I would like to gain a conceptual understanding of Root Mean Squared Error (RMSE) and Mean Bias Deviation (MBD). Having calculated these measures for my own comparisons of data, I've often been perplexed to find that the RMSE is high (for example, 100 kg), whereas the MBD is low (for example, less than 1%).
More specifically, I am looking for a reference (not online) that lists and discusses the mathematics of these measures. What is the normally accepted way to calculate these two measures, and how should I report them in a journal article paper?
It would be really helpful in the context of this post to have a "toy" dataset that can be used to describe the calculation of these two measures.
For example, suppose that I am to find the mass (in kg) of 200 widgets produced by an assembly line. I also have a mathematical model that will attempt to predict the mass of these widgets. The model doesn't have to be empirical, and it can be physically-based. I compute the RMSE and the MBD between the actual measurements and the model, finding that the RMSE is 100 kg and the MBD is 1%. What does this mean conceptually, and how would I interpret this result?
Now suppose that I find from the outcome of this experiment that the RMSE is 10 kg, and the MBD is 80%. What does this mean, and what can I say about this experiment?
What is the meaning of these measures, and what do the two of them (taken together) imply? What additional information does the MBD give when considered with the RMSE?