Ratio vs difference when testing for equality?

Jul 2016
4
0
Norway
When performing a test to see whether an estimator A for two populations is the same, is it more natural to use the difference

A1 – A2 = 0

or the ratio

A1 / A2 = 1

(or other)?

Is there a universal preference or is it situational?
 

romsek

MHF Helper
Nov 2013
6,666
3,005
California
comparing means I'd use the expected value of the difference.

comparing standard deviations (or higher moments) I'd use the expected value of the ratio.
 
Jul 2016
4
0
Norway
So would the logic "use difference for expectancy to account for potential expectancy = 0; use ratio everywhere else because it's generally easier."

Be correct?