Check my stats? How do I make a ratio that accommodates variability?

[Danny76]

Hi, I'm a newbie which a problem

I have two sets of data: A and B. Each is represented by a mean and a standard deviation. I want to generate a ratio: A/B and be able to accommodate the variability from each group in the ratio. What formula should I use?

My guess is that if C=A/B then:

(dC/C)2=(dA/A)2+(dB/B)2

where dC, dA and dB are the St. Dev, and my little 2 means square

I'd be really grateful for any help any one can give!

 

[JohnM]

I'm not aware of any measures that take into account both location and variability.

What's the application?

 

[quark]

Danny,

Welcome to the forum. Ratio of two independent variables is hard to work with. For example the ratio of two N(0,1) independent random variables is a Cauchy Distribtuion with undefined mean and variance. I'll need to search the net and go to my books to comment further...

 

[JohnM]

You can determine a simple ratio by estimating R = x/y, with the estimate of SEr having equation:

= R/sqrt(n) * [ (Vx)^2 + (Vy)^2 ]

where V is the coefficient of variation (s/x)

but where I'm getting hung up is developing a measure that accounts for both the mean and variation in one index.

In the DOE (Design of Experiments) world and industrial quality control, Taguchi Methods, in vogue in the early 1990s and not very popular now, there was a "signal-to-noise ratio" that combined both the mean and variation of a parameter, but these never really caught on....