Abstract
The objective of this work was to determine the sufficient number of replicates for estimation of dissimilarity measures among maize cultivars. Data of five variables were used, which were evaluated in an experiment with 15 maize cultivars, in randomized block design with nine replicates. A number of 511 data files were formed, being 9, 36, 84, 126, 126, 84, 36, 9, and 1 obtained, respectively from 1, 2, 3, 4, 5, 6, 7, 8, and 9 replicates. Three dissimilarity matrices were determined between i and i’ cultivars containing, respectively, Euclidean, Manhattan, and Chebyshev distances. For each of the 105 distances between cultivars, in each dissimilarity measure, the power function was adjusted for the coefficient of variation of the (dependent variable) as a function of the number of replicates (independent variable), totaling 315 equations. For each equation, the abscissa axis value (Xs, sufficient number of replicates) was determined, corresponding to the maximum curvature point. With the increase of the number of replicates, there is an improvement in the accuracy of the estimates of dissimilarity measures among maize cultivars, however, the gains in precision decrease gradually. Six replicates are sufficient to estimate the dissimilarity measures among maize cultivars expressed by the Euclidean, Manhattan, and Chebyshev distances.
Highlights
Resumo - O objetivo deste trabalho foi determinar o número suficiente de repetições para estimação de medidas de dissimilaridade entre cultivares de milho
Yij is the observed value for variable Y of the ith cultivar (i = 1, 2, ..., n) in the jth replicate(j = 1, 2, ..., r); μ is the overall mean; Ci is the effect of the ith cultivar (i = 1, 2,..., n), in this study considered as a fixed effect; Bj is the effect of the jth replicate (j = 1, 2, ..., r); and εij is the effect of the experimental error for Yij, assumed to be normal and independently distributed with a zero mean and common variance σ2 (Storck et al, 2016)
From the data of the experiment with the 15 cultivars evaluated in nine replicates, in this study considered as a reference, the F-test of the variance analysis revealed a significant effect (p ≤ 0.05) of cultivars for all variables
Summary
Resumo - O objetivo deste trabalho foi determinar o número suficiente de repetições para estimação de medidas de dissimilaridade entre cultivares de milho. Seis repetições são suficientes para estimar as medidas de dissimilaridade entre as cultivares de milho expressas pelas distâncias Euclidiana, Manhattan e Chebyshev. Other distances originated from the Minkowski metric, such as Euclidean, Manhattan (city block), and Chebyshev (maximum or supreme) can be estimated from a replicate (without experimental design) or from the mean value of replicates (in an experimental design). In this sense, Grenier et al (2013) used six dissimilarity measures, including the standard Euclidean distance, to study climate differences in Canada. It’s important to investigate whether there is a possibility of defining the sufficient number of replicates to estimate these dissimilarity measures
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