Coeficiente de variação e índice de variança

Bragantia, Feb 2019

The object of the present paper is a study of the usefulness of two relative measures of variation, the well known coefficient oj variation and a new term proposed in this paper and called the index of variance. These terms are defined by the equations : coefficient of variation : σ% = s /v/v. 100 index of variance :σ/ √. 1.  It is shown that, for theoretical reasons, only the index of variance may be expected to be constant. Six different experimental series actually proved this constancy, showing at the same time the variability of the coefficient of variation which proved to be dependent upon the respective mean. The coefficient of variation becomes approximately constant when the respective means are sufficiently distant from the absolute limit zero or other biological limits. 2.  Thus the index of variance may be used to prove the homogeneity of variation in samples with means of different dimensions. 3.  Through this it is shown that the index of variance should be constant, it is explained that for biological reasons we may not always find a good fit between the observed and the expected data, calculated by means of the equation = kv where k represents a biological constant. In two cases a better fit was obtained using more complicated formulae. 4.  While it seems justified in agricultural experimentation to accept proportionality between mean yield and area, no such relation exists for the standard error. We may only say that generally the index of variance for large areas is not equal, but bigger than that for smaller ones. 5.  The coefficient of variation cannot be used as a general term for comparing the variation in series of different dimensions, where we must apply the index of variance. But it still retains its value as a measure of the efficiency of experiments.

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Coeficiente de variação e índice de variança

Coeficiente de variação e índice de variança     F. G. Brieger(*)     SUMMARY The object of the present paper is a study of the usefulness of two relative measures of variation, the well known coefficient oj variation and a new term proposed in this paper and called the index of variance. These terms are defined by the equations : coefficient of variation : σ% = s /v/v. 100 index of variance :σ/ √. 1.  It is shown that, for theoretical reasons, only the index of variance may be expected to be constant. Six different experimental series actually proved this constancy, showing at the same time the variability of the coefficient of variation which proved to be dependent upon the respective mean. The coefficient of variation becomes approximately constant when the respective means are sufficiently distant from the absolute limit zero or other biological limits. 2.  Thus the index of variance may be used to prove the homogeneity of variation in samples with means of different dimensions. 3.  Through this it is shown that the index of variance should be constant, it is explained that for biological reasons we may not always find a good fit between the observed and the expected data, calculated by means of the equation = kv where k represents a biological constant. In two cases a better fit was obtained using more complicated formulae. 4.  While it seems justified in agricultural experimentation to accept proportionality between mean yield and area, no such relation exists for the standard error. We may only say that generally the index of variance for large areas is not equal, but bigger than that for smaller ones. 5.  The coefficient of variation cannot be used as a general term for comparing the variation in series of different dimensions, where we must apply the index of variance. But it still retains its value as a measure of the efficiency of experiments.     Texto completo disponível apenas em PDF. Full text available only in PDF format.     LITERATURA CITADA 1 . Brieger, F. G. Análise estatística da Experiência de café Bourbon e seleção de café por métodos modernos. (Capítulo II do trabalho : Melhoramento de Coffea arabica L. var. Bourbon, de I. E. Teixeira Mendes, F. G. Brieger, C. A. Krug e A. Carvalho.) Bragantia 1: 26-119, gráf. 1-32, 1941.         [ Links ] 2.  Brieger, F. G., S. Moreira e Z. Leme. Estudo sobre o melhoramento da laranja "Baía" III. Bragantia 1: 567-610, fig. l-10b, 1941.         [ Links ] 3.  Moreira, S. Experiências de cavalos para citrus I. Bragantia 1: 525-565, fig. 1-20, gráf. 1-6, 1941.         [ Links ]     (*) Da Escola Superior de Agricultura "Luiz de Queiroz".


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F. G. Brieger. Coeficiente de variação e índice de variança, Bragantia, 313-331, DOI: 10.1590/S0006-87051942000900001