Permutation approach for ordinal preference data

Best et al. (Best, D. J., Rayner, J. C. W., O'Sullivan, M. G. (2000 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.Crossref], Web of Science ®] , Google Scholar]). 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.