Tamanho amostral efetivo no estudo da variabilidade espacial de variáveis georreferenciadas usando as distribuições normal e t-student

Abstract

Trading competition has demanded to the Brazilian agribusiness greater production at lower costs. Thus, the Precision Agriculture (AP) comes to light as an alternative, which can identify the spatial variability of physical and chemical soil properties, in order to better know the agricultural area and, consequently, raise crop yield standard. Regardless of the PA’s use, knowing the spatial variability of a variable in the agricultural area requires adequate sampling planning that allows collecting as few sample points as possible, avoiding too many costs and maintaining quality in sampling. Regardless of the PA’s management, it is required to know the spatial variability of a variable in an agricultural area and this also asks for an adequate sample planning that makes possible the collection of the least number of sampling points, in order to avoid too much cost and to keep quality in sampling. So, this trial aimed at reducing the number of sample points collected by calculating the effective sample size (ESS). The univariate and multivariate ESS value was estimated for georeferenced variables with normal probability distribution using two methodologies: Griffith and Vallejos and Osorio. This study was carried out with simulated data, varying the values of the nugget effect as well as the range attributed to the variables, and with physical-chemical attributes of a soil. Therefore, variables do not always have normal probability distribution, mainly due to the presence of discrepant points. Thus, the value of univariate effective sample size for stationary and isotropic stochastic processes was estimated, considering that the covariance structure had a t-Student probability distribution. According to the multivariate results from variables with normal probability distribution, there was a decrease in the number of sample points from 48% to 93%. In both univariate and multivariate cases, the estimated ESS was lower by the Griffith method, indicating that this suggestion can make feasible a larger decrease in sample size. Univariate results derived from attributes with Student’s t-distribution showed a decrease from 40% to 95% in the number of sample points. Such variation in the sample size is justified by the different values of the spatial dependence parameters presented by the variables. It was also recorded that the radius of spatial dependence was the parameter with the greatest influence on the estimated value of uni and multivariate ESS, and the higher its value, because the smaller the effective sample size, the larger is the decrease in the sample size.