Correlation coefficients and p values for all pairs of rows of a matrix

Question

I have a matrix data with m rows and n columns. I used to compute the correlation coefficients between all pairs of rows using np.corrcoef:

Answer 1

The most consice way of doing it might be the buildin method .corr in pandas, to get r:

In [79]:

import pandas as pd
m=np.random.random((6,6))
df=pd.DataFrame(m)
print df.corr()
          0         1         2         3         4         5
0  1.000000 -0.282780  0.455210 -0.377936 -0.850840  0.190545
1 -0.282780  1.000000 -0.747979 -0.461637  0.270770  0.008815
2  0.455210 -0.747979  1.000000 -0.137078 -0.683991  0.557390
3 -0.377936 -0.461637 -0.137078  1.000000  0.511070 -0.801614
4 -0.850840  0.270770 -0.683991  0.511070  1.000000 -0.499247
5  0.190545  0.008815  0.557390 -0.801614 -0.499247  1.000000

To get p values using t-test:

In [84]:

n=6
r=df.corr()
t=r*np.sqrt((n-2)/(1-r*r))

import scipy.stats as ss
ss.t.cdf(t, n-2)
Out[84]:
array([[ 1.        ,  0.2935682 ,  0.817826  ,  0.23004382,  0.01585695,
         0.64117917],
       [ 0.2935682 ,  1.        ,  0.04363408,  0.17836685,  0.69811422,
         0.50661121],
       [ 0.817826  ,  0.04363408,  1.        ,  0.39783538,  0.06700715,
         0.8747497 ],
       [ 0.23004382,  0.17836685,  0.39783538,  1.        ,  0.84993082,
         0.02756579],
       [ 0.01585695,  0.69811422,  0.06700715,  0.84993082,  1.        ,
         0.15667393],
       [ 0.64117917,  0.50661121,  0.8747497 ,  0.02756579,  0.15667393,
         1.        ]])
In [85]:

ss.pearsonr(m[:,0], m[:,1])
Out[85]:
(-0.28277983892175751, 0.58713640696703184)
In [86]:
#be careful about the difference of 1-tail test and 2-tail test:
0.58713640696703184/2
Out[86]:
0.2935682034835159 #the value in ss.t.cdf(t, n-2) [0,1] cell

Also you can just use the scipy.stats.pearsonr you mentioned in OP:

In [95]:
#returns a list of tuples of (r, p, index1, index2)
import itertools
[ss.pearsonr(m[:,i],m[:,j])+(i, j) for i, j in itertools.product(range(n), range(n))]
Out[95]:
[(1.0, 0.0, 0, 0),
 (-0.28277983892175751, 0.58713640696703184, 0, 1),
 (0.45521036266021014, 0.36434799921123057, 0, 2),
 (-0.3779357902414715, 0.46008763115463419, 0, 3),
 (-0.85083961671703368, 0.031713908656676448, 0, 4),
 (0.19054495489542525, 0.71764166168348287, 0, 5),
 (-0.28277983892175751, 0.58713640696703184, 1, 0),
 (1.0, 0.0, 1, 1),
#etc, etc