In this study, we explore the effects of non-normality and heteroscedasticity when testing the hypothesis that the regression lines associated with multiple independent groups have the same slopes. The conventional approach involving the F-test and the t-test (F/t approach) is examined. In addition, we introduce two robust methods which allow simultaneous testing of regression slopes. Our results suggest that the F/t approach is extremely sensitive to violations of assumptions and tends to yield misleading conclusions. The new robust alternatives are recommended for general use.