## 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.