Hi All

This is a general stats problem that I am dealing with using R, so any help is greater appreciated.

I have two lognormal distributions with means M1 and M2.

If we have:

H0: log(M1/M2)=0

H1: log(M1/M2) !=0 equivalent to log(M1/M2)=log(1+P) where P<0 or P>0.

If we calculate the power for a value of P=0.1 or P=-0.1 (i.e. a 10% difference) and say assume SE{log(M1/M2)}=0.05, and confidence level= 100(1-alpha), alpha=0.05, then how is the power function calculated?

As far as I can see we can calculate the power in the two ways given below and if there is no assumed direction to difference between M1 and M2 are not both calculations valid?

> # P=-0.1
> qn <- qnorm(p=0.05, mean=0, sd=0.05, lower.tail=T)
> Power.1 <- pnorm(q=qn, mean=log(0.9), sd=0.05, lower.tail=T)
> # P=0.1
> qn <- qnorm(p=0.95, mean=0, sd=0.05, lower.tail=T)
> Power.2 <- pnorm(q=qn, mean=log(1.1), sd=0.05, lower.tail=F)
>
> print(c(Power.1,Power.2))
[1] 0.6780872 0.6030887
>
 So which value should I use? Or would the average of the two values be appropriate to use? Or is there a fault in my logic? After a quick lit search I contacted a colleague who has written two stats text books and taught at University level for many years and he has not come across this problem and suggested averaging the values. This post is to ask if anyone has come across this pretty basic problem and has a suggested approach.

thanks

Steve



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