Sample size to test means $\mu_1-\mu_2$
Use this calculator to find the minimum sample size required to test mean $\mu_1-\mu_2$.
| Sample Size to test means | ||
|---|---|---|
| Confidence Level ($1-\alpha$) | ||
| Power ($1-\beta$) | ||
| First group mean : ($\mu_1$) | ||
| Second group mean : ($\mu_2$) | ||
| 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 means $\mu_1-\mu_2$
The $ES$ is defined as
$$ ES=\frac{|\mu_1-\mu_2|}{\sigma} $$
where
- $\mu_1$ is the mean of the first group,
- $\mu_2$ is the mean of the second group,
- $\sigma$ is the standard deviation.
The formula for determining the sample size required in each group to ensure that the test has a specified power is
$$ n =2\bigg(\frac{Z_{1-\alpha/2}+Z_{1-\beta}}{ES}\bigg)^2 $$
where
- $\alpha$ is the selected level of significance,
- $1-\beta$ is the selected power and
- $ES$ is the effect size.
