One more thing

One thing I forgot to do is test the two_sample_t function. Here we draw samples of different sizes (m=2,n=4) from distributions A and B (normal with the same mean and standard deviation). Since A and B have the same mean, the expected difference is 0. We record how frequently p < 0.05 and it is, as expected, about 5%. The corresponding t-statistic is -2.133, which is also expected, for one-tailed application of the t-test with 4 degrees of freedom.

output:

0.0491 -2.133 0.0516 -2.133 0.0524 -2.133 0.0506 -2.133 0.0502 -2.133

code listing:

from __future__ import division import numpy as np from t_test import two_sample_t mu,sigma = 10,3 m,n = 2,4 alpha = 0.05 N = 10000 tmax = -N for i in range(5): counter = 0 for j in range(N): A = np.random.normal(mu,sigma,m) B = np.random.normal(mu,sigma,n) t,p = two_sample_t(A,B) if p < alpha: counter += 1 if t > tmax: tmax = t print '%3.4f' % (counter/N), print round(tmax,3)