Alternative methods in presence of violation of assumptions in factorial experiment designs - Meza Rodríguez, Aldo Richard (2021)
The objective of this research was to compare and test different methods and alternatives to approach factorial designs with fixed effects, when the assumptions of normality or homogeneity of variances are not met. Twenty methods investigated in the literature as an alternative to classical ANOVA (variance analysis) were described and tested, including non-parametric techniques, robust methods, permutations, methods for heterogeneous variances and transformations; which are currently available and implemented in R software. The methods were tested in a 3A2B factorial design, where factor A was varieties of pineapple (Golden, Cayenne Lisa and Hawaiian), factor B was type of crop management (conventional and organic), and the response variable was the average percentage of Brix degrees. Among the proposed methods, 15 rejected the interaction hypothesis, and when comparing the type I error rates through simulations it was found that the permutations methods, the robust methods, the ART, van der Waerder and the BDM yielded error rates by below nominal value. When selecting ART as an alternative to perform the post hoc test, the best combination of treatments was the Lisa Cayena variety in organic management and the Hawaiian variety with conventional management, obtaining with these combinations percentages of Brix degrees above the average.