Residuals – What Does the Y-Axis in Frequency vs Residuals Graph Mean

frequencyresiduals

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(Asner et al 2013)

This is on a paper I'm reading, and I get the residuals part, but I'm not so sure on what the frequency means. Can someone please explain these graphs?

Please let me know if you need more information.

Best Answer

The units on the vertical axes are relative frequencies per unit of $x.$ That is, these plots are histograms. They represent relative frequency in terms of areas under the curve rather than by heights of the curve.

The way you can tell is that the areas under all the graphs are unity. A quick visual check is to approximate one of these graphs as a triangle. For instance, the red Barro Colorado graph has a base of approximately $40 - (-75)=115$ and a height of $0.015,$ so its area must be close to $(1/2)\times 115\times 0.015 \approx 0.86,$ which is practically $1$ for such a rough estimate. The other graphs similarly check out.

According to the units calculus, then, the units on the vertical axes must be

(relative frequency) / (Mg C/Ha) = Ha / (Mg C)

because relative frequencies are unitless.

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