The researchers tested different methods for comparing two groups with different variances. They found that traditional tests like the t-test and Wilcoxon test can give wrong results when variances are unequal. Using a two-stage method based on a preliminary test of variances didn't work well either. The best approach was to use the Welch separate-variances t-test when sample sizes are unequal. This helped to avoid errors in the comparison of the two groups.