Statistical Analysis of Non-Replicated Experiments in Farmers’ Fields. A Case of Balanced Fertilization Trials for Bean in Burundi
Date
2019-05-01
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Abstract
Very 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
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Keywords
Fertilization, Farmers
Citation
Sanabria, J., and J. Wendt. 2019. “Statistical Analysis of Non-Replicated Experiments in Farmers’ Fields: A Case of Balanced Fertilization Trials for Bean in Burundi,” Agronomy Journal, 111(3):1165-1170. https://doi.org/10.2134/agronj2018.10.0655