Sample size to test mean difference $\mu_d$ in dependent samples
Use this calculator to find the minimum sample size required to test mean difference $\mu_d$.
| Sample Size to test means (paired) | ||
|---|---|---|
| Confidence Level ($1-\alpha$) | ||
| Power ($1-\beta$) | ||
| Mean of difference: ($\mu_d$) | ||
| Standard Deviation : ($\sigma_d$) | ||
| Results | ||
| Effect Size ($ES$) | ||
| Z value: $Z_{1-\alpha/2}$ | ||
| Z value: $Z_{1-\beta}$ | ||
| Required Sample Size : ($n$) | ||
Sample size to test means of dependent samples
The $ES$ is defined as
$$ ES=\frac{|\mu_d|}{\sigma_d} $$
where
- $\mu_d$ is the mean of the difference,
- $\sigma_d$ is the standard deviation of the difference.
The formula for determining the sample size required in each group 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.
