Shapiro-Wilk Test

The Shapiro-Wilk test is the gold standard for normality testing with small samples — precisely the situation quality engineers face most often. When you have 15 measurements from a pilot run or 25 parts from a capability study, Shapiro-Wilk gives you the most reliable answer about whether your data is normally distributed.

But "most reliable" is relative. With 15 measurements, even Shapiro-Wilk struggles to detect moderate skewness or kurtosis. The test tells you "I don't have enough evidence to say this isn't normal" — which is very different from "this data is normal." Engineers routinely misinterpret failure to reject as confirmation of normality, then proceed with Gaussian-based capability calculations on data that may well be non-normal.

The deeper problem is that the test asks the wrong question for quality engineering purposes. "Is this data exactly normally distributed?" matters less than "Will my capability calculations be accurate?" A slightly non-normal distribution might produce negligible Cpk error, while a moderately non-normal one could produce significant error — and the Shapiro-Wilk test does not quantify this practical impact.

EntropyStat eliminates the need for normality testing altogether. The EGDF does not require normality — or any distributional assumption — so the Shapiro-Wilk question becomes irrelevant. Whether your 15-measurement pilot run is normally distributed or not, the EGDF produces a reliable distribution estimate and accurate capability indices.

This is especially valuable for the small-sample scenarios where Shapiro-Wilk is supposed to shine. With 10–20 measurements, the test's statistical power is limited, meaning it often fails to detect meaningful non-normality. Meanwhile, the EGDF's entropy-based optimization is specifically designed for small samples — 5–8 measurements are sufficient for stable distribution estimates, compared to the 30+ that parametric methods require.

The practical benefit: teams can skip the "test for normality → choose method" decision tree entirely. One analytical approach works across all data types and sample sizes, removing a subjective decision point that often varies between engineers and between software packages.