1. What is the Shapiro-Wilk Test?

The Shapiro-Wilk test is a statistical test of normality that determines whether a given sample comes from a normally distributed population. It's particularly effective for small to medium sample sizes (3 ≤ n ≤ 5000).

2. How Does the Calculator Work?

The calculator uses the Shapiro-Wilk equation:

Where:

• \( W \) — Test statistic (dimensionless)
• \( a_i \) — Coefficients (dimensionless)
• \( x_i \) — Ordered sample values
• \( \bar{x} \) — Sample mean

Explanation: The test compares the ordered sample values with what would be expected if the data were normally distributed.

3. Importance of Normality Testing

Details: Many statistical tests assume normality of data. The Shapiro-Wilk test helps verify this assumption before applying parametric tests.

4. Using the Calculator

Tips: Enter your sample data as comma-separated values. The calculator will sort the data and compute the W statistic. Values of W close to 1 suggest normality.

5. Frequently Asked Questions (FAQ)

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

Q2: How do I interpret the W statistic?
A: W ranges from 0 to 1, with values close to 1 indicating normality. The exact critical values depend on sample size.

Q3: What are the limitations of Shapiro-Wilk?
A: The test is sensitive to sample size - with large samples, it may detect trivial departures from normality.

Q4: Should I always test for normality?
A: Normality tests are most important for small samples. With large samples (n > 50), graphical methods may be more informative.

Q5: Are there alternatives to Shapiro-Wilk?
A: Other normality tests include Kolmogorov-Smirnov, Anderson-Darling, and D'Agostino's K-squared test.