What is the Shapiro-Wilk Test?

The Shapiro-Wilk test is widely recognized by statisticians as the most powerful test for checking normality, particularly for sample sizes up to 5,000. It calculates a W statistic that tests whether a random sample comes from a normal distribution. Small values of W represent a departure from normality.

When to use it?

This is the first step in almost any rigorous statistical analysis. You use it to:

• Assumption Checking: Verify if you can use parametric tests like the T-Test, ANOVA, or Linear Regression.
• Data Cleaning: Identify if skewness or kurtosis is affecting your dataset.
• Decision Making: Decide whether to transform your data (e.g., Log transformation) or switch to non-parametric alternatives.

How our tool works (Accuracy & Stack)

Our engine uses Python’s `scipy.stats.shapiro` function running on Google Cloud. This implementation is known for its high power compared to other normality tests like Kolmogorov-Smirnov. We cross-reference our results with R’s base stats package to guarantee accuracy.

Visual confirmation of normality is just as important as the P-value. We provide:

• Q-Q Plots (Quantile-Quantile): The critical visualization for normality. Points deviating from the diagonal line indicate non-normality.
• Histograms with Normal Curve: Overlays a theoretical bell curve on your actual data for visual comparison.
• Box Plots: To quickly spot outliers causing non-normality.

Get all these insights in a downloadable PDF Report.

Input Requirements & Limitations

While the Shapiro-Wilk test is mathematically computationally intensive for massive datasets, our cloud architecture handles it efficiently within these bounds:

• Row Limit: Supports up to 5,000 rows per group.
• Column Limit: Supports up to 10 variables (columns) processed simultaneously.
• Total Data Points: Maximum 50,000 data points.

This constraint ensures that the Q-Q plot generation remains responsive. CSV import is fully supported.

Comparison: Shapiro-Wilk vs. Kolmogorov-Smirnov

While both tests check for normality, the Shapiro-Wilk test is proven to be more powerful (more likely to detect non-normality when it exists) than the Kolmogorov-Smirnov test, especially without the Lilliefors correction. For most modern statistical applications, the Shapiro-Wilk is the preferred method.