Using diagnostic residual plots to validate statistical assumptions in multi-environment sugar beet trials

Evaluating genotype performance across diverse environments is a fundamental challenge in plant breeding and cultivar recommendation. In multi-environment trials, the interaction of genotype and environment (G×E) and environmental variability can greatly influence the statistical interference, making validation of model assumptions essential for reliable conclusions. In this study, we examined the assumptions of normality and homogeneity of variances for root yield data from 20 sugar beet genotypes evaluated across three locations and two consecutive years using a randomized complete block design. A linear mixed model framework was applied, and inference on genotypic effects was based on ANOVA-type tests. Model assumptions were assessed using both formal statistical tests and graphical residual diagnostics. While classical tests such as Shapiro–Wilk and Levene’s test indicated significant deviations from normality and variance homogeneity, graphical methods including histograms, Q–Q plots, and residual plots provided easily interpretable evidence that these deviations were minor and not practically concerning. Residual diagnostics confirmed that the mixed model assumptions were largely satisfied, particularly when heterogeneous error variances were modeled. These results reinforce the importance of integrating graphical residual diagnostics into the routine analysis of agricultural multi-environment trials, as a practical and informative complement to formal statistical tests, thereby supporting more robust cultivar evaluation and recommendation.