The resistance for the transformable nonadditivity, due to J. W. Tukey, is based on the detection of a curvilinear relation between y-est(y) and est(y). A freedom degree for the transformable nonadditivity.
nonadditivity(y, factor1, factor2, df, MSerror)
| y | Answer of the experimental unit |
|---|---|
| factor1 | Firts treatment applied to each experimental unit |
| factor2 | Second treatment applied to each experimental unit |
| df | Degrees of freedom of the experimental error |
| MSerror | Means square error of the experimental |
P, Q and non-additivity analysis of variance
Only two factor: Block and treatment or factor 1 and factor 2.
1. Steel, R.; Torri,J; Dickey, D.(1997) Principles and Procedures of Statistics A Biometrical Approach
2. George E.P. Box; J. Stuart Hunter and William G. Hunter. Statistics for experimenters. Wile Series in probability and statistics
library(agricolae) data(potato ) potato[,1]<-as.factor(potato[,1]) model<-lm(cutting ~ date + variety,potato) df<-df.residual(model) MSerror<-deviance(model)/df analysis<-with(potato,nonadditivity(cutting, date, variety, df, MSerror))#> #> Tukey's test of nonadditivity #> cutting #> #> P : 15.37166 #> Q : 77.44441 #> #> Analysis of Variance Table #> #> Response: residual #> Df Sum Sq Mean Sq F value Pr(>F) #> Nonadditivity 1 3.051 3.0511 0.922 0.3532 #> Residuals 14 46.330 3.3093