2020
DOI: 10.1371/journal.pone.0228627
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The aggregation paradox for statistical rankings and nonparametric tests

Abstract: 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 te… Show more

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Cited by 2 publications
(3 citation statements)
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“…As RSS is a nonparametric form of scoring, only the order of elements influences the group ranking. We then aggregate the original data set with its ordinal replicate as in Nagaraja and Sanders [22] and consider whether (under what conditions) the pooled data yields a different group rank result under RSS than do its two constituent data sets. That is, we consider the conditions for strict Simpson Reversal, whereby the outcome in 1 (3) is obtained for each constituent data sequence, but outcome 3 (1) is obtained for the pooled sequence.…”
Section: Replicated Data Aggregationmentioning
confidence: 99%
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“…As RSS is a nonparametric form of scoring, only the order of elements influences the group ranking. We then aggregate the original data set with its ordinal replicate as in Nagaraja and Sanders [22] and consider whether (under what conditions) the pooled data yields a different group rank result under RSS than do its two constituent data sets. That is, we consider the conditions for strict Simpson Reversal, whereby the outcome in 1 (3) is obtained for each constituent data sequence, but outcome 3 (1) is obtained for the pooled sequence.…”
Section: Replicated Data Aggregationmentioning
confidence: 99%
“…Similarly, Sanders et al [21] find that variation in outcome by aggregation rule is fairly common for rank sum scoring and other aggregation common aggregation rules. For nonparametric statistical testing, Nagaraja and Sanders [22] consider a case in which a data set is ordinally replicated and then pooled with the replicate data set. In such an environment, the authors prove that Simpson Reversals cannot occur if the sign test for matched pairs is applied to the primitive and pooled data sets.…”
Section: Introductionmentioning
confidence: 99%
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