### Abstract

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 wariables, 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 effectiwe by using the correlation of biochemical variables for their characterizations than by separately statistical comparisons of means of the wariables. 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.

Original language | English |
---|---|

Pages (from-to) | 197-210 |

Number of pages | 14 |

Journal | Journal of Chemometrics |

Volume | 23 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 2009 |

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### Keywords

- Carbohydrates
- Enzyme correlation
- Grape
- Pendunculate oak
- State-dependent correlation

### ASJC Scopus subject areas

- Analytical Chemistry
- Applied Mathematics

### Cite this

*Journal of Chemometrics*,

*23*(4), 197-210. https://doi.org/10.1002/cem.1226

**State-dependent correlations of biochemical variables in plants.** / Németh, Z.; Sárdi, Éva; Stefanovits-Banyai, E.

Research output: Contribution to journal › Article

*Journal of Chemometrics*, vol. 23, no. 4, pp. 197-210. https://doi.org/10.1002/cem.1226

}

TY - JOUR

T1 - State-dependent correlations of biochemical variables in plants

AU - Németh, Z.

AU - Sárdi, Éva

AU - Stefanovits-Banyai, E.

PY - 2009/4

Y1 - 2009/4

N2 - 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 wariables, 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 effectiwe by using the correlation of biochemical variables for their characterizations than by separately statistical comparisons of means of the wariables. 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.

AB - 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 wariables, 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 effectiwe by using the correlation of biochemical variables for their characterizations than by separately statistical comparisons of means of the wariables. 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.

KW - Carbohydrates

KW - Enzyme correlation

KW - Grape

KW - Pendunculate oak

KW - State-dependent correlation

UR - http://www.scopus.com/inward/record.url?scp=64249088781&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=64249088781&partnerID=8YFLogxK

U2 - 10.1002/cem.1226

DO - 10.1002/cem.1226

M3 - Article

AN - SCOPUS:64249088781

VL - 23

SP - 197

EP - 210

JO - Journal of Chemometrics

JF - Journal of Chemometrics

SN - 0886-9383

IS - 4

ER -