D’Agostino’s $K^2$ Test

Tests whether a data sample has a Gaussian distribution.

Assumptions

• Observations in each sample are independent and identically distributed (iid).

Hypothesis Formulation

• H0: the sample has a Gaussian distribution.
• H1: the sample does not have a Gaussian distribution.

Code Implementation

# Example of the D'Agostino's K^2 Normality Test
from scipy.stats import normaltest
data = [0.873, 2.817, 0.121, -0.945, -0.055, -1.436, 0.360, -1.478, -1.637, -1.869]
stat, p = normaltest(data)
print('stat=%.3f, p=%.3f' % (stat, p))
if p > 0.05:
	print('Probably Gaussian')
else:
	print('Probably not Gaussian')

References