Sign Test Statistical Power Calculator

Understanding Statistical Power in the Sign Test

Statistical power represents the probability that a test correctly rejects a false null hypothesis. In non-parametric statistics, the sign test serves as a valuable alternative to the one-sample t-test when data fail to meet normality assumptions. By evaluating direction changes rather than raw magnitudes, researchers gain robust inference capabilities. Calculating power beforehand ensures adequate resource allocation and prevents underpowered studies that miss true effects.

Formula Used

The sign test relies directly on the binomial distribution. Given sample size $n$ and hypothesized probability $p$, the exact probability of observing $k$ positive differences is computed via:

$$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$$

Critical regions are established based on the significance level $\alpha$, and statistical power is determined by summing the binomial probabilities over the critical rejection regions under the alternative proportion $p_1$.

How to Use This Calculator

• Enter Sample Size: Input your target number of paired observations or subjects in field $n$.
• Set Proportions: Define your null proportion ($p_0$) and anticipated alternative proportion ($p_1$).
• Choose Alpha: Select your preferred significance threshold (e.g., 0.05).
• Submit Data: Click the calculate button to instantly review your comprehensive power evaluation results above.

Frequently Asked Questions