  It has been suggested by various authors that a significant anticorrelation
exists between the Homestake solar neutrino data and the sunspot cycle. Some of
these claims rest on smoothing the data by taking running averages, a method
that has recently undergone criticism. We demonstrate that no significant
anticorrelation can be found in the Homestake, data, or in standard 2- and
4-point averages of that data. However, when 3-, 5-, and 7-point running
averages are taken, an anticorrelation seems to emerge whose significance grows
as the number of points in the average increases. Our analysis indicates that
the apparently high significance of these anticorrelations is an artifact of
the failure to consider the loss of independence introduced in the running
average process. When this is considered, the significance is reduced to that
of the unaveraged data. Furthermore, when evaluated via parametric subsampling,
no statistically significant anticorrelation is found. We conclude that the
Homestake data can not be used to substantiate any claim of an anticorrelation
with the sunspot cycle.
