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 : ($\sigma$)
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.

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