def phik_from_hist2d(observed: np.ndarray, expected: np.ndarray, noise_correction: bool = True) -> float:
"""
correlation coefficient of bivariate gaussian derived from chi2-value
Chi2-value gets converted into correlation coefficient of bivariate gauss
with correlation value rho, assuming giving binning and number of records.
Correlation coefficient value is between 0 and 1.
Bivariate gaussian's range is set to [-5,5] by construction.
:param observed: 2d-array observed values
:param expected: 2d-array expected values
:param bool noise_correction: apply noise correction in phik calculation
:returns float: correlation coefficient phik
"""
if isinstance(observed, pd.DataFrame):
observed = observed.values
if isinstance(expected, pd.DataFrame):
expected = expected.values
# important to ensure that observed and expected have same normalization
expected = expected * (np.sum(observed) / np.sum(expected))
# chi2 contingency test
chi2 = chi_square(observed, expected, lambda_='pearson')
# noise pedestal
endof = estimate_simple_ndof(observed) if noise_correction else 0
pedestal = endof
if pedestal < 0:
pedestal = 0
# phik calculation adds noise pedestal to theoretical chi2
return phik_from_chi2(chi2, observed.sum(), *observed.shape, pedestal=pedestal)
def test_phik_calculation(self):
"""Test the calculation of Phi_K"""
chi2 = bivariate.chi2_from_phik(0.5, 1000, nx=10, ny=10)
self.assertTrue( np.isclose(chi2, 271.16068979654125, 1e-6) )
phik = bivariate.phik_from_chi2(chi2, 1000, 10, 10)
self.assertTrue( np.isclose(phik, 0.5, 1e-6) )