No abstract

Researchers can adopt one of many different measures of central tendency to examine the effect of a treatment variable across groups. These include least squares means, trimmed means, M-estimators and medians. In addition, some methods begin with a preliminary test to determine the shapes of distributions before adopting a particular estimator of the typical score. We compared a number of recently developed adaptive robust methods with respect to their ability to control Type I error and their sensitivity to detect differences between the groups when data were non-normal and heterogeneous, and the design was unbalanced. In particular, two new approaches to comparing the typical score across treatment groups, due to Babu, Padmanabhan, and Puri, were compared to two new methods presented by Wilcox and by Keselman, Wilcox, Othman, and Fradette. The procedures examined generally resulted in good Type I error control and therefore, on the basis of this critetion, it would be difficult to recommend one method over the other. However, the power results clearly favour one of the methods presented by Wilcox and Keselman; indeed, in the vast majority of the cases investigated, this most favoured approach had substantially larger power values than the other procedures, particularly when there were more than two treatment groups.

Consider the one-way ANOVA problem of comparing the meansSolutions are available based on (i) normal-theory procedures, (ii) linear rank statistics and (iii) M-estimators.The above model presupposes thathave equal variances ( homoscedasticity). However practising statisticans content that homoscedasticity is often violated in practice. Hence a more realistic problem to consider iswhere F is symmetric about the origin and s 1 Y F F F Y s c are unknown and possibly unequal ( heteroscedasticity). Now we have to compare m 1 Y m 2 Y F F F Y m c . At present, nonparametric tests of the equality of m 1 Y m 2 Y F F F Y m c 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 * Research supported in part by NSF grants DMS-9007717 and DMS-9208066.shapes of F 1 Y F F F Y F c are progressively relaxed and solutions are proposed for these cases as well. The procedures are all based on either the 15% trimmed means or the sample medians, whose quantiles are estimated by means of the bootstrap. Monte Carlo studies show that these procedures tend to be superior to the Wilcoxon procedure and Dunnett's normal theory procedure. A rigorous justification of the bootstrap is also presented. The methodology is illustrated by a comparison of mean effects of cocaine administration in pregnant female Sprague-Dawley rats, where skewness and heteroscedascity are known to be present.

Consider the one-way ANOVA problem of comparing the meansSolutions are available based on (i) normal-theory procedures, (ii) linear rank statistics and (iii) M-estimators.The above model presupposes thathave equal variances ( homoscedasticity). However practising statisticans content that homoscedasticity is often violated in practice. Hence a more realistic problem to consider iswhere F is symmetric about the origin and s 1 Y F F F Y s c are unknown and possibly unequal ( heteroscedasticity). Now we have to compare m 1 Y m 2 Y F F F Y m c . At present, nonparametric tests of the equality of m 1 Y m 2 Y F F F Y m c 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 * Research supported in part by NSF grants DMS-9007717 and DMS-9208066.shapes of F 1 Y F F F Y F c are progressively relaxed and solutions are proposed for these cases as well. The procedures are all based on either the 15% trimmed means or the sample medians, whose quantiles are estimated by means of the bootstrap. Monte Carlo studies show that these procedures tend to be superior to the Wilcoxon procedure and Dunnett's normal theory procedure. A rigorous justification of the bootstrap is also presented. The methodology is illustrated by a comparison of mean effects of cocaine administration in pregnant female Sprague-Dawley rats, where skewness and heteroscedascity are known to be present.

No abstract