The usual χ2goodness-of-fit criterion is considered when all cells have expectations of one and the cell boundaries are not estimated from the data. This situation arises in the use of a measure of consensus proposed by Coleman [1]. Under these circumstances the criterion reduces to X2= Σt=1Nni2−N, where niis the number of observations in cell i and N is the total number of observations in the sample. The exact distribution of X2is given for N = 1(1)25(5)40, 50. For N≥25, the χ2approximation to the exact distribution of X2errs by less than .007 or 20.3 percent for right-tail areas. For left-tail areas the errors are less than .0165 or 89.9 percent when N≥25.