## Sample size required to test proportion

Use this calculator to find the minimum sample size required to estimate proportion $p$.

Sample Size to test proportion | ||
---|---|---|

Confidence Level ($1-\alpha$) | ||

Power ($1-\beta$) | ||

Proportion under H0 : ($p_0$) | ||

Proportion under H1 : ($p_1$) | ||

Results | ||

Effect Size ($ES$) | ||

Z value: $Z_{1-\alpha/2}$ | ||

Z value: $Z_{1-\beta}$ | ||

Required Sample Size : ($n$) | ||

## Sample size required to estimate proportion

The minimum sample size required to estimate the proportion is
```
$$
\begin{aligned}
n &\approx \bigg(\frac{Z_{1-\alpha/2}+Z_{1-\beta}}{ES}\bigg)^2
\end{aligned}
$$
```

where

```
$$
\begin{aligned}
ES &\frac{|p_1-p_0|}{\sqrt{p_0*(1-p_0)}}
\end{aligned}
$$
```

- $p_0$ is the proportion under null hypothesis $H_0$
- $p_1$ is the proportion under alternative hypothesis $H_1$
- $Z_{1-\alpha/2}$ is the critical value of $Z$
- $Z_{1-\beta}$ is the aaaaaaaaa
- $ES$ is the effect size.