#Ex11.7
I=4;J=8;sigma=1
alpha = c(-0.25,-0.25,-0.25,0.75)
noncen = J*sum(alpha^2)/sigma^2
f.alpha = qf(0.05,I-1,I*(J-1),lower.tail=FALSE)
beta = pf(f.alpha,I-1,I*(J-1),noncen)

#Specifying J for given sum(alpha^2)/sig^2 = 4
I=4
J=2:20
f.alpha=qf(0.05,I-1,I*(J-1),lower.tail=FALSE)
plot(J,1-pf(f,I-1,I*(J-1),J*4),type="l",ylab=1-expression(beta))
abline(h=0.95)