normality.py

# generate gaussian data
from numpy.random import seed
from numpy.random import randn
from numpy import mean
from numpy import std
# seed the random number generator
seed(1)
# generate univariate observations
data = 5 * randn(100) + 50
# summarize
print('mean=%.3f stdv=%.3f' % (mean(data), std(data)))

# histogram plot
from numpy.random import seed
from numpy.random import randn
from matplotlib import pyplot
# seed the random number generator
seed(1)
# generate univariate observations
data = 5 * randn(100) + 50
# histogram plot
pyplot.hist(data)
pyplot.show()

# QQ Plot
from numpy.random import seed
from numpy.random import randn
from statsmodels.graphics.gofplots import qqplot
from matplotlib import pyplot
# seed the random number generator
seed(1)
# generate univariate observations
data = 5 * randn(100) + 50
# q-q plot
qqplot(data, line='s')
pyplot.show()

# Shapiro-Wilk Test
from numpy.random import seed
from numpy.random import randn
from scipy.stats import shapiro
# seed the random number generator
seed(1)
# generate univariate observations
data = 5 * randn(100) + 50
# normality test
stat, p = shapiro(data)
print('Statistics=%.3f, p=%.3f' % (stat, p))
# interpret
alpha = 0.05
if p > alpha:
	print('Sample looks Gaussian (fail to reject H0)')
else:
	print('Sample does not look Gaussian (reject H0)')

# D'Agostino and Pearson's Test
from numpy.random import seed
from numpy.random import randn
from scipy.stats import normaltest
# seed the random number generator
seed(1)
# generate univariate observations
data = 5 * randn(100) + 50
# normality test
stat, p = normaltest(data)
print('Statistics=%.3f, p=%.3f' % (stat, p))
# interpret
alpha = 0.05
if p > alpha:
	print('Sample looks Gaussian (fail to reject H0)')
else:
	print('Sample does not look Gaussian (reject H0)')

# Anderson-Darling Test
from numpy.random import seed
from numpy.random import randn
from scipy.stats import anderson
# seed the random number generator
seed(1)
# generate univariate observations
data = 5 * randn(100) + 50
# normality test
result = anderson(data)
print('Statistic: %.3f' % result.statistic)
p = 0
for i in range(len(result.critical_values)):
	sl, cv = result.significance_level[i], result.critical_values[i]
	if result.statistic < result.critical_values[i]:
		print('%.3f: %.3f, data looks normal (fail to reject H0)' % (sl, cv))
	else:
		print('%.3f: %.3f, data does not look normal (reject H0)' % (sl, cv))