Sample size required to estimate means dependent samples

Sample Size to estimate means(paired)
Confidence Level ($1-\alpha$)
Standard Deviation ($\sigma_d$)
Margin of Error ($E$)
Z value:
Required Sample Size : ($n$)

Sample size required to estimate difference between means of dependent samples

The formula to estimate the sample size required to estimate the mean of two dependent samples is

$$ n =\bigg(\frac{z\sigma_d}{E}\bigg)^2 $$


  • $n$ is the sample size,
  • $z$ is the $Z_{\alpha/2}$,
  • $\sigma_d$ is the population standard deviation of the difference and
  • $E$ is the margin of error.

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