title: Multidimensional scale types and invariant multivariate statistics.
abstract: This paper proposes an extension of the definition of one-dimensional ordinal, interval, ratio, difference and absolute scales to the multidimensional case. The connection between measurement structures and statistical structures suggested in a previous paper is also extended to the multivariate case, and examples of invariance properties of multivariate functions and statistics are discussed.
authors.affiliation: Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA 22807, USA. chiangcx@jmu.edu
authors.forename: Ching-Yuan
authors.initials: CY
authors.lastname: Chiang
mesh_terms: D000704:Analysis of Variance; D006801:Humans; D016014:Linear Models; D015999:Multivariate Analysis; D011594:Psychometrics / Q000706:statistics & numerical data*