On the solar-cycle modulation of the homestake solar neutrino capture rate and the shuffle test

There exists no significant correlation between the Homestake neutrino data up to run 133 and the monthly sunspot number, according to a test that is based on certain optimality properties for this type of problem. It is argued that priorly reported highly significant results for segments of the data are due to a statistical fallacy: the usual methods for evaluating the significance of common tests for correlation are not applicable in the sunspot-neutrino context. Moreover, an appropriate evaluation of these tests gives results that are compatible with the hypothesis of no correlation. Some new methods are introduced for assessing the significance of common measures of correlation in a time series setting, with a special emphasis on the Spearman rank correlation coefficient.