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Clinical Trial Sample Size Calculator

Compare digital endpoint and traditional rating scale sample requirements side by side. Powered by exact noncentral t-distribution calculations, not the normal approximation.

Parameters

Medium-small
80%

Results

Required n per arm63
Total participants126
Achieved power80.1%

Power Curve

80%n=63050100Sample Size per Arm (n)0%20%40%60%80%100%Statistical Power

Statistical Methodology

Noncentral t-Distribution

This calculator uses the exact noncentral t-distribution rather than the normal (z-test) approximation. The noncentral t accounts for the fact that the population standard deviation is estimated from the sample, which matters most at smaller sample sizes where the normal approximation can overstate power.

For a two-sample t-test with n participants per arm and effect size d:

df = 2(n - 1)

ncp = d × √(n/2)

tcrit = t1-α/2(df)

power = 1 - Fnct(tcrit; df, ncp)

Paired Design

For paired (within-subject) designs, the degrees of freedom are n - 1 and the noncentrality parameter is d × √n, where n is the total number of participants. The paired design achieves higher power per participant because within-subject variability is typically lower than between-subject variability.

Numerical Implementation

The noncentral t CDF is computed using the Algorithm AS 243 series expansion with Poisson-weighted incomplete beta function terms. The regularized incomplete beta function uses the continued fraction representation with modified Lentz iteration. The log-gamma function uses the Lanczos approximation with 9-term coefficients. All computations are numerically stable for sample sizes from 2 to 1,000 and effect sizes from 0.1 to 4.0.

Frequently Asked Questions

How does this calculator determine the required sample size?
This calculator uses the exact noncentral t-distribution to compute statistical power, rather than the normal approximation used by many online tools. For a given effect size (Cohen's d), significance level (alpha), and desired power, it finds the minimum sample size where the power of the t-test meets or exceeds your target. The noncentral t approach accounts for the uncertainty in estimating the population variance, providing more accurate results especially at small sample sizes.
What is the difference between two-sample and paired designs for sample size calculation?
In a two-sample (independent groups) design, participants are randomized to treatment or control, and the sample size shown is per arm. The total number of participants is twice the per-arm value. In a paired design, each participant serves as their own control (e.g., before vs. after treatment), and the sample size shown is the total number of participants needed. Paired designs typically require fewer participants because within-subject variability is lower than between-subject variability.
Why do digital endpoints often require smaller cohorts than traditional rating scales?
Continuous, high-frequency kinematic measurement provides higher sensitivity than ordinal subjective ratings. Higher sensitivity translates to larger standardized effect sizes for the same clinical change, which means the treatment-vs-control difference is easier to detect statistically — so smaller cohorts can achieve the same statistical power. This is why pairing digital endpoints with traditional clinician-rated scales is increasingly common in modern CNS trial designs.
What effect size should I use for my clinical trial power analysis?
The effect size (Cohen's d) should come from prior studies, pilot data, or the minimum clinically important difference divided by the expected standard deviation. As a general guide: d=0.2 is considered small, d=0.5 medium, and d=0.8 large. Use the calculator below to model how different effect-size assumptions translate to required sample sizes for your trial design.

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