Sample Size for Paired Means

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Formula

Sample Size for Paired Means

n = \frac{(Z_{\alpha/2} + Z_{\beta})^2 \times \sigma_d^2}{\Delta^2}

Where:

n = required number of pairs
$Z_{\alpha/2}$ = Z-score for significance level (e.g., 1.96 for 5%)
$Z_{\beta}$ = Z-score for power (e.g., 0.84 for 80%)
$\sigma_d$ = standard deviation of the differences
$\Delta$ = expected mean difference to detect

Power Analysis Visualization

Legend Power Curve

Legend Selected (N=100, Tooltip Power 99.9%)