#*********2-arm trial fixed-sample design in standardized scale

#*** given variance and alternative, calculate sample size (with 97.5% power):
dsgn <- seqDesign(prob.model="proportions",null.hypothesis=c(0.3,0.3),alt.hypothesis=c(0.2,0.3),test.type="less")

#*** Use the update() command to rescale the above design to get BinomFixed from the lecture notes:
binomFixed <- update(dsgn, alt.hypothesis=c(0.25,0.3),power=0.8)

#*** Use the update() command to rescale the above design to get BinomFixed.1700 from the lecture notes:
binomFixed.1700 <- update(binomFixed,sample.size=1700,power="calculate")

#*** Use the update() to find the alternative with 97.5% power for the BinomFixed.1700 design:

dsgn2 <- update(binomFixed.1700,alt.hypothesis="calculate",power=0.975)

#*** Explore the difference between binomFixed.1700 and dsgn2:

dsgn2a <- update(dsgn2,variance=0.3*0.7)
dsgn2b <- update(dsgn2,variance=0.275*(1-0.275))
dsgn2c <- update(dsgn2,variance=0.25*0.75)
dsgn2d <- update(dsgn2,variance=(0.25*0.75 + 0.3*0.7)/2)