Statistical Analysis of Non‐Replicated Experiments in Farmers’ Fields. A Case of Balanced Fertilization Trials for Bean in Burundi

Abstract

Core Ideas Often agronomic experiments in farmers’ fields do not allow replications. Between‐fields spatial variability can be used to model the error variance. The modeled error variance in a GLMM is used to test treatment‐related hypotheses. Using fields as replications can end in biased results due to fields’ autocorrelation. ABSTRACTVery often agricultural experiments in smallholder farms are conducted without actual replications due to land restrictions. Using fields as replications and performing the ANOVA with a randomized complete block design (RCBD) model can result in misleading conclusions about treatment’s performance due to a biased error variance matrix estimated under the wrong assumption of independence between fields. A better alternative is using the spatial variability modeling features of the GLMM to generate an error term to perform unbiased hypothesis tests. Non‐replicated trials to estimate bean response to three fertilization treatments were conducted across 175 farmers’ fields in Burundi. Yields were used to compare the performance of an ANOVA using a GLMM where the exponential autocorrelation pattern of the residuals was used to model the error variance‐covariance matrix against an ANOVA following a RCBD model where the fields are handled as blocks. The fields were grouped in three clusters prior to the ANOVA. AIC and the Generalized Chi‐Sq./DF ratio values for the model involving spatial modeling were 165.3 and 1, respectively. The same fit statistic values from the RCBD model were 330.1 and 0.1, respectively. The near‐half magnitude of AIC in the spatial model relative to the RCBD model indicates higher model goodness of fit for the spatial model. The 0.1 value for the Generalized Chi‐Sq./DF ratio in the RCBD model suggests underdispersion and violation of the independence‐between‐fields assumption. Detection of a significant CLUSTER*TREATMENT by the spatial model corroborates the superiority of the ANOVA model involving spatial variability.