#Biostatistics 301

#ANOVA FOR RANDOMIZED BLOCKS WITH REPLICATES

M=read.table("machinesR.txt",header=TRUE)
M
attach(M)
fMachine=factor(Machine)
fWorker=factor(Worker)

LM=lm(score~fMachine*fWorker)
anova(LM)

alpha = 0.05
MSA=anova(LM)[1,3]
MSB=anova(LM)[2,3]
MSAB=anova(LM)[3,3]
MSE=anova(LM)[4,3]
dfA=anova(LM)[1,1]
dfB=anova(LM)[2,1]
dfAB=anova(LM)[3,1]
dfE=anova(LM)[4,1]

#OMNIBUS F TEST FOR TREATMENT EFFECT:
F=MSA/MSAB
F
C=qf(1-alpha,dfA,dfAB)
C
P=1-pf(F,dfA,dfAB)
P

#OMNIBUS F TEST FOR BLOCK EFFECT:
F=MSB/MSE
F
C=qf(1-alpha,dfB,dfE)
C
P=1-pf(F,dfB,dfE)
P

#F TEST FOR TREATMENT BY BLOCK INTERACTION:
F=MSAB/MSE
F
C=qf(1-alpha,dfAB,dfE)
C
P=1-pf(F,dfAB,dfE)
P

#CORRESPONDING R CODE FOR MIXED MODELS:

library(nlme)

#MODEL WITH NO INTERACTION:
FM1=lme(score~Machine,random =~1|Worker)
summary(FM1)
anova(FM1)

#MODEL WITH TREATMENT BY BLOCK INTERACTION:
FM2=lme(score~Machine,random =~1|Worker/Machine)
summary(FM2)
anova(FM2)

#TEST OF MODEL INCLUDING INTERACTION:

anova(FM1,FM2)