Open AccessThe aggregation paradox for statistical rankings and nonparametric tests
Author(s) -
Haikady N. Nagaraja,
Shane Sanders
Publication year - 2020
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0228627
Subject(s) - sign test , nonparametric statistics , parametric statistics , mathematics , statistical hypothesis testing , consistency (knowledge bases) , econometrics , data aggregator , ambiguity , sign (mathematics) , statistics , computer science , discrete mathematics , computer network , mathematical analysis , wireless sensor network , wilcoxon signed rank test , programming language , mann–whitney u test
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.