stats

Shapiro-Wilk Normality Test

W statistic and p-value for normality — Q-Q plot, skewness/kurtosis, α=0.05/0.01 conclusions. Supports n = 3 to 50.

Input — Data Set (n = 3 to 50)
Results
Sample size n
W statistic
p-value
α = 0.05
α = 0.01
Skewness g₁
Excess kurtosis g₂
W = (Σaᵢ(x_(n+1-i)−x_(i)))² / Σ(xᵢ−x̄)²  ·  Shapiro & Wilk (1965)
p-value via Royston (1992) ln(1−W) approximation
W close to 1 → data consistent with normality
For n > 50 use the Kolmogorov-Smirnov test