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Multiple Comparisons Among Dependent Groups Based on a Modified One‐Step M‐Estimator
Author(s) -
Wilcox Rand R.
Publication year - 2002
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/1521-4036(200206)44:4<466::aid-bimj466>3.0.co;2-h
Subject(s) - estimator , truncated mean , mathematics , statistics , pairwise comparison , sample size determination , type i and type ii errors , nominal level , robust statistics , confidence interval
Currently, among multiple comparison procedures for dependent groups, a bootstrap‐t with a 20% trimmed mean performs relatively well in terms of both Type I error probabilities and power. However, trimmed means suffer from two general concerns described in the paper. Robust M‐estimators address these concerns, but now no method has been found that gives good control over the probability of a Type I error when sample sizes are small. The paper suggests using instead a modified one‐step M‐estimator that retains the advantages of both trimmed means and robust M‐estimators. Yet another concern is that the more successful methods for trimmed means can be too conservative in terms of Type I errors. Two methods for performing all pairwise multiple comparisons are considered. In simulations, both methods avoid a familywise error (FWE) rate larger than the nominal level. The method based on comparing measures of location associated with the marginal distributions can have an actual FWE that is well below the nominal level when variables are highly correlated. However, the method based on difference scores performs reasonably well with very small sample sizes, and it generally performs better than any of the methods studied in Wilcox (1997 b ).