Independent Means Testing

Calculation for comparing the means (μ₁ vs. μ₂) of two independent study groups.

Formula Used (Sample Size per Group, n):

$$n = \frac{2 \sigma^2 (Z_{1-\alpha/2} + Z_{1-\beta})^2}{(\mu_1 - \mu_2)^2}$$

Where σ is the common standard deviation, μ₁ - μ₂ is the detectable difference, and n is the sample size *per group*.

1. Estimated Standard Deviation (σ):

Expected variability in both groups (common SD).

2. Detectable Difference (μ₁ - μ₂):

The minimum difference between means you wish to detect.

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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