Permutation approach for ordinal preference data

ABSTRACT

Best et al. (Best, D. J., Rayner, J. C. W., O'Sullivan, M. G. (2000). Product maps for consumer categorical data. Food Quality and Preference, 11:91–97) suggested tests based on partitioning the X² statistic into relevant components of location, dispersion, and skewness effects for testing equality of each effect for ordinal preference data. It is known that the chi-square approximation requires large counts for categories. For this purpose, in this study, we investigate a permutation approach for these statistics and compare the performance of these tests with simulation study. In addition, the permutation approach can be used to produce a product map that classifies the products. We illustrate the approach with a real data example.

KEYWORDS:

• Partition of chi-squared
• Permutation approach
• Product map.

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62F40
• 62G10

Acknowledgments

The authors are sincerely grateful to the anonymous referees for their time and effort in providing very constructive, helpful, and valuable comments and suggestions that have led to a substantial improvement in the quality of the paper. Computer codes can be obtained from http://websitem.gazi.edu.tr/site/fikri/files.