Sorry, it has been a few years since I have done any sort of in depth statistical math and I am working on a problem and none of the solutions I have come up with seem to be very elegant or appear to be the right approach.
I have some performance data that I want to correlate to cost, to do some analysis with it. My issue is that the performance data can in fact be negative in some cases. If I want to do a real simple calculation of say cost over performance to try to do some analysis, I can not, as the few objects with negative performance do not work.
So my question is, is there a standard way that statisticians scale the performance data in a case like this or in a sense normalize the data? The current performance data runs from -70 to 70. It doesn't seem like shifting the data to run from say 0 to 140 is the proper approach.
I hope this makes sense.
Basically in my model, it is optimal to have lower costs and higher performance, and thus a lower ratio is best. I am trying to show each object spends per unit of performance. In this case negative costs make no sense as each object does in fact spend money, it just is not a very effective use of their money.
For example, if object one spent 7,500,000 and had performance of 61, it gives them a ratio of 122,604. Object two spent 9,090,000 and had a performance of 29.9 they have a ratio of 304,013. If Object three spent 14,297,900 and had a performance of -2.5, then their ratio is -5,7169,160.
In my mind, object three with higher costs and lower performance should have a ratio much higher than objects one and two. With a negative performance cost ratio, I can't really compare it in the same context as the other two.
If you are still unhappy you will need to go and examine what you are measuring as performance since no mathematical trick will justify manipulation without first understanding (anything else is just pseudoscience)