a <- 8
b <- 12
c <- 48
d <- 62
m <- a + b
n <- c + d
x <- matrix(c(a,b,c,d),nr=2)
t <- as.table(x)
rownames(t) <- c("Alive","Dead")
colnames(t) <- c("Standard","Penicillin")
print(t)
lambda <- a*d/(b*c)
better <- (a-0.5)*(d-0.5)/((b-0.5)*(c-0.5))
cat("\nCross ratio",lambda,"with log",log(lambda),"\n")
cat("Better approx",better,"with log",log(better),"\n")
varlog <- 1/a + 1/b + 1/c + 1/d
postpr <- 1 - pnorm(0,log(better),sqrt(varlog))
cat("Posterior prob of a difference",postpr,"\n")
u <- asin(sqrt(a/m))
v <- asin(sqrt(c/n))
diff <- u - v
vardiff <- 1/(4*m) + 1/(4*n)
postprdiff <- 1 - pnorm(0,diff,sqrt(vardiff))
cat("Arc sines",u,"and",v,"with variance of diff",vardiff,"\n")
cat("giving posterior prob of a difference",postprdiff,"\n")