Brunner Munzel test

Purpose: To test whether 2 samples are drawn from the same population without assuming equal variance.

Null hypothesis: Sample A and Sample B were drawn from the same population

Alternate hypothesis: Sample A and Sample B were not drawn from the same population

Note: Brunner-Munzel test is Mann-Whitney U test without assuming equal variance, and is a non-parametric version of 2-samples (independent samples) t-test.

Code:

>>> from scipy import stats
>>> X1 = [9.07, 8.97, 6.41, 3.03, 1.19, 2.67, 2.81, 9.2]
>>> X2 = [3.82, 8.26, 5.99, 3.81, 1.07, 5.06, 5.66, 4.47]
>>> result = stats.brunnermunzel(X1, X2)
>>> print("W = %.2f" % result[0])
W = -0.27
>>> print("p-value = %.2f" % result[1])
p-value = 0.79

Reference:

1. Brunner E, Munzel U. The nonparametric Benhrens-Fisher problem: Asymptotic theory and a small-sample approximation. Biometrical Journal 42(2000), 17-25.