The Lack of Consistency for Statistical Decision Procedures

Haunsperger, Deanna; Saari, Donald G.

doi:10.2307/2684305

Cited by 11 publications

(4 citation statements)

References 3 publications

(4 reference statements)

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“…This result suggests that instances of Yule-Simpson Paradox are fairly regularly occurring for small sample cases. Qualitatively, the result is in line with previous small sample results on Yule-Simpson Paradox incidence for other tests (see [28]; [54]).…”

Section: Application 4: Computation Of Yule-simpson Paradox For a Cassupporting

confidence: 92%

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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Section: Application 4: Computation Of Yule-simpson Paradox For a Cassupporting

confidence: 92%

The aggregation paradox for statistical rankings and nonparametric tests

Nagaraja

Sanders

2020

PLoS ONE

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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%

Statistical Significance of Ranking Paradoxes

Bargagliotti

Greenwell

2011

Communications in Statistics - Theory and Methods

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“…In [18], [10], and [12], Haunsperger and Saari investigated the universality of paradoxes in nonparametric methods. More recently, aggregation paradoxes have been investigated using the same tools.…”

Section: Introductionmentioning

confidence: 99%

Decomposition behavior in aggregated data sets

Bérubé

Crisman

2011

Mathematical Social Sciences

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Abstract. One kind of aggregation of nonparametric data sets involves combining two (or more) sets with the same structure, but with no interweaving of values. For instance, one could have prices of the same product at different stores on different days, but before and after a significant sales tax hike. In this paper, looking at the case of three 'candidates', we give a precise computation of how decomposition of the underlying voting data of these sets is related to the decomposition of the original set. Among other things, this proves it is possible to obtain data sets with arbitrarily large Basic components relative to their size. A second result gives congruence and other criteria for possible values of the sizes of the various components, and we exhibit pure Basic data sets (discovered using the computer program Sage) which exemplify those criteria.

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The Lack of Consistency for Statistical Decision Procedures

Cited by 11 publications

References 3 publications

The aggregation paradox for statistical rankings and nonparametric tests

The aggregation paradox for statistical rankings and nonparametric tests

Statistical Significance of Ranking Paradoxes

Decomposition behavior in aggregated data sets

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