Paradoxes in nonparametric tests

Haunsperger, Deanna

doi:10.2307/3315692

Cited by 4 publications

(4 citation statements)

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“…In doing so, we generalise earlier findings reported by Haunsperger (1992Haunsperger ( , 1996, and Taplin (1997), who focused mainly on characterising the kinds of inconsistencies that can occur for a particular choice of statistical test. Specifically, our result shows that no distribution-free rank sum procedure (hereafter, we use the shorthand 'test') with certain reasonable properties exists that always avoids both types of inconsistencies.…”

Section: Introductionmentioning

confidence: 79%

Consistency of choice in nonparametric multiple comparisons

Fey

Clarke

2012

Journal of Nonparametric Statistics

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In this paper, we are interested in the inconsistencies that can arise in the context of rank-based multiple comparisons. It is well known that these inconsistencies exist, but we prove that every possible distributionfree rank-based multiple comparison procedure with certain reasonable properties is susceptible to these phenomena. The proof is based on a generalisation of Arrow's theorem, a fundamental result in social choice theory which states that when faced with three or more alternatives, it is impossible to rationally aggregate preference rankings subject to certain desirable properties. Applying this theorem to treatment rankings, we generalise a number of existing results in the literature and demonstrate that procedures that use rank sums cannot be improved. Finally, we show that the best possible procedures are based on the Friedman rank statistic and the k-sample sign statistic, in that these statistics minimise the potential for paradoxical results.

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Section: Introductionmentioning

confidence: 79%

Consistency of choice in nonparametric multiple comparisons

Fey

Clarke

2012

Journal of Nonparametric Statistics

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“…We will now establish (10). Note that X N has the same distribution as X n + Y where Y is Binomial with parameters N − n and p = 1/2, and X n and Y are independent.…”

Section: Resultsmentioning

confidence: 99%

“…The relationship between social choice aggregation rules and non-parametric statistical analysis is well-established [see, e.g., 1,2,3,4,5,6,7,8,9]. In a related literature, fundamental relationships between discrete choice and non-parametric statistical analysis have been developed [see 10,11,12,13,14,15,16,17]. While violations of social choice principles can inform us as to the possible paradoxes present in non-parametric tests, the mapping is imperfect due to the issue of statistical significance.…”

Section: Introductionmentioning

confidence: 99%

The aggregation paradox for statistical rankings and nonparametric tests

Nagaraja

Sanders

2020

PLoS ONE

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The relationship between social choice aggregation rules and non-parametric statistical tests has been established for several cases. An outstanding, general question at this intersection is whether there exists a non-parametric test that is consistent upon aggregation of data sets (not subject to Yule-Simpson Aggregation Paradox reversals for any ordinal data). Inconsistency has been shown for several non-parametric tests, where the property bears fundamentally upon robustness (ambiguity) of non-parametric test (social choice) results. Using the binomial(n, p = 0.5) random variable CDF, we prove that aggregation of r(�2) constituent data sets-each rendering a qualitatively-equivalent sign test for matched pairs result-reinforces and strengthens constituent results (sign test consistency). Further, we prove that magnitude of sign test consistency strengthens in significance-level of constituent results (strong-form consistency). We then find preliminary evidence that sign test consistency is preserved for a generalized form of aggregation. Application data illustrate (in)consistency in non-parametric settings, and links with information aggregation mechanisms (as well as paradoxes thereof) are discussed.

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“…Depending on which procedure is used to analyze the ranks, different rank-orderings of the alternatives may occur (Bargagliotti and Saari, submitted manuscript, 2008). Particularly interesting types of inconsistencies are Simpson-like paradoxes, in which the individual data sets give rise to one overall ranking, but the aggregate of the data sets gives rise to a different ranking (Haunsperger and Saari 1991;Haunsperger 1992;Haunsperger 1996;Haunsperger 2003;Bargagliotti, submitted manuscript, 2008). Haunsperger (2003) has shown this paradox exists when the Kruskal-Wallis nonparametric statistical procedure on n samples is used to rank-order a list of alternatives.…”

Section: Introductionmentioning

confidence: 99%