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 moderate sample sizes.

2. How Does the Calculator Work?

The calculator uses the Shapiro-Wilk formula:

Where:

• \( W \) — Shapiro-Wilk test statistic
• \( a_i \) — Coefficients specific to sample size
• \( x_i \) — Ordered sample values
• \( \bar{x} \) — Sample mean

Explanation: The test compares the ordered sample values with what would be expected from a normal distribution using specific coefficients.

3. Importance of Normality Testing

Details: Normality testing is crucial for many statistical procedures that assume normally distributed data, including parametric tests like t-tests and ANOVA.

4. Using the Calculator

Tips: Enter your data points separated by commas. The calculator will sort the data and perform the Shapiro-Wilk normality test calculation.

5. Frequently Asked Questions (FAQ)

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

Q2: What sample sizes work best with Shapiro-Wilk?
A: The test works best with sample sizes between 3 and 5000, but is most commonly used for n ≤ 2000.

Q3: How do I interpret the p-value?
A: A p-value > 0.05 suggests the data may come from a normal distribution, while p-value ≤ 0.05 suggests non-normality.

Q4: Are there alternatives to Shapiro-Wilk?
A: Yes, other normality tests include Kolmogorov-Smirnov, Anderson-Darling, and Lilliefors tests.

Q5: When should I use normality tests?
A: Use normality tests to check assumptions before applying parametric statistical methods that require normally distributed data.