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—
Supporting Evidence
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
W close to 1 → data consistent with normality
For n > 50 use the Kolmogorov-Smirnov test