Normality Test: Is Your Data Normal?
The Principle of Normality Testing
A normality test uses hypothesis testing to decide whether data come from a normal population: the null hypothesis is that the data are normal, and a p-value below 0.05 (the usual alpha) rejects it. Common methods include the Anderson-Darling test (sensitive and comprehensive), the Shapiro-Wilk test (recommended for small samples) and the Kolmogorov-Smirnov test (requires specified parameters). Supporting graphs include the histogram and the normal probability plot (Q-Q plot). Running several tests in parallel gives cross-confirmation, and combining graphs with tests is more robust than a single p-value for judging the data shape.
When to Use It
Use a normality test as a prerequisite check before applying normality-assuming methods such as t-tests, ANOVA, control charts and CpK calculations; for data-distribution diagnostics; and as a mandatory step in capability analysis. The tool is also built into the CpK and SPC workflows as an automatic prerequisite check, prompting you when data are non-normal to prevent misuse of normal methods. As a front-end check for capability analysis, the tool automatically flags normality risk in the CpK and SPC flows, avoiding method misuse from the start.
How to Read the Results
Look at the p-value first: p >= 0.05 means normality cannot be rejected (the data can be treated as approximately normal); p < 0.05 indicates non-normality. Then look at the graphs: if the Q-Q plot points fall roughly on a straight line, the data are approximately normal, and slight deviation at the ends can be tolerated. The tool also shows the histogram with a fitted normal curve and supports AI interpretation to help with the overall judgment. Cross-check p-values with the graphs, note the approximate-normal assumption in reports when appropriate, and the tool automatically marks the applicable range of each test method.
Precautions
With large samples, tiny deviations can make the test reject normality significantly; combine the result with the graphs. For samples under 30, prefer the Shapiro-Wilk test. If the test is significant but the graphs look approximately normal, most statistical methods (such as large-sample t-tests) remain robust, so do not overreact; if non-normality is severe, use transformations or nonparametric methods. With large samples, graphical judgment is more reasonable; for non-normal data, prefer transformation first and nonparametric methods second, choosing the path by the data's nature.