Testing Coefficients of Variation from multiple samples

feltz_miller.py

import numpy as np
import scipy


def feltz_miller(*samples):
    k = len(samples)
    m_j = np.array([len(sample) - 1 for sample in samples])
    cv_j = np.array([np.std(sample, ddof=1) / np.mean(sample) for sample in samples])

    d = np.sum(m_j * cv_j) / np.sum(m_j)
    d_ad = np.sum(m_j * (cv_j - d) ** 2) / (d**2 * (0.5 + d**2))
    
    return d_ad, scipy.stats.chi2.sf(d_ad, k - 1)

This is a straightforward translation of Ben Marwick's R code into Python. For details see the cvequality vignette.

import pandas as pd

df = pd.read_csv("https://raw.githubusercontent.com/benmarwick/cvequality/master/vignettes/GaltonFamilies.csv")
male = df.loc[df.gender.eq("male"), "childHeight"]
female = df.loc[df.gender.eq("female"), "childHeight"]
d_ad, p = feltz_miller(male, female)
print(d_ad, p)  # 0.44163996742937056 0.5063319732170684

df = pd.read_csv("https://raw.githubusercontent.com/benmarwick/cvequality/master/vignettes/Handaxes.csv")
d_ad, p = feltz_miller(df.L, df.L1, df.B, df.B1, df.B2, df["T"], df.T1)
print(d_ad, p)  # 309.191946847004 8.766100959546317e-64