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 : ($\sigma_d$)
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.