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I want to compare two qualities, one considered positive which was measured on a scale of 1 - 45, and one considered negative which was measured on a scale of 1 - 30. Ideally the final index should be on a scale of -1 to +1. i.e. a value of -1 means the negative quality was at its maximum value and the positive quality was at 0 and vice versa for +1. A value of 0 would mean they were both relatively equal. How do I achieve this?

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    $\begingroup$ An article of faith here is that it is both desirable and possible to collapse two measures to one with at best only trivial loss of information. Perhaps it is for your data, but it would help to see the relationship between the variables as shown in a scatter plot. If I were obliged somehow to do this (e.g. at gunpoint) I would do what @Underminer suggests, but in principle the answer that this might be a bad idea should be considered. $\endgroup$
    – Nick Cox
    Nov 27, 2017 at 18:34

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There are many ways to do this, but a logical index could be created by taking a scaled version of the good quality and subtracting a scaled version of the bad quality.

For example, let's call the Good quality V1 and the Bad quality V2. Then we could scale V1 by dividing it by 45 and scale V2 by dividing it by 30. Then we just subtract the scaled version of V2 from the scaled version of V1. This gives a maximum index of 1 and a minimum index of -1.

See example results below given a variety of Good and Bad quality scores:

V1 (Good)   V1 Scaled   V2 (Bad)    V2 Scaled       Combined Index
45          1 (45/45=1) 30          -1 (30/-30=-1)  0 (1-1=0)
0           0           0           0               0
0           0           30          -1              -1
45          1           0           0               1
20          0.4         15          -0.5            -0.1
35          0.8         5           -0.2            0.6
5           0.1         20          -0.7            -0.6
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    $\begingroup$ Great thanks. Yes I understand I am losing information in my data by condensing it like this but it can be a useful metric for looking at net positives. $\endgroup$ Nov 28, 2017 at 10:42

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