## Sample size required to test proportion

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

The minimum sample size required to test the population proportion 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,
- $ES$ is the effect size.

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

where

- $p_0$ is the proportion under $H_0$ and
- $p_1$ is the proportion under $H_1$.