For simplicity we began this investigation with 2 x 2 tables. We constructed a number of sets of four-cell prob- abilities, covering a range of values of y, and used a computer to generate the exact distribution of sample G values for sample sizes up to 50 with appropriate multinomial probabilities. This motivated a further examination of some of the apparent problems with G: slowness of convergence to normality, appreciable probability at + 1, general distributional irregularity, bias, and skewness. For comparison we also looked at other measures of association, namely p (the usual correlation coefficient), Spearman's p, and Kendall's Tb. In the 2 x 2 case these last three measures become identical. In this article we report some of these results and comparisons, and come to some conclusions about the use of measures of association in 2 x 2 ordered tables