Confidence Interval python implementation based on http://www.evanmiller.org/how-not-to-sort-by-average-rating.html

ci_lower_bound.py

import math

import scipy.stats as st

def ci_lower_bound(pos, n, confidence=None, z=None):
    if n == 0:
        return 0
    if z is None:
        z = st.norm.ppf(1 - (1 - confidence) / 2)
    phat = 1.0 * pos / n
    return (phat + z * z / (2 * n) - z * math.sqrt((phat * (1 - phat) + z * z / (4 * n)) / n)) / (1 + z * z / n)