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I have a single parameter measured by two methods: A and B.

I need to see how these two methods compare against each other, so I thought of a Tukey mean-difference (TMD) plot. The issue is that the measured parameter spans a wide range of values, so the standard TMD plot shows very small differences and very large ones.

I thought that one way to bring this to the same scale would be to plot the relative differences (A-B)/(A+B) instead of the differences (A-B) as done in the standard TMD plot.

This is what I get:

enter image description here

There is a systematic trend where differences increase as do the average values, shown in the left ("standard") plot. But the right plot ("relative difference") would appear to imply that the mismatch between both methods is actually worse for smaller values of the measured parameter.

The question: is there some caveat in the "relative difference" plot I might be missing? Should I just stick to the standard TMD?

This is what I found online about this plot:

A relative difference plot (Pollock et al., 1993) shows the relative differences on the vertical axis, against the best estimate of the true value on the horizontal axis. It is useful when the methods show variability related to increasing magnitude, where the points on a difference plot form a band starting narrow and becoming wider as X increases.

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  • $\begingroup$ It is very difficult to assess such plots when the x variable is so skewed as the spread of the points will be greater where there are more points. Have you thought of working on the log scale? $\endgroup$ – mdewey Apr 29 '16 at 15:47
  • $\begingroup$ I thought of that, and this is what it looks like pasteboard.co/yikmhdx.png At this point I believe the relative differences plot gives more information. $\endgroup$ – Gabriel Apr 29 '16 at 16:40

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