[From Rick Marken (2006.12.18.0900)]

What am I thinking?!?! Martin's formula is correct! I said:

Rick Marken (2006.12.18.0850)]

Yes. But I think Martin is talking about a variance ratio, not an amplitude ratio. In which case his formula looks pretty good. Well, actually, I think it probably should just be just 1/CR^2. In that case, when there is no control, CR = 1 (the variance of d = the variance of p) and the minimum absolute correlation between d and o is 1.0. When the control is nearly perfect, the variance in d is >> than the variance in p, CR ~infinity and the minimum correlation between d and o is ~ 0.

But, of course, the correlation between d and o should be 0.0 when there is no control, and ~1.0 when control is nearly perfect.

So Martin's formula is correct: the minimum correlation between d and o is 1-1/CD^2

assuming CR is var(d)/var(p)

Best

Rick