test_students_t

#!/usr/bin/env python

from scipy.stats import t # Student's T distribution
import math

CONFIDENCE_LEVEL = 0.95

def get_nth_moment (result_times, n):
    """ 
    Calculates the nth moment of a list.

    Keyword values:
    result_times -- list of result times (floats)
    n -- integer describing that statistical moment of result_times which is returned
    """
    powers = map(lambda x: x**n, result_times)
    return sum(powers)/float(len(result_times))

def get_mean_and_unc(result_times):
    """ Returns mean and uncertainty of mean for a list. The uncertainty is 
    calculated from Student's T distribution since the population variance is
    unknown.

    Keyword values:
    result_times -- list of result times (floats)

    return values:
    sample_mean -- the observed mean
    unc -- The uncertainty according to Student's T distribution
    """
    N = len(result_times)
    sample_mean = get_nth_moment(result_times, 1)
    sample_variance = sum([(x - sample_mean)**2 for x in result_times])/float(N - 1)
    # since the uncertainty in each measurement is 0.5 ms, the
    # sample_variance should never go below 0.5/sqrt(N).
    if sample_variance < 0.5/math.sqrt(N):
        sample_variance = 0.5/math.sqrt(N)
    estimated_std_err = math.sqrt(sample_variance) / math.sqrt(N)
    print("sample_variance:", sample_variance)
    print("sqrt sample_variance:", math.sqrt(sample_variance))
    print("sample_std_err:", estimated_std_err)
    interval = t.interval(CONFIDENCE_LEVEL,
                          N - 1,
                          loc = sample_mean,
                          scale = estimated_std_err)
    unc = (interval[1] - interval[0])/2
    return (sample_mean, unc)

array1 = [2, 3, 5, 6, 9]
array2 = [1, 2, 3, 4, 5]
array3 = [-1, -1, -1, -1, -1, 1, 1, 1, 1, 1]
array4 = [-1, 1]
array5 = [746, 745, 744, 751, 747, 746, 757, 761, 751, 500]

mean1, unc1 = get_mean_and_unc(array1)
mean2, unc2 = get_mean_and_unc(array2)
mean3, unc3 = get_mean_and_unc(array3)
mean4, unc4 = get_mean_and_unc(array4)
mean5, unc5 = get_mean_and_unc(array5)

print("mean:", mean1)
print("unc:", unc1)
print("confidence interval:", mean1 - unc1, mean1 + unc1)

print("mean:", mean2)
print("unc:", unc2)
print("confidence interval:", mean2 - unc2, mean2 + unc2)

print("mean:", mean3)
print("unc:", unc3)
print("confidence interval:", mean3 - unc3, mean3 + unc3)

print("mean:", mean4)
print("unc:", unc4)
print("confidence interval:", mean4 - unc4, mean4 + unc4)

print("mean:", mean5)
print("unc:", unc5)
print("confidence interval:", mean5 - unc5, mean5 + unc5)