In this paper, six statistical tests of stochastic equality are compared with respect to Type I error and power through a Monte Carlo simulation. In the simulation, the skewness and kurtosis levels and the extent of variance heterogeneity of the two parent distributions were varied across a wide range. The sample sizes applied were either small or moderate and equal or unequal. The tests of stochastic equality were the rank "t" test, the rank Welch test, the Fligner-Policello test, Cliff's modified Fligner-Policello test, and two variations of the last two tests that used adjusted degrees of freedom (designated FPW and FPCW). An interesting result of the study is that the two new modifications proved to be substantially more accurate with regard to their Type I error rates than the others, although they kept to a similar power level. The estimated Type I error of the FPW method at the 0.05 nominal level always fell in the range of 0.043 to 0.063 even if the variance ratio of the 2 distributions was as large as 1:16. The other ranges were: (1 ) 0.049-0.068 for FPCW; (2) 0.029-0.160 for the rank "t" test; (3) 0.049-0.096 for the rank Welch test; (4) 0.035-0.075 for the Fligner-Policello test; and (5) 0.040-0.078 for Cliff's test. (Contains 2 figures, 10 tables, and 22 references.) (Author/SLD)