Psychology studies often have low statistical power. Sample size tables, as given by J. Cohen (1988), may be used to increase power, but they are based on Monte Carlo studies of relatively "tame" mathematical distributions, as compared to psychology data sets. In this study, Monte Carlo methods were used to investigate Type I and Type II error properties of the independent samples "t" test under a "discrete mass at zero with gap" data set to determine if the sample size tables given by Cohen yield correct results. Monte Carlo methods were used with a FORTRAN program to sample with replacement from a population of 516 responses to a survey regarding the age at which subjects first used cigarettes. Ten sample sizes were randomly drawn: (1) n1=5, n2=15; (2) n1=10, n2=10; (3) n1=10, n2=30; (4) n1=20, n2=20; (5) n1=15, n2=45; (6) n1=30, n2=30; (7) n1=20, n2=60; (8) n1=40, n2=40; (9) n1=30, n2=90; and (10) n1=60, n2=60. For the smallest unbalanced sample size (5,15), the "t" test was generally not robust. For the remaining sample sizes, results were in agreement with normal curve theory. When confronted with non-normal data sets, psychology researchers do not need to make any modifications to Cohen's (1988) tables when making sample size determinations. Two graphs illustrate the study. A 12-item list of references is included. (SLD)