spANOVA: biblioteca para análise de variância de experimentos com dependência espacial em ambiente R

Abstract

The inference procedures used in the analysis of variance (ANOVA) need some assump- tions about the experimental error so that its results are valid, namely: normality, ho- moscedasticity, and independence. One of the most frequent problems occurs when the independence of the errors is not satisfied, not even when the casualization is performed. One of the reasons that lead to the occurrence of this phenomenon is that in many expe- riments, especially in the agricultural area, there is a strong spatial dependence generated by the location of the experimental unit, which is not reduced by randomization or local control. In this context, work has been developed to model this dependency and include it in the analysis to obtain more reliable results. Some approaches include the modeling of spatial dependence directly from the error covariance matrix, as is the case with the geostatistical approach, while others use transformations in the response variable in order to neutralize the spatial correlation effect, as is the case of analysis of variance via spatial autoregressive models (SAR). Although these theories are already developed and ready to be used, the absence of software or libraries that perform such procedures becomes a drawback in their practical use, causing many researchers to misinterpret their results by opting to use models that do not consider spatial information. Thus, the objective of this work was to develop a library to be used in a programming environment, as well as an interactive graphical interface, in order to allow the inclusion of space dependence in the analysis of variance in a simple and intuitive way, using both the approach geostatis- tics approach using spatial autoregressive models, thus making it possible to obtain more precise results. For this, open source software was used. Specifically, R was used in the construction of a library based on this programming language, since much of the scientific community that makes use of statistical methods is familiar with its syntax. The cons- truction of the interactive graphical user interface was also performed in the R through the textit shiny library. In order to illustrate the functioning of the final product obtained by this work, an experiment was carried out with candeia (Eremanthus erythropappus) carried out in the Baependi - MG region, whose interest was to verify the effect of 13 types of fertilization treatments at the height of the trees. The results showed significant differences among the 13 treatments, which were later submitted to multiple comparison procedures revealing that the formulated NPK 8-28-16 fertilizer treatment provided the best results.