2 ms·
The main reason to use standard deviation instead of mean absolute deviation is that sqrt((f(x)-g(x))^2) is differentiable, while |f(x)-g(x)| is not. T
by amalcon 16y ago
The main reason to use standard deviation instead of mean absolute deviation is that
sqrt((f(x)-g(x))^2)
is differentiable, while
|f(x)-g(x)|
is not. Though exaggerating the larger differences is often a desirable property, the ability to do calculus is nearly always a desirable property.
- mturmon 16y agoYou point out a real problem with the article. The given rationale for (.)^2 vs. |.| is just wacko ("there is obviously more variation in the second data set than the first"). The reason it's mistaken is, there are other examples, typically with just one or a handful of outliers, in which the SD is "obviously" too high compared to mean absolute deviation. Futhermore, these type of examples are common in practice, so the SD is problematic to use if you have outliers. Often, in robust statistics, the Median Absolute Deviation (which is conventionally labeled MAD, http://en.wikipedia.org/wiki/Median_absolute_deviation http://en.wikipedia.org/wiki/Median_absolute_deviation) is used. As an estimate of scale, it's much more robust to outliers. But of course, you can't differentiate it!