test.py

#t-test for dependent samples
from math import sqrt
from numpy.random import seed
from numpy.random import randn
from numpy import mean
from scipy.stats import t

# function for calculating the t-test for two dependent samples
def dependent_ttest(data1, data2, alpha):
	# calculate means
	mean1, mean2 = mean(data1), mean(data2)
	# number of paired samples
	n = len(data1)
	# sum squared difference between observations
	d1 = sum([(data1[i]-data2[i])**2 for i in range(n)])
	# sum difference between observations
	d2 = sum([data1[i]-data2[i] for i in range(n)])
	# standard deviation of the difference between means
	sd = sqrt((d1 - (d2**2 / n)) / (n - 1))
	# standard error of the difference between the means
	sed = sd / sqrt(n)
	# calculate the t statistic
	t_stat = (mean1 - mean2) / sed
	# degrees of freedom
	df = n - 1
	# calculate the critical value
	cv = t.ppf(1.0 - alpha, df)
	# calculate the p-value
	p = (1.0 - t.cdf(abs(t_stat), df)) * 2.0
	# return everything
	return t_stat, df, cv, p

# seed the random number generator
seed(1)
# generate two independent samples (pretend they are dependent)
data1 = 5 * randn(100) + 50
data2 = 5 * randn(100) + 51

data1=data1.reshape([100,-1])
data2=data2.reshape([100,-1])

print('==============data1==========',data1)
print('==============data2==========',data2)
# calculate the t test
alpha = 0.05
t_stat, df, cv, p = dependent_ttest(data1, data2, alpha)
print('t=%.3f, df=%d, cv=%.3f, p=%.3f' % (t_stat, df, cv, p))
# interpret via critical value
if abs(t_stat) <= cv:
	print('Accept null hypothesis that the means are equal.')
else:
	print('Reject the null hypothesis that the means are equal.')
# interpret via p-value
if p > alpha:
	print('Accept null hypothesis that the means are equal.')
else:
	print('Reject the null hypothesis that the means are equal.')