## Sample size to estimate proportions

Use this calculator to find the minimum sample size required to estimate proportions $p_1-p_2$.

Sample size to estimate proportions | ||
---|---|---|

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

Proportion of success ($p_1$) | ||

Proportion of success ($p_2$) | ||

Margin of Error ($E$) | ||

Results | ||

Z value: | ||

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

## Sample size required to estimate proportions

The minimum sample size required to estimate the proportions $p_1-p_2$ is

```
$$
n =\big[p_1*(1-p_1)+p_2*(1-p_2)\big]\bigg(\frac{z}{E}\bigg)^2
$$
```

where

- $p_1$ is the proportion of successes in first group,
- $p_2$ is the proportion of successes in second group,
- $z$ is the $Z_{\alpha/2}$ and
- $E$ is the margin of error.