## 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.