How can I represent the difference between two values relative to the magnitude of the values?

Question

I have a series of values: here's a sample:

Val1(s)     Val2(s)     abs(difference)(s) 
0.0347251   0.0405869   0.0058618
0.0705912   0.0772789   0.0066877
0.1117939   0.096079    0.0157149
0.156394    0.1282144   0.0281796

Rather than showing the difference as a value, I would like to represent it relative to the magnitudes of val1 and val2. My first thought is a ratio but that doesn't make sense, because it could be diff/val1 or diff/val2 or diff/avg(val1,val2) but none of these seem like an appropriate way to go about this.

How should I represent the difference so that it is easy to see the magnitude of the difference relative to the values?

Answer 1

There are two approaches you could take, depending on what you mean by "relative to their values."

If you mean that you want the values to be put on comparable scales, you could divide each one by its standard deviation and take differences afterwards.

If you mean that you want to know how big the difference is, relative to some combined scale for both variables, you could take differences first and then scale the differences by the pooled standard deviation (the square root of the pooled variance) of the two variables.