sampling stats

gistfile1.py

import math
import matplotlib
import matplotlib.pyplot as plt

def confidence_for_sampling(pop_size=1000, con_level=0.99, sample_rate=0.1):
    if con_level not in (0.99, 0.95):
        raise Exception("don't know those zvals")
    zval = 1.96 if con_level == 0.95 else 2.58

    variance = (pop_size * sample_rate) * (1 - sample_rate)
    stdev = math.sqrt(variance)
    mean = pop_size * sample_rate

    con_int = (stdev * zval) / mean

    return con_int

def confidence_by_sampling(pop_size, con_level):
    x = []
    y = []
    for s in xrange(1, 100, 1):
        con_int = confidence_for_sampling(pop_size, con_level, sample_rate=s/100.0)
        x.append(s)
        y.append(con_int)
    return (x,y)

def main():
    con_level = 0.95
    pop_size = 20*1000
    (x,y) = confidence_by_sampling(pop_size, con_level)

    x_formatter = matplotlib.ticker.ScalarFormatter(useOffset=False)
    axes = plt.gca()
    axes.xaxis.set_major_formatter(x_formatter)
    axes.ticklabel_format(style='plain',axis='x')
    plt.title('Effect of sample rate on %% error at pop_size=%d' % (pop_size,))
    plt.xlabel('Sample rate (%)')
    plt.ylabel('%% error (confidence interval) at %d%% confidence level' % (con_level*100,))

    plt.plot(x,y)
    plt.show()

if __name__ == '__main__':
    main()