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State‐dependent correlations of biochemical variables in plants
Author(s) -
Németh Zsolt István,
Sárdi Éva,
StefanovitsBányai Éva
Publication year - 2009
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.1226
Subject(s) - mathematics , covariance , statistics , basis (linear algebra) , correlation , variables , distribution (mathematics) , regression analysis , identity (music) , regression , linear regression , normal distribution , sampling distribution , rank (graph theory) , statistical physics , mathematical analysis , combinatorics , physics , geometry , acoustics
Distributions of biochemical variables in plant foliage are mainly similar to normal distributions. The correlations between two variables belonging to a given sampling time or a given physiological stage are regarded as state‐dependent correlations. The conditions of existence of strong state‐dependent correlation are the dependence of values of the variables from each other and the identity of their distributions. An assumed identity of distributions can manifest itself in the very strong similarity of their empirical distributions. Two distributions with finite number of elements are considered the same in their type when they approximate a characteristic distribution, for example, the normal distribution in the same manner. In this situation, the rank or normal score patterns of the data producing linear correlation are also very similar to each other. On the basis of identity criteria and the interdependence of the variables, an equation for state‐dependent correlation has been derived in theoretical way from standardization of the distributions. Thus, not only statistical but also physical meanings can be attached to the parameters of the regression of experimental results. In this paper, we show that the distinction of plant physiological and/or stress states from each other can be more effective by using the correlation of biochemical variables for their characterizations than by separately statistical comparisons of means of the variables. Covariance analysis (ANCOVA) of linear regressions of state‐dependent correlations is able to distinguish actually various states that, on the basis of the means, seem undistinguishable. Copyright © 2009 John Wiley & Sons, Ltd.