Simple implementation of the Fleiss' kappa measure in Python

kappa.py

def fleiss_kappa(ratings, n, k):
    '''
    Computes the Fleiss' kappa measure for assessing the reliability of 
    agreement between a fixed number n of raters when assigning categorical
    ratings to a number of items.
    
    Args:
        ratings: a list of (item, category)-ratings
        n: number of raters
        k: number of categories
    Returns:
        the Fleiss' kappa score
    
    See also:
        http://en.wikipedia.org/wiki/Fleiss'_kappa
    '''
    items = set()
    categories = set()
    n_ij = {}
    
    for i, c in ratings:
        items.add(i)
        categories.add(c)
        n_ij[(i,c)] = n_ij.get((i,c), 0) + 1
    
    N = len(items)
    
    p_j = {}
    for c in categories:
        p_j[c] = sum(n_ij.get((i,c), 0) for i in items) / (1.0*n*N)
    
    P_i = {}
    for i in items:
        P_i[i] = (sum(n_ij.get((i,c), 0)**2 for c in categories)-n) / (n*(n-1.0))
    
    P_bar = sum(P_i.itervalues()) / (1.0*N)
    P_e_bar = sum(p_j[c]**2 for c in categories)
    
    kappa = (P_bar - P_e_bar) / (1 - P_e_bar)
    
    return kappa



example = (                                                     [( 1,5)] * 14 +
                 [( 2,2)] * 2 + [( 2,3)] * 6  + [( 2,4)] * 4  + [( 2,5)] * 2  + 
                                [( 3,3)] * 3  + [( 3,4)] * 5  + [( 3,5)] * 6  + 
                 [( 4,2)] * 3 + [( 4,3)] * 9  + [( 4,4)] * 2  +
  [( 5,1)] * 2 + [( 5,2)] * 2 + [( 5,3)] * 8  + [( 5,4)] * 1  + [( 5,5)] * 1  + 
  [( 6,1)] * 7 + [( 6,2)] * 7 + 
  [( 7,1)] * 3 + [( 7,2)] * 2 + [( 7,3)] * 6  + [( 7,4)] * 3  + 
  [( 8,1)] * 2 + [( 8,2)] * 5 + [( 8,3)] * 3  + [( 8,4)] * 2  + [( 8,5)] * 2  + 
  [( 9,1)] * 6 + [( 9,2)] * 5 + [( 9,3)] * 2  + [( 9,4)] * 1  + 
                 [(10,2)] * 2 + [(10,3)] * 2  + [(10,4)] * 3  + [(10,5)] * 7  )


print '%.03f' % fleiss_kappa(example, 14, 5) # 0.210

A trivial comment: The signature of the function (and the documentation) needs updating as k is not used anywhere in the function.

Another trivial comment: I would suggest using "k" as a parameter and let the user decide how many categories there are. Just because nobody voted for a category doesn't mean it wasn't available.

A trivial +1 to the 2nd "trivial comment".