1. What is the Shapiro-Wilk Normality Test?

The Shapiro-Wilk test is a statistical test of the null hypothesis that a sample came from a normally distributed population. It is one of the most powerful tests for normality, especially for small sample sizes.

2. How Does the Calculator Work?

The calculator uses the Shapiro-Wilk test formula:

Where:

• \( W \) — Test statistic (0 ≤ W ≤ 1)
• \( x_{(i)} \) — i-th order statistic (sorted sample values)
• \( a_i \) — Coefficients generated from the means, variances and covariances of the order statistics
• \( \bar{x} \) — Sample mean
• \( n \) — Sample size

Interpretation: Values of W close to 1 indicate normality. Small values indicate non-normal distributions.

3. Importance of Normality Testing

Details: Many statistical tests (t-tests, ANOVA, etc.) assume normally distributed data. The Shapiro-Wilk test helps verify this assumption before applying parametric tests.

4. Using the Calculator

Tips: Enter numeric values separated by commas. The test works best with sample sizes between 3 and 5000. For very large samples, even small deviations from normality may be statistically significant.

5. Frequently Asked Questions (FAQ)

Q1: What sample size is appropriate for Shapiro-Wilk?
A: The test works well for 3 ≤ n ≤ 5000, but is most commonly used for n ≤ 50.

Q2: What's a good W value for normality?
A: Typically W > 0.90 suggests normality, but the critical value depends on sample size and significance level.

Q3: How does this compare to other normality tests?
A: Shapiro-Wilk is more powerful than Kolmogorov-Smirnov or Anderson-Darling for small samples.

Q4: What if my data isn't normal?
A: Consider data transformation or non-parametric statistical tests.

Q5: Can I use this for very large datasets?
A: For n > 5000, other tests like Kolmogorov-Smirnov may be more appropriate.