What is a known caveat of the Shapiro-Wilk test in very large samples?

• A. It becomes completely unreliable.
• B. It only detects non-normality for extreme deviations.
• C. A significant result may occur for tiny deviations from normality.
• D. It cannot detect non-normality at all.

Answer: (C)

In very large samples, the Shapiro-Wilk test becomes extremely sensitive to even tiny departures from normality. This means that even minute deviations—practically negligible in many contexts—can produce a statistically significant result. So the caveat is that a significant result may reflect only a trivial deviation from normality, rather than a meaningful lack of normality. This is why the test can flag normal-looking data as non-normal in large samples, whereas in smaller samples it’s less likely to overreact.