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Sample size governs precision, not correctness. A small study is compatible with a wide range of true effects, which is why its striking headline figure is weaker evidence than it looks.
A study measures some people and draws a conclusion about more people than it measured. The sample is standing in for a population, and sample size governs how well it can do that job. A small sample is not wrong; it is imprecise, and the distinction matters because imprecision is quantifiable while wrongness is not.
Every estimate from a sample comes with a range it is plausibly compatible with. Smaller samples produce wider ranges. A study of twelve people might be compatible with a large effect, no effect, and a small harm all at once — which means it has not settled the question, whatever its headline figure says.
Counter-intuitively, the eye-catching results often come from the smallest studies. With few participants, chance variation is large relative to any real effect, so the results that happen to look impressive are disproportionately the ones that got published. Reading a striking figure from a tiny study as strong evidence inverts the actual relationship.
A study too small to detect an effect that exists will usually report finding nothing. That is a statement about the study, not about the world, and reporting it as 'no effect was found' quietly converts a limitation into a finding. The useful question of any null result is whether the study could have detected the effect had it been there.
Several independent studies agreeing is stronger evidence than one larger study, because replication tests the method and the population as well as the hypothesis. One large trial can be wrong in a way no amount of its own size corrects. This is also why a single study, however impressive, rarely settles anything on its own.
Before the result, look for how many participants there were, how many were in each group, and how many dropped out. Those three numbers tell you how much weight the conclusion can carry, and they are usually easier to find than the statistics. A paper that makes them hard to locate is worth more suspicion than one with a modest n stated plainly.
The same reasoning governs any claim built on a handful of observations, including product testing. Three excellent results prove very little about a process; thirty across different batches begin to describe one. Sample size is a general property of evidence rather than a feature of medical papers.
The participant count belongs in the abstract and often is not there. It appears in the methods, in a flow diagram, or only in a table. Where a summary quotes a percentage without the denominator it was computed from, that denominator is the first thing to go and find, because a percentage of a very small number is a different claim from the same percentage of a large one and the two are written identically.
Small studies are worth reading and worth discounting. They generate hypotheses efficiently and settle them poorly. Treat a small-n result as a reason to look for replication rather than as a conclusion, and treat the absence of replication as the finding it usually is.
Observations that are not independent carry less information than their count suggests. Measuring the same person ten times is not ten independent observations, and neither is measuring ten people in one household. Analyses that ignore this report intervals that are too narrow, and the correction is routine but not universal.
Calculating power after a study using its own observed effect adds nothing, because it is a deterministic function of the p-value already reported. A non-significant result will always yield low observed power, which is why the practice persists and why it answers no question the reader had.
The claims on this page about why n matters, and what a result from a small group does and does not support can be checked against sources outside this site:
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