  The classic chi-squared statistic for testing goodness-of-fit has long been a
cornerstone of modern statistical practice. The statistic consists of a sum in
which each summand involves division by the probability associated with the
corresponding bin in the distribution being tested for goodness-of-fit.
Typically this division should precipitate rebinning to uniformize the
probabilities associated with the bins, in order to make the test reasonably
powerful. With the now widespread availability of computers, there is no longer
any need for this. The present paper provides efficient black-box algorithms
for calculating the asymptotic confidence levels of a variant on the classic
chi-squared test which omits the problematic division. In many circumstances,
it is also feasible to compute the exact confidence levels via Monte Carlo
simulation.
