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,
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$z$ is the $Z_{\alpha/2}$ (critical value of $Z$),
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$\sigma_d$ is the population standard deviation of difference between scores,
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$E$ is the margin of error.
