# 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.

## Formulas

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:

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

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

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