Imagine I have a model that predicts a person’s height from a photo (just an example). Each individual has their ground-truth height (H), and the model outputs a predicted height (h). The model error is then error = h - H, and can be either positive or negative. One possible measure of model performance would be the standard deviation of these errors. Another possible measure would be the mean absolute deviation. However I’ve also seen people compute the standard deviation of the absolute errors, and this feels wrong to me. The distribution of absolute errors is not centred on zero, and doesn’t look like a normal distribution at all (it’s more like a half-normal distribution).
Am I correct in thinking that we shouldn’t compute the standard deviation of absolute values?