Dispersion of Responses over Cells

The usual requirement for testing hypotheses regarding the dispersion of responses distributed over taxa uses a Pearson's goodness of fit chi-square. More recently maximum likelihood statistics have also come into vogue. Standard recommendations for either technique is to have at least five observations expected under each taxon. An alternative procedure proposed in this paper is to use the distribution of the number of cells that are either empty or are singly occupied. Recursive formula were developed and rationalizations provided for analyzing either of these situations. A table showing number of cases needed to achieve .10, .05, and .01 significance for excessive numbers of empty cells was developed.