An Extension of the Chi-Square Procedure for Non-NORMAL Statistics, with Application to Solar Neutrino Data

摘要

Using the chi-square statistic, one may conveniently test whether a series of measurements of a variable are consistent with a constant value. However, that test is predicated on the assumption that the appropriate probability distribution function (pdf) is normal in form. This requirement is usually not satisfied by experimental measurements of the solar neutrino flux. This article presents an extension of the chi-square procedure that is valid for any form of the pdf. This procedure is applied to the GALLEX-GNO dataset, and it is shown that the results are in good agreement with the results of Monte Carlo simulations. Whereas application of the standard chi-square test to symmetrized data yields evidence significant at the 1% level for variability of the solar neutrino flux, application of the extended chi-square test to the unsymmetrized data yields only weak evidence (significant at the 4% level) of variability.