Sample size for baseline and endline surveys

Introduction

This calculator is appropriate when you are planning two independent samples of the same population, before and after an intervention.

The formula used by this calculator is based on the following equality from Wang (2007)

$$ n = (Z_{α/2}+Z_β)^2 \frac{f p_1(1-p_1)+f p_2(1-p_2)}{(p_1-p_2)^2} $$

Where f is the finite population correction factor, which is

$$ f = \sqrt{\frac{N - n}{N-1}} $$

Substituting and solving for n yields:

$$ n = \frac{XA}{1+XB} $$

Where:

$$ X = \frac{(Z_{α/2}+Z_β)^2}{(p_1-p_2)^2} $$

$$ A = \frac{N p_1 (1-p_1) }{N-1} + \frac{N p_2(1-p_2)}{N-1} $$

$$ B = \frac{p_1(1-p_1)}{N-1} + \frac{p_2(1-p_2)}{N-1} $$