  We calculate with Monte Carlo the goodness of fit and the confidence level of
the standard allowed regions for the neutrino oscillation parameters obtained
from the fit of solar neutrino data. We show that the values of the goodness of
fit and of the confidence level of the allowed regions are significantly
smaller than the standard ones. Using Neyman's method, we also calculate exact
allowed regions with correct frequentist coverage. We show that the standard
allowed region around the global minimum of the least-squares function is a
reasonable approximation of the exact one, whereas the size of the other
regions is dramatically underestimated in the standard method.
