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The Races of Maize: II. Use of Multivariate Analysis of Variance to Measure Morphological Similarity 1
Author(s) -
Goodman Major M.
Publication year - 1968
Publication title -
crop science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.76
H-Index - 147
eISSN - 1435-0653
pISSN - 0011-183X
DOI - 10.2135/cropsci1968.0011183x000800060016x
Subject(s) - mahalanobis distance , statistics , mathematics , multivariate statistics , covariance , rank correlation , biology , randomized block design , rank (graph theory) , residual , multivariate analysis of variance , multivariate analysis , similarity (geometry) , multivariate normal distribution , covariance matrix , combinatorics , algorithm , artificial intelligence , computer science , image (mathematics)
The racial means and the residual covariance matrix from the multivariate analysis of variance of an experiment based on a randomized block design involving 15 races of maize ( Zea mays L.) from southeastern South America were used to calculate generalized distances between the races. Sixteen characters commonly used in taxonomic studies of the races of maize were employed. The effects of transformations designed to eliminate some of the heterogeneity among the withinrace, within‐row covariance matrices were studied, and the effects of within‐plot sampling were investigated. It was shown that the use of transformations had very little effect on the relative distances (and hence that highly significant heterogeneity — as measured by the multivariate extension of Bartlett's test — had little effect on the analysis of the non‐transformed data). Similarly, essentially the same relative distances were obtained when only a single plant from each race was used per block (eight blocks were used). In all cases the distances obtained were relatively very similar (i.e., Spearman rank correlation coefficient between 0.91 and 0.99) to the distances obtained from the commonly employed Mahalanobis’ generalized distance technique.