Financial investment with collection and laboratory analysis of soil samples is an important factor to be considered when mapping agricultural areas with soybean planting. One of the alternatives is to use the spatial autocorrelation between the sample points to reduce the number of elements sampled, thus restricting the collection of redundant information. This work aimed to reduce the sample size of this agricultural area, composed of 102 sample points, and use it to analyze the spatial dependence of soil macro- and micro- nutrients, as well as the soil penetration resistance. The agricultural area used in this study has 167.35 ha, cultivated with soybean, which the soil is Red Dystroferric Latosol, and the sampling design has used in this agricultural area is the lattice plus close pairs. The reduction of the sample size was made by the multivariate effective sample size (ESSmulti) methodology. The studies with the simulation data and the soil attributes showed an inverse relationship between the practical range and the estimated value of the univariate effective sample size. With the calculation of ESSmulti, the sample configuration was reduced to 53 points. The Overall Accuracy and Tau concordance index showed differences between the thematic maps elaborated with the original and reduced sampling designs. However, the analysis of the variance inflation factor and the standard error of the spatial dependence parameters showed efficient results with the resized sample size.

Aim of study: To reduce the sample size in an agricultural area of 167.35 hectares, cultivated with soybean, to analyze the spatial dependence of soil penetration resistance (SPR) with outliers. Area of study: Cascavel, Brazil Material and methods: The reduction of sample size was made by the univariate effective sample size ( ) methodology, assuming that the t-Student model represents the probability distribution of SPR. Main results: The radius and the intensity of spatial dependence have an inverse relationship with the estimated value of the . For the depths of SPR with spatial dependence, the highest estimated value of the  reduced the sample size by 40%. From the new sample size, the sampling redesign was performed. The accuracy indexes showed differences between the thematic maps with the original and reduced sampling designs. However, the lowest values of the standard error in the parameters of the spatial dependence structure evidenced that the new sampling design was appropriate. Besides, models of semivariance function were efficiently estimated, which allowed identifying the existence of spatial dependence in all depth of SPR.Research highlights: The sample size was reduced by 40%, allowing for lesser financial investments with data collection and laboratory analysis of soil samples in the next mappings in the agricultural area. The spatial t-Student model was able to reduce the influence of outliers in the spatial dependence structure.

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In agricultural soils with low cation exchange capacity, it is essential to analyze the bivariate spatial correlation of soybean productivity and organic matter with the soil chemical attributes. Using bivariate spatial correlation makes it possible to identify patterns and behaviors that suggest a spatial association between two soil attributes, thus enabling better soil management and more efficient use of resources. The main objective of this study was to analyze bivariate spatial correlation considering variables with different spatial dependence structures. The bivariate Lee index was also calculated for this purpose. To model and describe the spatial pattern of two spatially correlated variables, the Bivariate Gaussian Common Component Model was used. In addition to calculating the bivariate spatial correlation of soil chemical attributes with soybean productivity and organic matter, the Lee index was also calculated for pairs of simulated variables with different weight matrices and geographic distance functions. It was observed that the greater the common practical range, the higher the Lee index value, indicating a higher bivariate spatial correlation. Furthermore, shorter distances between neighboring point pairs caused higher Lee index values. The distance function to calculate the distance between the point pairs was more relevant than the weight matrix in estimating the spatial dependence radius and the Lee index value. Soybean productivity showed a direct spatial correlation with the sum of bases, as well as with the calcium and magnesium contents. Organic matter had a direct spatial correlation with the sum of bases and an inverse one with the phosphorus content