Model Assumptions Testing of Annual Ryegrass-Egyptian Clover Cultivars Component in Mixtures and Repeated-Measure Harvests

Abstract

It is a myth that a dataset a priori may not violate the assumptions of univariate general linear model (GLM). Validation of hypothesis testing (HT) is threatened if assumptions are violated. This research aims to check normality and variance homogeneity for between- and within-factor levels. In a 2-year field trial, Lolium multiflorum cv ‘Local’ was seeded in 6 percentage mixtures with 3 Trifolium alexandrinum cvs components in mixtures. A factorial model was fitted to forage yield, with 2 between-factors, and one within. Quantile-Quantile (Q-Q) plots and Shapiro-Wilk test were used to check normality. For between-factors, variance homogeneity is tested using plots of residuals and HT’s Levene’s test. For repeated measures, Mauchly’s test is used to estimate sphericity. Six extreme outliers were spotted overall in the 2 years. The Q-Q plots showed that most residuals lay on the fitted lines, implying that normality was not violated. Residual error variance homogeneity was violated in Year 1. Inspecting repeated-harvests variances, Mauchly’s W declared a minor violation of sphericity. Violations of model assumptions exist in real-life data.