Jc. Gower et Wj. Krzanowski, Analysis of distance for structured multivariate data and extensions to multivariate analysis of variance, J ROY STA C, 48, 1999, pp. 505-519
Citations number
21
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS
Many data sets in practice fit a multivariate analysis of variance (MANOVA)
structure but are not consonant with MANOVA assumptions. One particular su
ch data set from economics is described. This set has a 2(4) factorial desi
gn with eight variables measured on each individual, but the application of
MANOVA seems inadvisable given the highly skewed nature of the data. To es
tablish a basis for analysis, we examine the structure of distance matrices
in the presence of a priori grouping of units and show how the total squar
ed distance among the units of a multivariate data set can be partitioned a
ccording to the factors of an external classification. The partitioning is
exactly analogous to that in the univariate analysis of variance. It theref
ore provides a framework for the analysis of any data set whose structure c
onforms to that of MANOVA, but which for various reasons cannot be analysed
by this technique. Descriptive aspects of the technique are considered in
detail, and inferential questions are tackled via randomization tests. This
approach provides a satisfactory analysis of the economics data.