1. What is the Shapiro-Wilk Test?

The Shapiro-Wilk test is a statistical test of normality that determines whether a given sample comes from a normally distributed population. The p-value helps assess the significance of the test statistic W.

2. How Does the Calculator Work?

The calculator estimates the p-value based on the Shapiro-Wilk test statistic:

Where:

• \( W \) — Shapiro-Wilk test statistic (0 ≤ W ≤ 1)
• \( n \) — Sample size (number of observations)

Explanation: The p-value represents the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis (that the data are normally distributed) is true.

3. Importance of P-value Calculation

Details: The p-value helps determine whether to reject the null hypothesis of normality. Typically, p-values below 0.05 indicate significant departure from normality.

4. Using the Calculator

Tips: Enter the W statistic (between 0 and 1) and sample size (n ≥ 3). The calculator will estimate the corresponding p-value for the normality test.

5. Frequently Asked Questions (FAQ)

Q1: What does a high W value mean?
A: W values closer to 1 indicate the sample is more likely to be normally distributed.

Q2: What sample size is appropriate?
A: The test works best with sample sizes between 3 and 5000. Very small samples may lack power, while very large samples may detect trivial deviations from normality.

Q3: How accurate is this calculator?
A: This provides an approximation. For research purposes, use exact statistical software or tables.

Q4: When should I use this test?
A: Use before parametric tests that assume normality. If p < 0.05, consider non-parametric alternatives.

Q5: Are there alternatives to Shapiro-Wilk?
A: Yes, including Kolmogorov-Smirnov, Anderson-Darling, and Lilliefors tests, but Shapiro-Wilk is often most powerful.