Both Root Mean Square and Average absolute deviation seem like the measures of the magnitude of variability (especially when the variates are both +ve and -ve). What are the rules of thumb to choose one of them over the other?
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$\begingroup$ @mbq, Thanks for the edits. They are much appreciated. As you can probably see, I am new to statistics. $\endgroup$– Mohit RankaCommented Feb 21, 2011 at 12:01
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1 Answer
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In theory, this should be determined by how important different sized errors are to you, or in other words, your loss function.
In the real world, people put ease of use first. So RMS deviations (or the related variances) are easier to combine, and easier to calculate in a single pass, while average absolute deviations are more robust to outliers and exist for more distributions. Basic linear regression and many of its offshoots are based on minimsing RMS errors.
Another point is that the mean will minimise RMS deviations while the median will minimise absolute deviations, and you may prefer one of these.
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2$\begingroup$ +1 Nice summary. I like that you point out the role of the loss function first. $\endgroup$– whuber ♦Commented Feb 21, 2011 at 14:21