# SET THE SIMULATION SAMPLE SIZE
m     <- 10000000
# GENERATE m NORMALS WITH MEAN 0.6 AND STANDARD DEVIATION sqrt(0.6*(1-0.6)/96)
p.hat <- rnorm(m,0.6,sqrt(0.6*(1-0.6)/96))
# CREATE A CONFIDENCE INTERVAL MATRIX THAT IS m * 2 BIG
p.ci  <- cbind(p.hat - 1.96*0.5/sqrt(96),p.hat + 1.96*0.5/sqrt(96))
# GET THE PROPORTION OF LOWER BOUNDS GREATER THAN ONE-HALF
sum(p.ci[,1] > 0.5)/m
[1] 0.4997

n     <- 196
m     <- 10000000 
p.hat <- rnorm(m,0.6,sqrt(0.6*0.4/n))
p.ci  <- cbind(p.hat - 1.96*0.5/sqrt(n),p.hat + 1.96*0.5/sqrt(n))
sum(p.ci[,1] > 0.5)/m
[1] 0.80417

( delta <- 354*1.20 - 354 )    [1] 70.8
( sigma <- sqrt(18357*1.5) )   [1] 165.94 #1.5 MULTIPLIER TO BE MORE CONSERVATIVE
( n <- (sigma/(delta/2.8))^2 ) [1] 43.067

p <- c(0.25,0.20,0.10,0.45);  q <- c(0.20,0.15,0.15,0.50)
n.wilcox.ord(power = 0.8, alpha = 0.05, t = 0.45, p, q)
[1] 1446
$m
[1] 795
$n
[1] 651

( obs <- data.frame("freq"=c(8,6,6,10,8,23,21,59),
             "PtDry.12mos"=gl(n=2,k=4,labels=c("no","yes")),
             "Status"=c("obese.inactive","obese.active",
                        "nonobese.inactive","nonobese.active")) )

  freq PtDry.12mos            Status
1    8          no    obese.inactive
2    6          no      obese.active
3    6          no nonobese.inactive
4   10          no   nonobese.active
5    8         yes    obese.inactive
6   23         yes      obese.active
7   21         yes nonobese.inactive
8   59         yes   nonobese.active

xtabs(freq ~ PtDry.12mos + Status, data=obs)

            Status
PtDry.12mos nonobese.active nonobese.inactive obese.active obese.inactive
        no               10                 6            6              8
        yes              59                21           23              8

summary(xtabs(freq ~ PtDry.12mos + Status, data=obs))

Call: xtabs(formula = freq ~ PtDry.12mos + Status, data = obs)
Number of cases in table: 141 
Number of factors: 2 
Test for independence of all factors:
	Chisq = 9.8, df = 3, p-value = 0.020

p.1 <- 6/(6+23);   p.2 <- 8/(8+8)    
( sigma.sq <- (6+23)*(6/(6+23))*(23/(6+23)) )
    [1] 4.7586
( log.HR <- log(log(p.1)/log(p.2)) )
    [1] 0.82111
( n.1 <- (qnorm(0.8)-qnorm(0.025))^2 * sigma.sq/(log.HR^2) )
    [1] 55.397
( n.needed.obese.nonobese <- n.1*(1+96/45) )
    [1] 173.58

s.2 <- 1; d <- 0.3; r <- 1

# NORMAL APPROXIMATION
sample.size <- function(r,alpha,beta,d,S2) 
	((r+1)*(qnorm(beta)+qnorm(1-alpha/2))^2*S2)/(r*d^2)+qnorm(1-alpha/2)
( n <- sample.size(r,0.05,0.8,d,s.2) )
[1] 176.38

power.size <- function(r,alpha,beta,d,S2,N)  {
	DF <- N*(r+1)-2
	NCP <- sqrt((r*N*d^2)/((r+1)*s.2))
	TVAL <- qt(1-alpha/2,DF)
	1-pt(q=TVAL, df=DF, ncp=NCP)
}
power.size(r,0.05,0.8,d,s.2,n)
[1] 0.80138

s.2 <- 3; d <- 0.1; r <- 1.5
( n <- sample.size(r,0.05,0.8,d,s.2) )
[1] 3926.4
power.size(r,0.05,0.8,d,s.2,n)
[1] 0.80012