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.
