Nonparametric multiple comparison procedures for unbalanced one-way factorial designs

By Xin Gao, M. Alvo, Jie Chen, Gang Li. 2008

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Rank-based multiple test procedures and simultaneous confidence intervals (2012, background): “This representation of the estimator provides an unified approach for both the usual ranks as well as the so-called pseudo ranks (Gao and Alvo 2005 [15], 2008 [16]; Gao et al.”
Rank‐based procedures in factorial designs: hypotheses about non‐parametric treatment effects (2016, methodology): “These unweighted effects, which were proposed by Brunner and Puri (2001), section 3.2, and later considered in detail by Domhof (2001) as well as Gao and Alvo (2005) and Gao et al. (2008), can be regarded as non-parametric treatment effects which are defined by the distributions in the designs.”
nparcomp: An R Software Package for Nonparametric Multiple Comparisons and Simultaneous Confidence Intervals (2015, methodology): “where H = 1 a ∑a j=1 Fj denotes a mean distribution in its unweighted (Brunner and Puri 2001; Gao et al. 2008) form.”