A blood-pressure drug truly lowers systolic pressure by 0.4 mmHg — an amount no patient would ever feel. Run it as a 40-patient pilot and nothing shows. Run it across half a million health records and the same trivial effect comes back with a p-value smaller than one in a hundred billion. Slide the sample size and watch it happen.
The effect itself — drawn to scale
standard care μ = 128on the drug
Cohen's d
—
Curve overlap
—
Coin-flip test
—
The test's ruler — it shrinks with n
results at least this extreme — area = p
Set a true effect and a sample sizethen read both verdicts
Design the study
The true effect — the thing the drug actually does
0.40 mmHg lower
How many patients you look at
n = 400
observed drop
—
std. error
—
test z
—
p-value
—
σ = 12 mmHg is treated as known; H₀: μ = 128 against a two-tailed alternative at α = 0.05. Sliding n holds this trial's luck of the draw fixed so you see only what sample size does — press the button for fresh noise.
What the p-value does as the study grows
The curve is the p-value a trial would get if it landed exactly on the true effect; the solid dot is the trial you actually ran, knocked off the curve by sampling noise. Any non-zero effect, however small, eventually drags this curve to the floor.
How big could the real effect be?
—
Two different questions. “Is the effect distinguishable from zero?” is answered by the p-value and is answered better by a bigger n. “Is the effect big enough to bother with?” is answered by the size of the effect and its interval — and no sample size on earth can turn a small answer into a large one.