Sample size to test mean
Use this calculator to find the minimum sample size required to test mean $\mu$.
| Sample Size to test mean | ||
|---|---|---|
| Confidence Level ($1-\alpha$) | ||
| Power ($1-\beta$) | ||
| Mean under H0 : ($\mu_0$) | ||
| Mean under H1 : ($\mu_1$) | ||
| Standard Deviation ($\sigma$) | ||
| Results | ||
| Effect Size ($ES$) | ||
| Z value: $Z_{1-\alpha/2}$ | ||
| Z value: $Z_{1-\beta}$ | ||
| Required Sample Size : ($n$) | ||
Sample size to test mean
The $ES$ is defined as $$ ES=\frac{|\mu_1-\mu_0|}{\sigma} $$
where $\mu_0$ is the mean under $H_0$ and $\mu_1$ is the mean under $H_1$, $\sigma$ is the standard deviation.
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.
