#2008 HALF-SIB ANALYSIS IN LYNCH & WALSH CH18

#DATA

N=20
T=171
n=c(10,10,10,10,10,9,9,9,9,9,9,9,9,8,8,8,8,7,6,4)
length(n)
MSS=0.1156
MSE=0.0370

#CALCULATED ESTIMATES

n0=(T-(t(n)%*%n)/T)/(N-1)
n0
Vars=(MSS-MSE)/n0
Vars
Vare=MSE
Vare
Varz=Vars+Vare
Varz
t=Vars/Varz
t
hsq=4*t
hsq
Vart=((2*(1-t)^2)*(1+(n0-1)*t)^2)/(N*n0*(n0-1))
Vart
SEh=4*sqrt(Vart)
SEh
AGV=4*((MSS-MSE)/n0)
AGV

#F-TEST OF BETWEEN-FAMILY VARIANCE=0
alpha=0.01
F=MSS/MSE
F
CV=qf(1-alpha,N-1,T-N)
CV
P=1-pf(F,N-1,T-N)
RESULTS=c(F,CV,P)
RESULTS

#CONFIDENCE INTERVALS
alpha=0.05

#CI FOR Vare=SSE:
SSE=MSE*(T-N)
XL=qchisq(alpha/2,T-N)
XU=qchisq(1-alpha/2,T-N)
Le=SSE/XL
Ue=SSE/XU
RESULTS=c(Le,Vare,Ue)
RESULTS