Robust One-Way ANOVA under Possibly Non-Regular Conditions

Consider the one-way ANOVA problem of comparing the means m1; m2; . . . ; mc of c distributions F1…x† ˆ F…x ÿ m1†; . . . ; Fc…x† ˆ F…x ÿ mc†. Solutions are available based on (i) normal-theory procedures, (ii) linear rank statistics and (iii) M-estimators. The above model presupposes that F1; F2; . . . ; Fc have equal variances (ˆ homoscedasticity). However practising statisticans content that homoscedasticity is often violated in practice. Hence a more realistic problem to consider is F1…x† ˆ F……x ÿ m1†=s1†; . . . ; Fc…x† ˆ F……x ÿ mc†=sc†, where F is symmetric about the origin and s1; . . . ; sc are unknown and possibly unequal (ˆ heteroscedasticity). Now we have to compare m1; m2; . . . ; mc. At present, nonparametric tests of the equality of m1; m2; . . . ; mc are available. However, simultaneous tests for paired comparisons and contrasts and do not seem to be available. This paper begins by proposing a solution applicable to both the homoscedastic and the heteroscedastic situations, assuming F to be symmetric. Then the assumptions of symmetry and the identical Biometrical Journal 41 (1999) 3, 321±339