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ASSESSING CONGRUENCEAMONG DISTANCE MATRICES: SINGLE‐MALT SCOTCH WHISKIES REVISITED
Author(s) -
Legendre Pierre,
Lapointe FrançoisJoseph
Publication year - 2004
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2004.00357.x
Subject(s) - mathematics , distance matrices in phylogeny , mantel test , generalization , distance matrix , matrix (chemical analysis) , statistics , congruence (geometry) , similarity (geometry) , combinatorics , artificial intelligence , computer science , geometry , image (mathematics) , mathematical analysis , population , materials science , demography , sociology , genetic diversity , composite material
Summary A test of congruence among distance matrices is described. It tests the hypothesis that several matrices, containing different types of variables about the same objects, are congruent with one another, so they can be used jointly in statistical analysis. Raw data tables are turned into similarity or distance matrices prior to testing; they can then be compared to data that naturally come in the form of distance matrices. The proposed test can be seen as a generalization of the Mantel test of matrix correspondence to any number of distance matrices. This paper shows that the new test has the correct rate of Type I error and good power. Power increases as the number of objects and the number of congruent data matrices increase; power is higher when the total number of matrices in the study is smaller. To illustrate the method, the proposed test is used to test the hypothesis that matrices representing different types of organoleptic variables (colour, nose, body, palate and finish) in single‐malt Scotch whiskies are congruent.