Symmetry of Nonparametric Statistical Tests on Three Samples | Science Publications

Journal of Mathematics and Statistics

Anna E. Bargagliotti¹  Donald G. Saari¹ 

关键词: Nonparametric;    symmetry;    ranked data;    Kruskal-Wallis;   

DOI  :  10.3844/jmssp.2010.395.408

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

Problem statement: Many different nonparametric statistical procedures can be used toanalyze ranked data. Inconsistencies among the outcomes of such procedures can occur whenanalyzing the same ranked data set. Understanding why these peculiarities can occur is imperative toproviding an accurate analysis of the ranking data. In this context, this study addressed whyinconsistent outcomes can occur and which types of data structures cause the different procedures toyield different outcomes. Approach: Appropriate properties were identified and developed to explainwhy different methods can define different rankings of three samples with the same data. The approachidentifies certain symmetry structures that are implicitly contained within the data and analyzes howthe procedures utilize these structures to produce an outcome. Results: We proved that all possibledifferences among the nonparametric rules are caused because different rules place different levels ofemphasis on the specified symmetry configurations of data. Our findings explain and characterize whydifferent procedures can output different results using the same data set. Conclusion: This studytherefore served as crucial step in deciding which nonparametric procedure to use when analyzingranked data. In addition, it serves as the building block to defining new techniques to analyze rankings.Because different procedures use different aspects of the data in different ways, then one maydetermine the choice of analysis procedure based on what parts of the data one deems important.

【 授权许可】

Unknown