1. What is the Shapiro-Wilk Test?

The Shapiro-Wilk test is a statistical test of normality that determines whether a given sample of data comes from a normally distributed population. It's particularly effective for small to medium sample sizes (n < 50).

2. How Does the Calculator Work?

The calculator uses the Shapiro-Wilk formula:

Where:

• \( W \) — Test statistic (0 ≤ W ≤ 1)
• \( a_i \) — Coefficients derived from expected normal order statistics
• \( x_i \) — Ordered sample values
• \( \bar{x} \) — Sample mean
• \( n \) — Sample size

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 (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 your data points separated by commas. The calculator works best with sample sizes between 3 and 5000. For accurate results, use statistical software for exact coefficient values.

5. Frequently Asked Questions (FAQ)

Q1: What does the W statistic mean?
A: W ranges from 0 to 1, with values closer to 1 indicating stronger evidence for normality.

Q2: What sample size is appropriate?
A: The test works best for 3 ≤ n ≤ 5000, but is most powerful for n < 50.

Q3: How does this compare to other normality tests?
A: Shapiro-Wilk is generally 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: Are there limitations to this test?
A: The test can be too sensitive with large samples, detecting trivial departures from normality.