If I have the below data and my difference measure is "actual/extrapolated-1" for the same observation.

What does the RMSD tell me that the mean difference doesn't? If I understand the 'mean difference' is a summary measure of systematic bias, so then, is it that the RMSD is a summary measure of the of the spread of this bias acros all five observations?

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    $\begingroup$ Note that your use of "actual/extrapolated-1" isn't the standard measure of residuals in linear regression so your RMSD wouldn't be what would normally be reported. Also note that the mean difference can balance off negative from positive differences, which won't happen with RMSD. Did you perhaps mean to use the mean absolute difference instead of mean difference? $\endgroup$
    – EdM
    Oct 23 '19 at 20:45
  • $\begingroup$ I think you made a mistake and want to use mean squared or mean absolute error, but the reason not to use the pure mean is because you could have half of your observations miss high by a trillion and the other half miss low by a trillion. That performance is not ideal, yet the average error is zero. $\endgroup$
    – Dave
    Oct 23 '19 at 20:58

This really comes down to an issue of "dimensionality". Imagine that each of the five "difference" values is a vector (i.e., a line pointing positively or negatively with length equal to the difference value). Geometrically, the mean (of) difference value is obtained by putting these vectors end-to-end in a single dimension, to get the aggregate difference, and then dividing by five. Contrarily, the RMSE is a Euclidean distance obtained by putting these vectors end-to-end in five different dimensions.

In terms of which measure is more suitable, this depends on whether the five difference values are measuring the same characteristic, or five different characteristics. If they are measuring the same characteristic then it is probably sensible that they be aggregated over one dimension. If they are measuring different things then it is more sensible to aggregate them over different dimensions using the RMSE.


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