A quick check for size and power of mannwhitneyu if data is poisson

mc_mannwhitenyu.py

# -*- coding: utf-8 -*-
"""

Created on Sat Feb 16 20:52:22 2013

Author: Josef Perktold
"""

import numpy as np
from scipy import stats

quantiles = np.array([0.01, 0.05, 0.10, 0.25]) 

n_mc = 1000
nobs1, nobs2 = 10, 10 #20, 20
print 'lam1, lam2, nobs1, nobs2, [0.01, 0.05, 0.10, 0.25]'
for lam1 in range(1, 10, 2):
    for lam2 in range(1, 10, 2):
        mc = np.zeros((n_mc,2))
        for i in xrange(n_mc):       
            rvs1 = np.random.poisson(lam1, nobs1)
            rvs2 = np.random.poisson(lam2, nobs2)
            mc[i] = stats.mannwhitneyu(rvs1, rvs2)

        null = 'null' if lam1 == lam2 else ''
        print lam1, lam2, nobs1, nobs2, (mc[:,1:2]*2 < quantiles).mean(0), null

'''
lam1, lam2, nobs1, nobs2, [0.01, 0.05, 0.10, 0.25]
1 1 20 20 [ 0.013  0.045  0.085  0.22 ] null
1 3 20 20 [ 0.949  0.991  0.995  0.999] 
1 5 20 20 [ 1.  1.  1.  1.] 
1 7 20 20 [ 1.  1.  1.  1.] 
1 9 20 20 [ 1.  1.  1.  1.] 
3 1 20 20 [ 0.947  0.989  0.998  0.999] 
3 3 20 20 [ 0.007  0.062  0.107  0.243] null
3 5 20 20 [ 0.604  0.843  0.911  0.973] 
3 7 20 20 [ 0.992  1.     1.     1.   ] 
3 9 20 20 [ 1.  1.  1.  1.] 
5 1 20 20 [ 1.  1.  1.  1.] 
5 3 20 20 [ 0.629  0.832  0.899  0.964] 
5 5 20 20 [ 0.009  0.047  0.098  0.247] null
5 7 20 20 [ 0.407  0.685  0.792  0.921] 
5 9 20 20 [ 0.96   0.996  0.998  1.   ] 
7 1 20 20 [ 1.  1.  1.  1.] 
7 3 20 20 [ 0.996  1.     1.     1.   ] 
7 5 20 20 [ 0.433  0.703  0.804  0.911] 
7 7 20 20 [ 0.012  0.047  0.102  0.239] null
7 9 20 20 [ 0.288  0.564  0.699  0.861] 
9 1 20 20 [ 1.  1.  1.  1.] 
9 3 20 20 [ 1.  1.  1.  1.] 
9 5 20 20 [ 0.964  0.992  0.995  0.998] 
9 7 20 20 [ 0.308  0.575  0.706  0.865] 
9 9 20 20 [ 0.01   0.045  0.103  0.259] null
'''

''' n=10 slightly underrejects if lambda > 1
lam1, lam2, nobs1, nobs2, [0.01, 0.05, 0.10, 0.25]
1 1 10 10 [ 0.012  0.062  0.105  0.245] null
1 3 10 10 [ 0.59   0.84   0.909  0.966] 
1 5 10 10 [ 0.982  0.999  1.     1.   ] 
1 7 10 10 [ 0.998  1.     1.     1.   ] 
1 9 10 10 [ 1.  1.  1.  1.] 
3 1 10 10 [ 0.549  0.814  0.895  0.964] 
3 3 10 10 [ 0.01   0.041  0.081  0.221] null
3 5 10 10 [ 0.234  0.516  0.671  0.84 ] 
3 7 10 10 [ 0.819  0.953  0.986  0.996] 
3 9 10 10 [ 0.981  0.998  1.     1.   ] 
5 1 10 10 [ 0.978  0.999  1.     1.   ] 
5 3 10 10 [ 0.231  0.554  0.695  0.859] 
5 5 10 10 [ 0.016  0.06   0.095  0.238] null
5 7 10 10 [ 0.131  0.346  0.507  0.705] 
5 9 10 10 [ 0.598  0.854  0.929  0.976] 
7 1 10 10 [ 1.  1.  1.  1.] 
7 3 10 10 [ 0.798  0.962  0.985  0.998] 
7 5 10 10 [ 0.132  0.36   0.492  0.709] 
7 7 10 10 [ 0.006  0.042  0.091  0.245] null
7 9 10 10 [ 0.098  0.298  0.429  0.648] 
9 1 10 10 [ 1.  1.  1.  1.] 
9 3 10 10 [ 0.981  1.     1.     1.   ] 
9 5 10 10 [ 0.616  0.86   0.936  0.986] 
9 7 10 10 [ 0.095  0.3    0.426  0.643] 
9 9 10 10 [ 0.008  0.037  0.082  0.232] null
'''