Question
While working on an analysis, I computed some ratios. Now I wish to visualize them. Should I use logarithmic scale or arithmetic scale? For example, should I use option A or option B?
(Arithmetic Scale here means plotting ratios as is)
Answer
In general, choosing logarithmic scale makes sense for plotting ratios, because ratios behave differently when reflecting increases than decreases. The ratio \(200/100\) is \(200%\) above baseline, but \(100/200\) is only \(50%\) below, despite being a similar magnitude change. On arithmetic scale (as in Option B), the ratios which are less than 1, get squished into a finite region between 0 to 1, whereas ratios greater than 1 are stretched across the infinite region above 1.
But on logarithmic scale, the unit ratios divide the plot symmetrically. For example, \(log_2(2/1)=1\) and \(log_2(1/2)=-1\), which have a similar magnitude change, are equally displaced with respect to unit ratio i.e \(log_2(2/2)=0\). This symmetry addresses the visual imbalance of ratios on arithmetic scale.
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