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 (3 ≤ n ≤ 5000).

2. How Does the Calculator Work?

The calculator uses the Shapiro-Wilk test formula:

Where:

• \( W \) — Test statistic (values closer to 1 indicate normality)
• \( x_{(i)} \) — Ordered sample values
• \( a_i \) — Coefficients generated from the means, variances and covariances
• \( \bar{x} \) — 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 (not normal).

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 numerical data points separated by commas. The test works best with sample sizes between 3 and 5000. For very large datasets, other normality tests may be more appropriate.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Shapiro-Wilk and Kolmogorov-Smirnov?
A: Shapiro-Wilk is generally more powerful for small samples, while Kolmogorov-Smirnov is more general but less sensitive to non-normality.

Q2: What sample size is too small for Shapiro-Wilk?
A: The test works for n ≥ 3, but results become more reliable with n ≥ 20.

Q3: What if my data fails the normality test?
A: Consider data transformations or non-parametric statistical tests.

Q4: Can I use this for categorical data?
A: No, the Shapiro-Wilk test is only for continuous numerical data.

Q5: How accurate is this online calculator?
A: For critical research, verify results with statistical software like R or SPSS.