The empirical performance of the technique proposed by P. O. Johnson and J. Neyman (1936) (the JN technique) and the modification of R. F. Potthoff (1964) was studied in simulated data settings. The robustness of the two JN techniques was investigated with respect to their ability to control Type I and Type III errors. Factors manipulated in the Monte Carlo simulations were conditional distribution shape, conditional variance rate, and sample size ratio, yielding 120 simulated data conditions with 10,000 experiments for each. Results indicate that the original JN technique produces unacceptably high Type I error rates, while the modified JN technique usually controls Type I error at the nominal alpha level. The original JN technique controls Type III error at the nominal alpha level, and the modified JN technique yields a Type III error rate well below the nominal alpha level. Analysis of variance indicated that the effect of conditional distribution shape was practically negligible for both JN techniques. The effect of the conditional variance ratio was confounded by the sample size equality factor. When sample sizes were equal, the effect of the conditional variance ratio was practically negligible. However, when sample sizes were unequal, the effect of the conditional variance ratio appeared strong. There are 14 tables of analysis data, 1 figure, and a 13-item list of references. (SL)