I'm trying to detect a condition between two variables, but each variable is using a different unit of measurement, and there is no standard of conversion (such as 12 inches = 1 foot).
My 1st variable will always be a positive integer, for example, a measurement of the input of force, sample data = 10,000
My 2nd variable seems to be a derivative of the 1st input, because it is "created" as a result of the input of force. Sample data = 3.5
There appears to be no linear relation between the two vars that could be used for conversion to a common base unit of measurement.
I have an expectation, based upon observable historical data, that var2 (derivative) would be in proportion to var1 (input), and I want to write a formula that calculates this proportion, and be able to detect when it is not in correlation (i.e. the output is not proportional to the input).
I am only trying to work with 1 instance of var1 and var2, but maybe this is impossible?
Maybe I need to try to establish a correlation of proportion between the 2 variables from recent historical data points, (i.e. a mean of var1 typically produces a mean ouput of var2, and the current var2 is 50% deviant from the mean, even though var1 is within the mean), before I can declare a result as "not in expected proportion"?
I don't know if I am using the proper vocabulary to describe the concept, which makes it difficult to find a solution, since I don't know what it is named.
Any suggestions are appreciated, thanks.
Aha, while typing tags for this question, some interesting terms appeared. Is the phrase "expected value" a good description of what I am trying to accomplish?
Update: Here is a plot illustrating the 2 different data sets I have.
The values of each data set are different, so I can't directly compare is var1 > var2, etc. I can visually compare them, and detect when a white bar has a similar value to the previous white bar, BUT the orange square has a lower value than it's previous square.
But I want to do this using math, and not sure what the concept is named.
Also I don't always want to compare the latest value with the previous value, because those might differ wildly. I want to compare the current value of the white bar with the value of the current orange square, and detect when it's value is not as expected. Does that make sense? Or do I need to include historical references to previous data points to establish a pattern or relationship between the two variables, in order to detect when that relationship becomes non-proportional, or non-correlated, or non-expected value?
Let the two variables be $x,y$. There is no problem if the units are different. If you think they are proportional, the relationship would be $y=kx$ and $k$ can have units to make the units of the equation match. You could also have a relationship of the form $y=k\frac {dx}{dt}$, where again $k$ can have the necessary units to achieve balance. If you have a number of data points you can do a least squares fit to get a value of $k$ under each model.