Nonlinear growth models: an alternative to anova in tomato trials evaluation


The aim of this work was to use growth models as an alternative analysis of experiments with tomatoes. The data were obtained from field experiments of tomatoes carried out in the 2015/2016 and 2016/2017 growing seasons. Six and nine harvests were carried out in 2015/2016 and 2016/2017, respectively. In each harvest, the number and mass of fruits per plant were assessed. The ANOVA for repeated measures was performed to analysis of the data, and the residuals were assessed. Also for each variable, the Brody, Gompertz, Logistic and von Bertalanffy growth models were fitted as a function of the accumulated values per plant in each harvest and days after the transplant of the seedlings. The assumptions of normality, homogeneity and independence of residuals were verified by the Shapiro-Wilk, Breusch-Pagan and Durbin-Watson tests, respectively. The bias of the parameters was evaluated by the intrinsic and parametric nonlinearity, by the difference between OLS-based and the mean of 10.000 bootstrap-based parameter estimates, and by evaluating the symmetry of the sampling distributions of such parameters. Among the models tested, the one that presented a high coefficient of determination and less non-linearity was selected. The parameters of the selected model were compared by the F test. From the second-, third- and fourth-order derivatives with respect to x (days after transplant), the maximum acceleration point, inflection point, maximum deceleration point, and point of asymptotic deceleration were estimated. The residuals increased with the mean when ANOVA was used, and the data transformation did not fix the violated assumption. The violation of the model’s assumptions motivated us to propose nonlinear models as an alternative to statistical analysis with ANOVAs. The logistic model had parameters close to being unbiased, and all assumptions have been meeting. Due to this, the logistic model was selected. The critical points of this model allowed assessing the productive precocity, crop concentration period and productive behavior of the genotypes during the productive period. Finally, we have shown that growth models may be an interesting alternative to standard ANOVA procedures to analyze experiments with horticultural crops in future studies.