A multivariate approach to understanding trait interactions in soybean plants

Abstract

Despite widespread use of statistical methods, advanced techniques like multivariate analysis are often underutilized, a trend that can lead to methodological missteps. This article focuses on Multivariate Analysis of Variance (MANOVA) and its necessary follow‑up procedures, addressing why MANOVA often remains overlooked. We review its conceptual foundation, analysing multiple dependent variables collectively rather than separately, as in ANOVA, and illustrate its advantages, particularly the reduction of Type I error and the ability to detect multivariate patterns unnoticed in univariate analysis. Drawing on a practical case study involving a 2025 Kaggle soybean dataset (55,450 records across 13 agronomic traits), we apply MANOVA (via Jamovi) across 36 treatment combinations of genotype, salicylic acid, and water stress. Multivariate tests (Pillai’s trace, Wilks’ lambda, Hotelling’s trace, and Roy’s largest root) were all highly significant (p < 0.001), indicating group-level differences across variables. Subsequent univariate ANOVA revealed significance for each trait, and post‑hoc pairwise comparisons (630 total) identified numerous significant differences. Finally, mean comparisons highlight the S1C3G3 group as top-performing across multiple key metrics. Our findings demonstrate the value of MANOVA in agricultural research and recommend adopting genotype 3 with salicylic acid at 450 mg under minimal water stress.