#Biostatistics 321

#THREE FACTOR DESIGN WITH
#ONE FACTOR NESTED INSIDE ANOTHER
#FACTORS A & B ARE CROSSED FACTORS
#FACTOR B IS NESTED WITHIN A

#EXAMPLE FROM NETER ET AL 1990 P. 1152

NET=read.table("NKNWTA28.12.txt")
NET
attach(NET)

A=factor(A)
B=factor(B)
C=factor(CinA)

#ANOVA TABLE:
anova(lm(Y~A*B+B:C%in%A+C%in%A))

#FROM ANOVA TABLE:
MSA=420.25
MSB=182.25
MSAB=2.25
MSCinA=0.25
MSBCinA=1.25
MSE=13.25
dfA=1
dfB=1
dfAB=1
dfCinA=2
dfBCinA=2
dfE=8

alpha=0.05

#TEST FOR INDEPENDENT FACTOR A:
FA=MSA/MSCinA
FA
CA=qf(1-alpha,dfA,dfCinA)
CA
PA=1-pf(FA,dfA,dfCinA)
PA

#TEST FOR INDEPENDENT FACTOR B:
FB=MSB/MSBCinA
FB
CB=qf(1-alpha,dfB,dfBCinA)
CA
PB=1-pf(FB,dfB,dfBCinA)
PB

#TEST FOR INTERACTION OF FACTORS A & B:
FAB=MSAB/MSBCinA
FAB
CAB=qf(1-alpha,dfAB,dfBCinA)
CAB
PAB=1-pf(FAB,dfAB,dfBCinA)
PAB

#TEST FOR NESTED FACTOR C SPECIFIC EFFECTS:
FC=MSCinA/MSE
FC
CC=qf(1-alpha,dfCinA,dfE)
CC
PC=1-pf(FC,dfCinA,dfE)
PC

#TEST FOR INTERACTION OF INDEPENDENT FACTOR B WITH
#NESTED FACTOR C IN A:
FBC=MSBCinA/MSE
FBC
CBC=qf(1-alpha,dfBCinA,dfE)
CBC
PBC=1-pf(FBC,dfBCinA,dfE)
PBC