Shapiro-Wilk Normality Test Calculator

Real-time statistical analysis for data distribution testing

Data Input & Visualization

Enter at least 3 and up to 5000 data points for analysis.
Sample Size (n)
20
Mean
7.07

Test Results

Shapiro-Wilk Test Result

NORMAL
W Statistic
0.981
P-Value
0.962
Interpretation: The data appears to be normally distributed (p > 0.05).

Test Configuration

Additional Statistics

Median
7.25
Std. Deviation
2.15
Skewness
0.12
Kurtosis
-0.85

Advanced Options & Additional Tests

Understanding the Shapiro-Wilk Test

The Shapiro-Wilk test is one of the most powerful and widely used statistical tests for assessing whether a dataset follows a normal distribution. Normality testing is a crucial step in many statistical analyses, as many parametric tests assume normally distributed data.

What is the Shapiro-Wilk Test?

The Shapiro-Wilk test evaluates the null hypothesis that a sample comes from a normally distributed population. Developed by Samuel Shapiro and Martin Wilk in 1965, this test is particularly effective for small to medium sample sizes (3 to 5000 observations).

How to Use This Tool

  1. Input Your Data: Enter your numerical data in the text area. You can separate values with commas, spaces, or line breaks.
  2. Review Data Summary: Check the sample size, mean, and visual distribution in the histogram.
  3. Run the Test: Click "Run Shapiro-Wilk Test" to calculate the W statistic and p-value.
  4. Interpret Results:
    • p-value > α (alpha): Fail to reject the null hypothesis - data appears normal
    • p-value ≤ α (alpha): Reject the null hypothesis - data does not appear normal
  5. Explore Advanced Options: Use additional tests and visualization options for comprehensive analysis.

Interpreting the Results

The Shapiro-Wilk test produces two key outputs:

  • W Statistic: Ranges from 0 to 1, where values closer to 1 indicate stronger evidence for normality.
  • P-value: The probability of obtaining the observed results if the null hypothesis (data is normal) is true.

Typically, if the p-value is less than your chosen significance level (α = 0.05 by default), you reject the null hypothesis and conclude the data is not normally distributed.

When to Use the Shapiro-Wilk Test

  • Before applying parametric statistical tests (t-tests, ANOVA, regression)
  • When checking assumptions for statistical process control
  • During data quality assessment and exploratory data analysis
  • When selecting appropriate statistical methods for research

Limitations and Considerations

While the Shapiro-Wilk test is powerful, keep these points in mind:

  • The test is sensitive to sample size - with very large samples, it may detect trivial deviations from normality
  • It tests for complete normality, which is a strict criterion
  • Consider visual methods (QQ plots, histograms) alongside formal testing
  • Some statistical procedures are robust to moderate deviations from normality

This tool provides a comprehensive solution for performing the Shapiro-Wilk test with real-time calculations, visualization, and detailed reporting. For research and academic purposes, always consult with a statistician when making critical decisions based on normality test results.