Paired Means Testing

Calculation for comparing the means of two dependent (paired) measurements, such as before and after an intervention.

Formula Used (Sample Size, n):

$$n = \frac{\sigma_d^2 (Z_{1-\alpha/2} + Z_{1-\beta})^2}{d^2}$$

Where σ_d is the standard deviation of the difference (paired SD), d is the detectable difference, and n is the number of pairs.

1. SD of the Difference (σ_d):

Expected standard deviation of the **differences** between paired measurements.

2. Detectable Difference (d):

The minimum change you wish to detect in the paired measurements.

3. Significance Level (α):

Probability of a Type I error.

4. Desired Power (1-β):

Probability of correctly detecting the difference.

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