increases the likelihood that we are in situation one (significant result with the null) rather than in situation two (significant result with the alternative)."
