## Sample size required to test proportion

Use this calculator to find the minimum sample size required to test hypothesis about proportion $p$.

## Sample size required to test proportion

The $ES$ is defined as $$ES=\frac{|p_1-p_0|}{\sqrt{p_0*(1-p_0)}}$$

where

• $p_0$ is the proportion under null hypothesis,
• $p_1$ is the proportion under alternative hypothesis.

The formula for determining the sample size required to ensure that the test has a specified power is

$$n =\bigg(\frac{Z_{1-\alpha/2}+Z_{1-\beta}}{ES}\bigg)^2$$

where

• $\alpha$ is the selected level of significance,
• $1-\beta$ is the selected power and
• $ES$ is the effect size.