  Goodness-of-fit tests based on the Euclidean distance often outperform
chi-square and other classical tests (including the standard exact tests) by at
least an order of magnitude when the model being tested for goodness-of-fit is
a discrete probability distribution that is not close to uniform. The present
article discusses numerous examples of this. Goodness-of-fit tests based on the
Euclidean metric are now practical and convenient: although the actual values
taken by the Euclidean distance and similar goodness-of-fit statistics are
seldom humanly interpretable, black-box computer programs can rapidly calculate
their precise significance.
