  We consider the asymptotic distribution of a cell in a 2 x ... x 2
contingency table as the fixed marginal totals tend to infinity. The asymptotic
order of the cell variance is derived and a useful diagnostic is given for
determining whether the cell has a Poisson limit or a Gaussian limit. There are
three forms of Poisson convergence. The exact form is shown to be determined by
the growth rates of the two smallest marginal totals. The results are
generalized to contingency tables with arbitrary sizes and are further
complemented with concrete examples.
