Clinical Trial Power & Sample Size Simulator

Trial Design

Patients per arm (n) 40

Treatment effect size (Cohen’s d) 0.50

Significance level (α)

Live Results

Statistical power

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n needed for 80% power

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Last trial: t-test p-value

run a trial →

Observed mean difference

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Control arm Treatment arm

How it works

Each patient's outcome is drawn from a normal distribution. Control-arm outcomes ~ N(0, 1); treatment-arm outcomes ~ N(d, 1), where d is Cohen's standardized effect size — the true mean difference measured in standard deviations. The dashed curves above the patient swarm are these two theoretical distributions; their overlap is exactly the probability of a false-negative (Type II) error.

Power ≈ Φ( d·√(n/2) − z(1−α/2) )
n for 80% power = 2·( z(1−α/2) + z(0.80) )² / d²
t = (mean_T − mean_C) / SE_pooled,  df = 2n−2

n slider — patients enrolled per arm. More patients shrink the standard error and raise power.
Effect size d — how far apart the two populations really are. d≈0.2 is a small effect, 0.5 medium, 0.8+ large.
α — the false-positive rate you're willing to accept; a stricter α (0.01) demands more evidence to call a result significant, which lowers power at fixed n.
Enroll & Run Trial — draws n random patients per arm from the two distributions above and runs a real two-sample Student's t-test (via the regularized incomplete beta function) on the simulated data — the p-value is genuinely computed from that draw, not looked up.

Real-world relevance: this is the exact power-analysis logic biostatisticians use to decide how many patients a randomized controlled trial needs before it starts recruiting — under-powering a trial risks missing a real treatment effect, while over-powering it exposes more patients than necessary to an unproven intervention.

Control patients Treatment patients

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