How to Calculate Minimum Sample Size for a T-Test in Python

Compute the minimum sample size per group for a two-sample t-test using effect size, significance level, and statistical power.

Easy Python 3.9+ Aug 9, 2026 A/B testing & experimentation 15 views 0 copies

sample-size statistics ab-testing scipy t-test
Requires third-party packages — install first
pip install scipy

Python code

28 lines
Python 3.9+ 
import math
from scipy.stats import norm


def min_sample_size(effect_size, alpha=0.05, power=0.8):
    """
    Calculate minimum sample size for a two-sample t-test (equal groups).

    Args:
        effect_size: Cohen's d (standardized mean difference)
        alpha: significance level (Type I error)
        power: desired statistical power (1 - Type II error)

    Returns:
        Minimum sample size per group (rounded up)
    """
    z_alpha = norm.ppf(1 - alpha / 2)
    z_beta = norm.ppf(power)

    n = (2 * (z_alpha + z_beta) ** 2) / (effect_size ** 2)
    return math.ceil(n)


if __name__ == "__main__":
    # Example: effect size 0.5, 95% confidence, 80% power
    n_per_group = min_sample_size(effect_size=0.5)
    print(f"Minimum sample size per group: {n_per_group}")
    print(f"Total sample size (two groups): {n_per_group * 2}")

Output

stdout 
Minimum sample size per group: 64
Total sample size (two groups): 128

How it works

The function uses the normal approximation to estimate the required sample size per group for a two-sample t-test. It computes z-scores for the chosen alpha and power using scipy.stats.norm.ppf. The formula n = 2 * (z_alpha + z_beta)^2 / effect_size^2 balances Type I and Type II error rates. math.ceil rounds up to ensure you meet the minimum statistical requirement. This approach is standard for balanced A/B tests before data collection begins.

Common mistakes

  • Using `math.floor` instead of `math.ceil`, underestimating needed participants
  • Forgetting to account for unequal group sizes in real experiments
  • Using one-tailed z-values when a two-tailed test is required

Variations

  1. Use `statsmodels` `NormalIndPower` for more complex designs
  2. Add a correction factor for finite populations

Real-world use cases

  • Determining participant counts for an A/B test on a marketing landing page.
  • Sizing a clinical trial cohort before recruiting patients for a drug study.
  • Estimating required sample sizes for user research experiments in product analytics.

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