Shapiro-Wilk test

The Shapiro-Wilk test checks whether measurements fit a normal distribution. W close to 1 means good agreement. If p is smaller than .05, the distribution departs from the normal distribution; otherwise the test does not indicate a departure.

Example: Reaction times of 60 people: W = .912, p < .001. The distribution is skewed; the median describes the center better.

Caution: With many people the test flags even small departures; with few it misses large ones. The Q-Q plot complements it. A result that is not clear does not prove a normal distribution.