Nonparametric rank tests for independence in opinion surveys

Leung Ho Philip YU, K.F. LAM, Mayer ALVO

Research output: Contribution to journalArticlespeer-review

Abstract

Nonparametric rank tests for independence between two characteristics are commonly used in many social opinion surveys. When both characteristics are ordinal in nature, tests based on rank correlations such as those due to Spearman and Kendall are often used. The case where some ties exist has already been considered whereas Alvo and Cabilio (1995) have studied the case when there are missing values but no ties in the record. However, it frequently happens that the survey data may contain simultaneously many tied observations and/or many missing values. A naive approach is to simply discard the missing observations and then to make use of the rank correlations adjusted for ties. This approach would be less powerful as it does not fully utilize the information associated with the incomplete data set. In this article, we generalize Alvo and Cabilio’s notion of distance between two rankings to incorporate tied and missing observations, and define new test statistics based on the Spearman and Kendall rank correlation coefficients. We determine the asymptotic distribution of the Spearman test statistic and compare its efficiency with the corresponding statistic based on the naive approach. The proposed test is then applied to a real data set collected from an opinion survey conducted in Hong Kong. Copyright © 2002 by the author(s).
Original languageEnglish
Pages (from-to)279-290
JournalAustrian Journal of Statistics
Volume31
Issue number4
DOIs
Publication statusPublished - 2002

Citation

Yu, P. L. H., Lam, K. F., & Alvo, M. (2002). Nonparametric rank tests for independence in opinion surveys. Austrian Journal of Statistics, 31(4), 279-290. doi: 10.17713/ajs.v31i4.490

Keywords

  • Opinion surveys
  • Asymptotic relative efficiency
  • Incomplete rankings
  • Ties
  • Rank correlation
  • Spearman and Kendall distances

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