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.

2. How Does the Calculator Work?

The calculator uses the Shapiro-Wilk test formula:

Where:

• \( W \) — Test statistic
• \( x_{(i)} \) — Ordered sample values
• \( a_i \) — Constants generated from the means, variances and covariances of the order statistics
• \( \bar{x} \) — Sample mean

Interpretation: The null hypothesis is that the data is normally distributed. A p-value < 0.05 typically leads to rejecting the null hypothesis.

3. Importance of Normality Testing

Details: Many statistical tests (t-tests, ANOVA, etc.) assume normally distributed data. Checking normality helps ensure the validity of these tests.

4. Using the Calculator

Tips: Enter your numerical data points separated by commas. The test requires at least 3 observations (works best with 5+). Remove any non-numeric values before submitting.

5. Frequently Asked Questions (FAQ)

Q1: What sample size works best?
A: The Shapiro-Wilk test works well for sample sizes between 3 and 5000, but is most powerful for n < 50.

Q2: What are alternatives to Shapiro-Wilk?
A: For larger samples (>50), Kolmogorov-Smirnov or Anderson-Darling tests may be used.

Q3: What if my data isn't normal?
A: Consider data transformations (log, square root) or non-parametric tests that don't assume normality.

Q4: Can I use this for very small samples?
A: The test has low power for very small samples (n < 5) - consider graphical methods like Q-Q plots instead.

Q5: How strict is the 0.05 threshold?
A: This is conventional but arbitrary. For critical applications, consider both tests and visual inspection.