Why n=30 Is Not the Same as n=3,000

Two things n buys, and one it doesn't

Precision. A bigger trial gives you a narrower range around the estimate, not a different estimate.

Visibility of rare events. A harm that happens in one person per thousand is invisible in thirty people, and nearly invisible in three hundred.

What n does not buy is validity. A large trial with the wrong comparator, or the wrong endpoint, is a precisely measured answer to a question no reader was asking.

The arithmetic, on a real trial

The published phase 3 of a thymosin beta-4 ophthalmic solution in neurotrophic keratopathy enrolled 18 patients. Complete healing at four weeks occurred in 6 of 10 treated patients and 1 of 8 on placebo, which the authors reported at p = 0.0656 and described as a strong efficacy trend rather than a significant difference¹.

Take those two fractions and put a 95% interval around each.

6 of 10 is 60%. The 95% interval runs from about 31% to about 83%.

1 of 8 is 12.5%. The 95% interval runs from about 2% to about 47%.

Those two ranges overlap across a span from 31% to 47%. The point estimates look like a large difference. The intervals are consistent with a large difference, a small one, or none. That is not a criticism of the trial — it is what eighteen patients can resolve, and the authors said so.

Why small trials read as more impressive than they are

A meta-epidemiological study of critical care meta-analyses compared effect sizes from small and large trials within the same questions and found that small studies may overestimate effect sizes².

The mechanism is not fraud. It is selection. A small trial that finds nothing is easy to leave in a drawer; a small trial that finds a large effect gets written up. Over time the small-trial literature is enriched for large effects, and the large-trial literature is not.

Which means: when a compound's case rests entirely on small studies, the expected direction of error is toward overstatement.

"No adverse events reported" at n=42

There is a shortcut for this, and it is worth memorising. If zero events are observed in n participants, the upper bound of the 95% interval is roughly 3 divided by n.

n = 18 — zero events is consistent with a true rate as high as about 17%.

n = 42 — zero events is consistent with a true rate as high as about 7%.

n = 1,961 — zero events is consistent with a true rate up to about 0.15%.

n = 17,604 — zero events is consistent with a true rate up to about 0.02%.

So a phase 1 safety trial in 42 healthy volunteers that reports no adverse events has ruled out a common harm and has said essentially nothing about an uncommon one. A ClinicalTrials.gov search for BPC-157 returned 3 studies in August 2026, the oldest of which is a 42-participant phase 1 safety and pharmacokinetics trial with no results posted³. Our BPC-157 page reads that file line by line.

The other end of the scale

STEP 1 randomised 1,961 adults to once-weekly semaglutide 2.4 mg or placebo over 68 weeks and reported a mean weight change of −14.9% against −2.4%⁴.

SELECT randomised 17,604 participants and ran for years, because its question was not weight — it was whether cardiovascular events happen less often⁵.

The jump from roughly two thousand to roughly eighteen thousand is not a jump in ambition. It is the price of measuring an outcome that is rare per person per year. If the event you care about happens to 2% of people annually, you need a great many person-years before the difference between two arms is readable.

Precision, quantified

For a continuous outcome such as percent weight change, the width of the interval shrinks with the square root of n — which is slower than most people expect.

Assume a standard deviation of 8 percentage points, purely as an illustration. At n = 30, the half-width of a 95% interval around the mean is about 2.9 points. At n = 300 it is about 0.9. At n = 3,000 it is about 0.3.

Going from 30 to 3,000 — a hundredfold increase in cost — buys a tenfold narrowing. That is the whole trade, and it is why a sponsor will not fund a 3,000-person trial to answer a question a 30-person trial could settle.

What to do with a small trial

Do not dismiss it. A small, well-conducted, blinded, placebo-controlled trial is worth more than a large open-label case series.

Do read the interval, not the point estimate. If the paper reports one, use it. If it does not, the fractions are usually enough to reconstruct it.

Do ask what the trial was powered for. A trial powered to detect a 20-point difference will report "no significant difference" for a 10-point one, and that is not evidence of no effect.

Do check whether it is the only trial. One small positive result is a hypothesis. Two independent ones start to be a finding. Where a compound sits on that scale is what our evidence grading is trying to capture.

The question that cuts through

Ask what would have to be true for this result to be a fluke — and then ask whether the trial was large enough to rule that out. For eighteen patients, quite a lot could be a fluke. For seventeen thousand, much less.