Python script implementing "Combining Multiple Averaged Data Points and Their Errors" by Ken Tatebe

combine.py

from typing import Tuple, List

"""A 'bin' of observations in the form (average, error, # of observations)"""
Bin = Tuple[float, float, int]

"""Based on http://isi.ssl.berkeley.edu/~tatebe/whitepapers/Combining%20Errors.pdf"""
def combine(a: Bin, b: Bin) -> Bin:
    a_avg, a_err, n_a = a
    b_avg, b_err, n_b = b
    n = n_a + n_b

    s_avg = ((n_a / n) * a_avg) + ((n_b / n) * b_avg)

    N = n ** 2 - n
    N_a = n_a ** 2 - n_a
    N_b = n_b ** 2 - n_b

    s_err = ((N_a / N) * (a_err ** 2)
             + (N_b / N) * (b_err ** 2)
             + (n_a * n_b * (a_avg - b_avg) ** 2) / (n * N)
             ) ** .5

    return (s_avg, s_err, n)


def combine_all(x: List[Bin]) -> Bin:
    if (len(x) == 1):
        return x[0]
    if (len(x) == 2):
        return combine(x[0], x[1])
    if (len(x) > 2):
        return combine(x[0], combine_all(x[1:]))
    else:
        raise ValueError("Can't combine without any observations")