A Single degree of freedom for Nonadditivity

See Steel & Torri. "Principles and procedures of statistics a biometrical approach". Third Edition
Example pag. 396:
Data: Amount of Na2PO4 added (ppm)
 bloques T0  T50 T100 T150 T200
 1     3.51 3.68 3.62 3.75 3.71
 2     5.07 3.94 3.97 4.03 5.14
 3     2.97 2.86 2.92 2.93 3.60
 4     2.68 2.50 2.47 2.45 3.12
 5     6.54 7.25 7.27 7.13 7.96
 6     2.30 3.51 3.38 3.40 3.40
 7     2.06 2.06 2.61 2.06 2.22
Save file: NonAdd.txt.
Script R:
library(agricolae)
soil<-read.table("NonAdd.txt",header=T)
bloques<-soil[,1]
trat <-names(soil)[2:6]
datos<-data.frame(trat=trat[1],bloques=soil[,1],y=soil[,2])
for (i in 3:6) {
temp<-data.frame(trat=trat[i-1],bloques=soil[,1],y=soil[,i])
datos<-rbind(datos,temp)
}
rm(bloques,trat)
datos[,2]<-as.factor(datos[,2])

# analisis
model <- aov(y ~ bloques + trat, datos)
anova(model)
Analysis of Variance Table

Response: y
            Df Sum Sq Mean Sq  F value Pr(>F)
bloques     6  84.920  14.153 109.7996 3.03e-16 ***
trat        4   1.426   0.357   2.7658 0.05062 .
Residuals  24   3.094   0.129
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Df<-df.residual(model)
MSerror<-deviance(model)/Df
attach(datos)
analysis<-nonadditivity(y, bloques, trat, Df, MSerror)
Tukey's test of nonadditivity
y

P : 1.981695
Q : 13.84030

Analysis of Variance Table

Response: residual
                Df  Sum Sq Mean Sq F value Pr(>F)
Nonadditivity    1 0.28374 0.28374  2.3225 0.1411
Residuals       23 2.80990 0.12217
detach(datos)

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