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Rank Regression for Analyzing Ordinal Qualitative Data for Treatment Comparison

First author: School of Mathematics and Statistics, Xi'an Jiaotong University, Shanxi Province, China; first and second authors: Centre for Applications in Natural Resource Mathematics, School of Mathematics and Physics, The University of Queensland, Queensland 4072, Australia; and third author: CSIRO Plant Industry, 306 Carmody Road, St. Lucia, QLD 4067, Australia.

Ordinal qualitative data are often collected for phenotypical measurements in plant pathology and other biological sciences. Statistical methods, such as t tests or analysis of variance, are usually used to analyze ordinal data when comparing two groups or multiple groups. However, the underlying assumptions such as normality and homogeneous variances are often violated for qualitative data. To this end, we investigated an alternative methodology, rank regression, for analyzing the ordinal data. The rank-based methods are essentially based on pairwise comparisons and, therefore, can deal with qualitative data naturally. They require neither normality assumption nor data transformation. Apart from robustness against outliers and high efficiency, the rank regression can also incorporate covariate effects in the same way as the ordinary regression. By reanalyzing a data set from a wheat Fusarium crown rot study, we illustrated the use of the rank regression methodology and demonstrated that the rank regression models appear to be more appropriate and sensible for analyzing nonnormal data and data with outliers.

Additional keywords: linear rank regression model.