Nonparametric methods in factorial designs

By Edgar Brunner, Madan Lal Puri. 2001

275 citations recorded by the source corpus.

SummaryIn this paper, we summarize some recent developments in the analysis of nonparametric models where the classical models of ANOVA are generalized in such a way that not only the assumption of normality is relaxed but also the structure of the designs is introduced in a broader framework and also the concept of treatment effects is redefined. The continuity of the distribution functions is not assumed so that not only data from continuous distributions but also data with ties are included in this general setup. In designs with independent observations as well as in repeated measures designs, the hypotheses are formulated by means of the distribution functions. The main results are given in a unified form. Some applications to special designs are considered, where in simple designs, some well known statistics (such as the Kruskal-Wallis statistic and the χ2-statistic for dichotomous data) come out as special cases. The general framework presented here enables the nonparametric analysis of data with continuous distribution functions as well as arbitrary discrete data such as count data, ordered categorical and dichotomous data.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b68f206b6659610d107869c6cdefdce05a6288f5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Invasive and native Rhododendron ponticum populations: is there evidence for genotypic differences in germination and growth? (2005, background): “2000; for appropriateness of rank transformation see Brunner and Puri 2001).”
nparcomp: An R Software Package for Nonparametric Multiple Comparisons and Simultaneous Confidence Intervals (2015, methodology): “Therefore, the marginal distribution functions are used to describe treatment effects by pi = ∫ HdFi = P (Z < Xi1) + 1/2P (Z = Xi1), i = 1, . . . , a, (3) where H = 1a ∑a j=1 Fj denotes a mean distribution in its unweighted (Brunner and Puri 2001; Gao et al. 2008) form.”
Rank-based multiple test procedures and simultaneous confidence intervals (2012, methodology): “For the computation of consistent estimates for the unknown quantities σ2i , and a comprehensive overview of different global test procedures for HF0 , we refer to Akritas et al. (1997) [1] and Brunner and Puri (2001) [10].”
Nonparametric Analysis of Longitudinal Data in Factorial Experiments (2003, methodology): “Then, the distribution of the ANOVA-type statistic (ATS) An(C) = n tr(TV̂) p̂>Tp̂ (4) can be approximated by the F (f̂ ,∞) distribution, where f̂ = [tr(TV̂)] 2/tr(TV̂TV̂) (Brunner, Dette, and Munk 1997; Brunner et al. 1999; Brunner and Puri 2001).”
Greenhouse–Geisser Adjustment and the ANOVA-Type Statistic: Cousins or Twins? (2009, methodology): “On the other hand, Huynh and Feldt (1976; correction note by Lecoutre 1991) have proposed a further adjustment to Greenhouse–Geisser, appropriate for small samples, and it would be of interest to study this in the nonparametric context of Brunner and Puri (2001).”
The excess-zero problem in soil animal count data and choice of appropriate models for statistical inference (2008, methodology): “Non-parametric methods for multi-way ANOVA have become available after Brunner and Puri’s (2001) work that laid the theoretical foundations for analyzing data originating in factorial designs.”
Nonparametric analysis of longitudinal data in factorial experiments (2012, methodology): “Then, the distribution of the ANOVA-type statistic (ATS) An(C) = n tr(TV̂) p̂>Tp̂ (4) can be approximated by the F (f̂ ,∞) distribution, where f̂ = [tr(TV̂)] 2/tr(TV̂TV̂) (Brunner, Dette, and Munk 1997; Brunner et al. 1999; Brunner and Puri 2001).”
Randomization Tests for Weak Null Hypotheses in Randomized Experiments (2018, background): “or the FRT because their distributions do not depend on the outcome values under Fisher’s sharp null hypothesis (Lehmann 1975; Rosenbaum 2002a). They are useful for testing some weak null hypotheses (Brunner and Puri 2001; Chung and Romano 2016a; Brunner et al. 2017; Umlauft et al. 2017). However, i”
Synchronized permutation tests in replicated I×J designs (2007, methodology): “In the usual linear model for the analysis of variance, if the error components are not normally distributed, parametric analysis may not be appropriate, even if Rasch and Guiard (2004), recalling previous results by Ito (1969), show that generally parametric tests are robust also in presence of non”
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.”