I want to create a simple representation of "rate of change" for a number of different metrics, which aren't really comparable with each other. To illustrate my problem, let's say I have the following metrics: temperature in Celsius, temperature in Fahrenheit, and air pressure in mbar.
Each metric supplies a continuous stream of data points.
For each of these points, I want to illustrate the "trend", i.e., if the metric is going up or down, and ideally by how much. However, for each such calculation I only have access to two values - the most recent value (let's call it x0) and the previous value (let's call it x1). I know the time in between these two data points.
So first I thought I'd just illustrate the rate of change by the time derivative, so I did (x1 - x0) / (t1 - t0). This of course gives an indication of how this metric has changed (and possibly where it's heading).
However, this value for rate of change isn't really comparable between different metrics, because e.g. a change of 10 for Celsius temperature represents almost twice as much as a change of 10 for Fahrenheit temperature, and isn't at all comparable to a change of 10 for air pressure in mbar.
So then I thought I'd use the fraction of change, so I used (x1 - x0) / x0, which tells you by how much the value changed relative to its previous value. But there are at least two problems here:
- This ignores how quickly the change was made - were the two values 1 minute apart or 1 hour apart?
- This is also skewed as a comparison between different metrics: a change in Celsius temperature from 10 to 20°C is a 100% increase, but represents the same physical temperature change of 50 to 68°F, which is just 36%. This also makes the rate of change values impossible to compare.
This also illustrates that saying "it's twice as warm as yesterday" doesn't really make sense in either Celsius or Fahrenheit.
Even using a combination of these to use "percentage of change per time unit" doesn't fix problem 2.
So I guess I need to normalize my rate of change value somehow. For temperature, perhaps actually using the difference in K is the only thing that makes "physical" sense (as it's proportional to the kinetic energy). But when comparing completely different metrics such as temperature vs air pressure, I just don't have any clue.
Am I making this too complicated or is it just a bad idea to even try to have a comparable rate of change more refined than having three values "going up", "going down" and "the same"? Is it feasible to come up with something that makes it possible to illustrate that a temperature is going "rapidly up" while air pressure has just gone "slightly up" in the last hour without having custom formulas for each metric (such as percentage of change measured Kelvin per time unit for temperature)?