Poll Result Analysis

poll-results.py

# Blog post: https://scribu.net/twitter-poll-analysis.html
import sys
import math

positive = int(sys.argv[1])

z = 1.9599    # 95% confidence
n = 7         # number of votes
classes = 3   # number of possible answers


def standard_error(p, n):
    """The estimate of a proportion p out of n samples

    Arguments:
        p: proportion
        n: number of trials
    """
    return np.sqrt(p * (1 - p) / n)


def maximum_error(z, n, prior=0.5):
    """
    Maximum error, used for calculating confidence intervals

    Arguments:
        z: confidence level
        n: number of trials
    """
    return z * standard_error(prior, n)


e = maximum_error(z, n, 1 / classes)

p = positive / n

low = max(0, p - e)
high = min(1, p + e)


# r is the likelyhood that the next vote would be "disagree"
print(f"{low:.0%} <= r <= {high:.0%}")