Confidence score calculation

I was looking for a way to calculate a score 'x' for each pair of elements in two separate arrays. The goal of the code is to return an output array containing the score for each entry in the input arrays.

from math import sqrt
import numpy as np

downs = np.genfromtxt('path\file.csv', dtype=long, delimiter=',', skiprows=1, usecols=(1,))
ups = np.genfromtxt('path\file.csv', dtype=long, delimiter=',', skiprows=1, usecols=(2,))

n = np.add(ups,downs)

def _confidence(n):

   for i, j in zip[n, ups]:

    z = 1.0 #1.0 = 85%, 1.6 = 95%

    if n == 0:
        return 0 

    phat = float(ups) / n

    x = ((phat + z*z/(2*n) - z * sqrt((phat*(1-phat)+z*z/(4*n))/n))/(1+z*z/n))

    print [x]

It looks like you are trying to calculate the Wilson Score lower confidence bound for ranking as described here: http://www.evanmiller.org/how-not-to-sort-by-average-rating.html

There are a couple issues with the code. The main one that jumps out is that only some of the needed variables (n) are passed into the function and the other simply read from the module namespace (ups, downs). Encapsulating into functions can help. Another issue is where i and j are not actually used within the loop and are bad variable names anyway.

The following code also generates synthetic data so I could test the full code.

from math import sqrt
import numpy as np

def generate_data(filename):
    """ Generate synthetic data for StackExchange example """
    ratings_per_example = 10
    ratings = np.random.binomial(ratings_per_example,0.4,100)
    fake_ups = ratings
    fake_downs = ratings_per_example-ratings
    fake_ids = np.arange(len(ratings))
    merged = np.asarray(zip(fake_ids, fake_downs, fake_ups))
    np.savetxt(filename, merged, fmt='%d', delimiter=",", header='Fake Header')

def confidence(filename):
    """ Returns an array of lower confidence bounds from up/down rankings in file """    
    downs = np.genfromtxt(filename, dtype=long, delimiter=',', skip_header=1, usecols=(1,))
    ups = np.genfromtxt(filename, dtype=long, delimiter=',', skip_header=1, usecols=(2,))

    lower_bound_ranks = [wilson_lower_bound(up, down) for up, down in zip(ups, downs)]

    return lower_bound_ranks

def wilson_lower_bound(up, down, z=1.0):
    """ http://www.evanmiller.org/how-not-to-sort-by-average-rating.html """
    n = up + down
    if n == 0:
        return 0.0
    else:
        phat = float(up) / n
        return ((phat + z*z/(2*n) - z * sqrt((phat*(1-phat)+z*z/(4*n))/n))/(1+z*z/n))

generate_data('foo.csv')
confidence('foo.csv')

StackExchange Code Review Q#73479, answer score: 3