Heteroscedasticity in Whole Plant Growth Curves Developed from Nonreplicated Data

Abstract

AbstractAgronomic researchers usually neglect heteroscedasticity in crop growth formulae and analysis. When they consider it they are not consistent in the methods they use. This study was conducted to: (i) find a method of testing for heteroscedasticity in nonreplicated whole plant growth data and (ii) determine the best weighting for such crop growth data. We developed seven different crop growth models with yield data collected during the growing season of five different crops (14 sets total, six with replicates). Next we performed tests for heteroscedasticity on model residuals and heterogeneity of variance tests on replicated data. Finally we conducted simulations to assess the confidence interval coverage of various weighted predictions based on one model fit to two of the replicated crop sets. Five of the models usually exhibited realistic growth responses throughout the growing season. All heterogeneity of variance tests were significant (P < 0.05) and most suggested a logarithmic weighting. In contrast, tests devised from groups of sequential residuals usually indicated a square root weighting but were generally not significant (P ≥ 0.05). Simulations revealed that weighting was needed but that none of the variance models always adequately characterized the true variance. While not a good variance model, a linear trend in a model's squared residuals (P < 0.10) proved to be a sound test for heteroscedasticity in growth curves developed from nonreplicated data. Crop growth curves need to be weighted with an exact Box‐Cox variance model when replicates are available and one intermediate between the logarithmic and square root model when replicates are unavailable.