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This is what Taleb is saying. MAD is more intuitive to humans, and we can see this in particular because experienced statisticians, when asked to describe what
by reso 10y ago
This is what Taleb is saying. MAD is more intuitive to humans, and we can see this in particular because experienced statisticians, when asked to describe what standard deviation "means", actually describe MAD.
- kevhito 10y agoI don't understand. The usual explanation I hear (and that I think of) when explaining what a STD of x is, fall somewhere along the lines of "most (about 2/3rds) of the data will be within +/- x of the average". Is this wrong? If not, can you give me an example of the typical description people give for STD that actually describes MAD?
- closed 10y agoYes, that is wrong. It sounds like you might be thinking about the standard deviation of normally distributed data. In this case, you can say something like, "the probability an observation will be within about [mean-2sd, mean+2sd] is 95%". But that's assuming the distribution is normal. In other cases, this doesn't hold, but there are more general statements, like Chebyshev's inequality. Chebyshev's inequality: https://en.wikipedia.org/wiki/Chebyshev%27s_inequality https://en.wikipedia.org/wiki/Chebyshev%27s_inequality EDIT: I have no idea when people would describe SD as MAD, but wouldn't be too surprised, since people first coming into statistics often seem to have trouble conceptualizing how a squared difference could be viewed. It would be surprising if a trained statistician mixed the two up, because SD and MAD arise from something they should be familiar with--Lebesgue spaces.
- juped 10y agoI've got a very non-statistics math background, but what you say suggests that there would be a nice way to visualize standard deviations two-dimensionally (since they arise from an L_2 norm), and that it's the one-dimensional "bell curve cross-section width" pictures that confuse people.