Two Proportions Sample Size Calculator

Free

Calculate the sample size needed to detect a difference in proportions between two independent groups using chi-square test.

Study Parameters
Results

Required Sample Size

188

Group 1: 94 | Group 2: 94

Achieved Power

80.4%

Effect Size

0.412

Method: Two Proportions (Fleiss 1981)
Allocation ratio1:1
Cohen's h0.412
Risk difference0.200
  • Independent samples
  • Binary outcome in each group
  • Normal approximation to the binomial distribution
  • Two-sided hypothesis test
  • Equal allocation (1:1 randomization)
  • No continuity correction
Formula
n1 = [z_{alpha/2} * sqrt((1+1/k) * p_bar * q_bar) + z_beta * sqrt(p1*q1 + p2*q2/k)]^2 / (p1 - p2)^2
References
  1. Fleiss JL (1981). Statistical Methods for Rates and Proportions, 2nd ed. Wiley.
  2. Fleiss JL, Tytun A, Ury HK (1980). A simple approximation for calculating sample sizes for comparing independent proportions. Biometrics, 36, 343-346.