## Sample size required to estimate means dependent samples

The formula to estimate the sample size required to estimate the difference between means of dependent samples is

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

where,

• $z$ is the $Z_{\alpha/2}$ (critical value of $Z$),

• $\sigma_d$ is the population standard deviation of difference between scores,

• $E$ is the margin of error.