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 (unitless, between 0 and 1)
• \( a_i \) — Coefficients derived from the expected values of standard normal order statistics
• \( x_i \) — 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 (like t-tests, ANOVA) assume normally distributed data. The Shapiro-Wilk test helps verify this assumption before applying parametric tests.

4. Using the Calculator

Tips: Enter your data as comma-separated values. The test works best with sample sizes between 3 and 5000. For n > 50, other normality tests might be more appropriate.

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 is most reliable for sample sizes between 3 and 50. For larger samples, consider other tests like Kolmogorov-Smirnov.

Q3: What are typical critical values?
A: For α=0.05: ~0.90-0.98 depending on sample size. Exact values come from Shapiro-Wilk tables.

Q4: When should I test for normality?
A: Before using parametric tests that assume normality, or when exploring data distributions.

Q5: What if my data isn't normal?
A: Consider non-parametric tests, data transformations, or check for outliers that might affect the distribution.