Testing Linear Contrasts of Means in Experimental Design Without Assuming Normality and Homogeneity of Variances

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Abstract
We investigate the efficiencies of TIKU'S (1967, 1980) modified maximum likelihood (MML) estimators of location and scale parameters of symmetric distributions and show that they are remarkably efficient (jointly). We develop test statistics (based on MML estimators), analogous to the classical tests based on sample means and variances, for testing the equality of two means (the population variances not necessarily equal). We show that these tests are remarkably robust to distributional assumptions and generally more powerful than the well‐known nonparametric tests (WILCOXON, normal‐score, KOLMOGOROV‐SMIRNOV). We generalize the results to testing linear contrasts of means in experimental design (the error variances not necessarily equal). We show that the analogous tests based on ‘adaptive’ robust estimators (wave, bisquare, HAMPEL,) etc., GROSS (1976, and other ‘adaptive’ robust estimators) give misleading Type I errors.

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