Improving performance of Cronbach Alpha code python numpy

Question

I made some code for calculating Cronbach Alpha that works. But I am not too good using lambda functions. Is there a way to reduce the code and improve efficiency by using lambda instead of the svar() function and getting rid of some of the for loops by using numpy arrays?

import numpy as np


def svar(X):
    n = float(len(X))
    svar=(sum([(x-np.mean(X))**2 for x in X]) / n)* n/(n-1.)
    return svar


def CronbachAlpha(itemscores):
    itemvars = [svar(item) for item in itemscores]
    tscores = [0] * len(itemscores[0])
    for item in itemscores:
       for i in range(len(item)):
          tscores[i]+= item[i]
    nitems = len(itemscores)
    #print "total scores=", tscores, 'number of items=', nitems

    Calpha=nitems/(nitems-1.) * (1-sum(itemvars)/ svar(tscores))

    return Calpha

###########Test################
itemscores = [[ 4,14,3,3,23,4,52,3,33,3],
              [ 5,14,4,3,24,5,55,4,15,3]]
print "Cronbach alpha = ", CronbachAlpha(itemscores)

Answer 1

def CronbachAlpha(itemscores):
    itemscores = numpy.asarray(itemscores)
    itemvars = itemscores.var(axis=1, ddof=1)
    tscores = itemscores.sum(axis=0)
    nitems = len(itemscores)

    return nitems / (nitems-1.) * (1 - itemvars.sum() / tscores.var(ddof=1))

NumPy has a variance function built in. Specifying ddof=1 uses a denominator of N-1, giving a sample variance. There's also a sum builtin.