Autoregressive analysis of variance for experiments with spatial dependence between plots: a simulation study

Abstract

The analysis of variance remains one of the most appreciated techniques of field experiment, even despite almost a hundred years of its first proposal. However, in many cases, its application can be several impaired due the fact of lack –or even forgotten -of assumptions. In several experiments, the researchers make use of blocks to control the local heterogeneity, nevertheless, in some cases, only thisitcannot be enough, especially in experiments where the data have some kind of spatial dependence. Therefore, to increase the accuracy of comparisons between treatments, an alternative is to consider the study of the spatial dependence of the variables in the analysis. With the knowledge of the relative positions of the plots (referenced data), the spatial variability canbe used as a positive factor, collaborating with the experimental results. To develop this study we used data generated by simulation. The data was generated according a Randomized Complete Block Design (RCBD), with eighteen and five treatments per block;and several scenarios of spatial dependence in the error. We compared the non-spatial analysis (which considers the errors independent) with spatial analysis (analysis of variance considering the autoregressive model -ANOVA-AR). The use of spatial statistical tools in the analysis of data increased the precision of the analysis, through the reduction of the Mean Squared Error. We also noticed a reduction of Mean Squared Block and Mean Squared Treatment. The greater reduction was notice in ANOVA-AR3 for great part of the simulated scenarios, mainly in those with strong spatial dependence. The experiments with a small number of treatments per block did not present a reduction of Mean Squared Error, however, the reduction of Mean Squared Block and Mean Squared Treatment, ally to the fact that data are spatial dependent justify the use of ANOVA-AR.