dfM1<-10 # degrees of freedom of M1

dfM2<-12 # degrees of freedom of M2

delta1<-dfM2*.033ˆ2 # define delta* in the alternative hypothesis

delta2<-dfM2*.064ˆ2 # define delta** in the alternative hypothesis

alpha<-.05

for (n in 1:100000) {

cv<-qchisq(1-alpha,df=dfM2-dfM1,ncp=n*delta1) # Critical value under H0

power<-1-pchisq(cv,df=dfM2-dfM1,ncp=n*delta2)

if (power>=.80) break # reach the desirable power

}

N<-n+1

print(N)