I have three variables I am comparing: two have scores which can range from 0 to 3 and one has scores which can range from 6 to 30. I want to present these variables together to allow comparison between them, for example on a line graph, but I can't find a good way to rescale them to be on the same scale. I want to compare mean levels in different groups over time so Z scores don't seem like a good solution here. I am hoping there is a simple mathematical solution I am missing.
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1$\begingroup$ There is no obvious need to rescale at all. On this evidence, variables with range 0 to 3 can go in one graph and that with range 6 to 30 can go in another graph presented. Then present the two graphs together. $\endgroup$– Nick CoxCommented Sep 21, 2023 at 13:48
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There are different solutions depending on what you want to make equal and what you know about the variables.
If you want the ranges to be equal, one way is multiply by 8 (to get 0 to 24) and add 6 (to get 6 to 30). Or, if the 0 to 3 is an integer score (which seems likely) you could make a mapping based on substantive knowledge e.g 0 = 6, 1 = XXX, 2 = XXX, 3 = XXX.
If you want the means to be equal, then you can just find the mean of each variable and multiply to make them equal.
If you want percentiles to be equal, that can get trickier.
But if you want "meaning" to be equal (for some definition of meaning) then that gets into a subject called test equating, which is complicated. You almost certainly do not have the data for that.
answered Sep 21, 2023 at 10:41