Geostatistical Models in Agricultural Field Experiments: Investigations Based on Uniformity Trials

Abstract

The probability of detecting treatment differences can often be increased by using geostatistical instead of classical statistical models. Geostatistical approaches require the selection of the best fitted model from a set of alternative models. This additional analysis effort could be reduced if the same model shows consistently the best fit for a given field or crop. To prove whether this reduction can be expected for designed on‐station trials, we analyzed five uniformity trials conducted on the same field. We studied whether different layouts of randomized complete block designs, the positions on the field, and the randomized plans influenced the model decision and analyzed the precision achieved. For this, the designs were shifted across the field, and 1000 randomized plans were projected onto each position. The model fit was evaluated using the corrected Akaike information criterion (AICC). The ranked AICC values were used for assessing model preference. In the means of all crops, designs, and models, the variation of the ranks depended on an individual decision for the combination of position and randomized plan by 62.6%. Therefore, the best fitted model was not predictable for a single experiment. As in the classical approach, the proper layout of a trial determines precision and unbiasedness of treatment differences. Randomization and blocking still should be the basic principles of experiment planning; however, their roles have partially changed. The detected bias of the Type I errors, both of the t‐test and F test, needs further investigation. Basic findings are also valid for on‐farm trials.

Can Spatial Modeling Substitute for Experimental Design in Agricultural Experiments?

“…We found that under high Fig. Therefore, spatial modeling should be considered as a supplemental strategy rather than an alternative to experimental design, as was also suggested by Richter and Kroschewski (2012) and Piepho et al (2015). Recovery of the best genotypes (Best_Gen), Pearson's correlation coefficient between true and estimated genotypic effects (COR), and the SE of the difference between cultivar means (SED) for six experimental designs: completely randomized design (CRD), randomized complete block design (RCBD) incomplete blocks and a-lattice design with block size of 5 (ALPHA_5), incomplete blocks and a-lattice design with block size of 10 (ALPHA_10), partially replicated design with 200 genotypes (PREP g , this experiment preserved the number of genotypes and thus used fewer experimental units), and a partially replicated design with 428 genotypes (PREPn, this experiment preserved the number of experimental units and thus evaluated more genotypes).…”

“…On the other hand, spatial modeling did not outperform experimental design in any of our situations. Therefore, spatial modeling should be considered as a supplemental strategy rather than an alternative to experimental design, as was also suggested by Richter and Kroschewski (2012) and Piepho et al (2015). Under high field variability, CRD or RCBD with spatial corrections were similar to ALPHA without spatial correction for precision.…”

“…There is a growing interest in the literature for these spatial designs (Piepho and Williams, 2010;Williams and Piepho, 2013;Piepho et al, 2016). The best spatial model seems to be, most likely, case specific (Cullis and Gleeson, 1991;Richter and Kroschewski, 2012;Moehring et al, 2014). Furthermore, even if soil spatial variation was previously well characterized and experiments are designed accordingly, there is still variation that cannot be predicted a priori (Cooper et al, 2014), making it even more challenging to produce good randomizations.…”

Why Randomize Agricultural Experiments?

“…For the randomized design, we used a new randomization for each window. Because the designs were superimposed onto uniformity trial data, the resulting trials simulated the global null hypothesis of no treatment differences (Richter and Kroschewski 2012). With proper randomization, the analytical P-values for the F-tests should be uniformly distributed.…”

Spatial Variability Effects on Precision and Power of Forage Yield Estimation

“…While the NNA indirectly uses covariates to model spatial variation, the CE models directly account for the spatial variation using covariance structures among residuals based on distance (isotropic models) and both distance and direction (anisotropic models) (Littell et al, 2006). Therefore, a spatial model that is adequate for one trial may not be adequate for other trials, hence comparison of different spatial models to determine the best plausible model for each trial is recommended (Gilmour et al, 1997;Richter and Kroschewski, 2012). Therefore, a spatial model that is adequate for one trial may not be adequate for other trials, hence comparison of different spatial models to determine the best plausible model for each trial is recommended (Gilmour et al, 1997;Richter and Kroschewski, 2012).…”