A nonparametric procedure for testing partially ranked data

• Published in: Journal of nonparametric statistics Vol. 29; no. 2; pp. 213 - 230
• Main Authors: Wu, Jyh-Shyang, Deng, Wen-Shuenn
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.04.2017; Taylor & Francis Ltd
• Subjects: Anderson's test; chi-square test; Consumption; contingency table; imposed rank; Nonparametric statistics; partially ranked data; Ranking; Regression analysis; root-n local alternatives; U-statistics
• ISSN: 1048-5252; 1029-0311
• DOI: 10.1080/10485252.2017.1303055

In consumer preference studies, it is common to seek a complete ranking of a variety of, say N, alternatives or treatments. Unfortunately, as N increases, it becomes progressively more confusing and undesirable for respondents to rank all N alternatives simultaneously. Moreover, the investigators may only be interested in consumers' top few choices. Therefore, it is desirable to accommodate the setting where each survey respondent ranks only her/his most preferred k (k < N) alternatives. In this paper, we propose a simple procedure to test the independence of N alternatives and the top-k ranks, such that the value of k can be predetermined before securing a set of partially ranked data or be at the discretion of the investigator in the presence of complete ranking data. The asymptotic distribution of the proposed test under root-n local alternatives is established. We demonstrate our procedure with two real data sets.