Nassim Taleb: We should retire the notion of standard deviation

http://www.edge.org/response-detail/25401

by pyduan • 13 years ago

248 244 13 years ago

truthteller3• 13 years ago

he's really lost the plot. :(

zeidrich• 13 years ago

It's not that we should retire the notion of standard deviation. It's more that we should understand the tools that we are using and use the appropriate tool for the job.

dschiptsov• 13 years ago

Why, it is pretty good in describing probability distributions. What we should retire are idiots, who assume that it predicts an outcome of the next event.

regularfry2• 13 years ago

Everyone is an idiot some of the time.

valtron• 13 years ago

He makes a good point about infinite MAD vs. STD.

scythe• 13 years ago

While the mean deviation as presented is slightly nicer than sigma for intuitive purposes, it isn't as appropriate (iirc) for statistical tests on normal distributions and t-distributions.

More importantly, it doesn't fix the real problem, which is that the mean and standard deviation don't tell you everything you need to know about a data set, but often people like to pretend they do. It's not rare to read a paper in the soft sciences which might have been improved if the authors had reported the skewness, kurtosis, or similar data which could shed light on the phenomenon they're investigating. These latter statistics can reveal, for instance, a bimodal distribution, which could indicate a heterogeneous population of responders and non-responders to a drug, and that's just one example.

I'm not a statistician, so some of this might be a bit off.

drblast2• 13 years ago

Whenever you try to describe a large data set with a single number, you lose a lot of information, like you said. Having more measurements helps, but I think the larger point is that we don't have to do this anymore, we could publish the entire data set instead.

Without computers, this would be a waste of paper, but transmitting the data electronically is cheap.

So why argue over the measurements? Publish the data and my software can give me any measurement I'm interested in.

cwyers5• 13 years ago

"In fact, whenever people make decisions after being supplied with the standard deviation number, they act as if it were the expected mean deviation."

Boy, is that statement useless without any kind of context, example or citation.

icebraining• 13 years ago

The next two paragraphs have examples with some context.

cwyers5• 13 years ago

Like this?

"But it is not just journalists who fall for the mistake: I recall seeing official documents from the department of commerce and the Federal Reserve partaking of the conflation, even regulators in statements on market volatility. What is worse, Goldstein and I found that a high number of data scientists (many with PhDs) also get confused in real life."

It doesn't tell us what happened, it just asserts that it did in certain contexts. It doesn't cite the paper he presumably wrote with Goldstein (which Goldstein?) about it. I feel like I'm getting a summary of an abstract with all the citations missing.

cgrubb• 13 years ago

Wherein the author makes the suspect claim that newspapers discussing the stock market always define standard deviation using the definition for mean deviation.

SilasX• 13 years ago

- Strips a statement of context, examples, and citations.

- Claims it is useless therewithout.

cwyers5• 13 years ago

No. There are absolutely no citations or specific examples. There is the claim that "every time a newspaper has attempted to clarify the concept of market 'volatility', it defined it verbally as mean deviation yet produced the numerical measure of the (higher) standard deviation," which is not an example, it's a fact claim without a shred of evidence behind it (and as it is an absolute claim, you only need to find one example of a journalistic article on the stock market that properly defines standard deviation to prove it wrong).

ClementM• 13 years ago

This article is based on paper Taleb published in 2007. If you want to test yourself, submit yourself to experiment in page 3: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=970480

drblast2• 13 years ago

Thanks! Always nice to read the full research.

CamperBob2• 13 years ago

   A stock (or a fund) has an average return of 0%. It moves 
   on average 1% a day in absolute value; the average up move 
   is 1% and the average down move is 1%.

How does that yield an average return of 0%?

MaysonL3• 13 years ago

It goes up a little more often than it goes down?

baking3• 13 years ago

The usual way to do this is to take the natural log, so an up 1% day followed by a down 1% day (or vice versa) will always net out to a 0% change.

baking3• 13 years ago

Yes, start by writing a confusing question. One that starts talking about average up moves and average down moves and then switches to asking about the standard deviation of moves. Then publish a paper showing that people were confused by your question. Now you have "research" to back up your claim that everyone is confused by "mean deviation" and "standard deviation".

n00b101• 13 years ago

Taleb has a good point about people mistakenly interpreting standard deviation (sigma) as Mean Absolute Deviation (MAD). I like that he gives some conversions (sigma ~= 1.25 * MAD, for Normal distribution).

I think it's rather silly to talk about "retiring" standard deviation, but we can't blame Taleb - the publication itself posed the question "2014: What Scientific Idea is Ready for Retirement?" to various scientific personalities.

What Taleb failed to mention is that, once properly understood, standard deviation has distribution interpretations that can be much more useful than MAD. For example, if the data is approximately normally distributed, then there is approximately a 99.99% probability that the next data observation will be <= 4 * sigma.

Not everything is approximately normally distributed, but a lot of phenomena ARE normally distributed. It's a well known fact that the phenomena which Taleb is most interested in (namely, financial return time-series) are not normally distributed. But I would like to know how Taleb proposes to "retire" volatility (sigma) from financial theory and replace it with MAD? Standard deviation is so central in finance that even the prices of some financial instruments (options) are quoted in terms of standard deviation (e.g. "That put option is currently selling at 30% vol"). How do we rewrite Black-Scholes option pricing theory and Markowitz portfolio theory in terms of MAD and remove all the sigmas everywhere? Surely Taleb has already written that paper for us so that we can retire standard deviation?

regularfry2• 13 years ago

I think his point is that Black-Scholes et al are holed beneath the waterline precisely because they involve standard deviations. In his world, you're better off being unable to price an option than you would be with Black-Scholes. Your example of "That put option is currently selling at 30% vol" is actually an example of why the system is so completely broken: if volatility as standard deviation was valid, all options against the same underlying instrument would have the same implied volatility. The volatility smile shouldn't exist.

This wouldn't matter if the down-side wasn't so crippling.

I don't think Taleb has to be the one to propose a replacement for portfolio theory, and I think criticism of him for not doing so is pointless. You don't need to have a spare tire handy to point out that your neighbour's car has a flat, and you don't have to run an airline to tell people not to get on a plane with the engines visibly on fire.

tdees40• 13 years ago

I've never understood this part of Taleb's argument. Of course, constant vol Black-Scholes does not hold. BUT NO ONE USES THIS. Everyone in the financial industry is well aware of the volatility skew, and spends lots of time adjusting for it.

B-S vols are putting the "wrong number into the wrong equation to get the right price" as Rebonnato famously said.

repsilat• 13 years ago

For example, if the data is approximately normally distributed, then there is approximately a 99.99% probability that the next data observation will be <= 4 * sigma.

Could you sketch out why similar statements couldn't be made about MAD? My (possibly flawed) intuition is that the expected proportion of observations within n\*MAD should be similarly independent of the parameters of the normal distribution.

bluecalm12• 13 years ago

So first about the article:

>The notion of standard deviation has confused hordes of scientists

What an assertion! It also proved to be very useful for hordes of scientists... what about some examples of confused scientists ?

>There is no scientific reason to use it in statistical investigations in the age of the computer

As someone who uses it daily I am eagerly awaiting his argument.

>Say someone just asked you to measure the "average daily variations" for the temperature of your town (or for the stock price of a company, or the blood pressure of your uncle) over the past five days. The five changes are: (-23, 7, -3, 20, -1). How do you do it?

Ok... if I am to calculate the average I am calculating the average if I need to know standard deviation I calculate standard deviation...

> It corresponds to "real life" much better than the first—and to reality.

What the flying fuck. What "real life" ? Standard deviation tells you how volatile measurements are not what mean deviation is. Those are both very real life things just not the same thing.

>It is all due to a historical accident: in 1893, the great Karl Pearson introduced the term "standard deviation" for what had been known as "root mean square error". The confusion started then: people thought it meant mean deviation.

I don't know how one can read it and not think: "is this guy high or just stupid?".

>. The confusion started then: people thought it meant mean deviation.

I am yet to see anybody who thinks that standard deviation is mean deviation. It's Taleb though. Baseless assertions insulting groups of people are his craft.

>What is worse, Goldstein and I found that a high number of data scientists (many with PhDs) also get confused in real life.

One example please ? I can give hundreds when std dev is useful and mean deviation isn't. Anything when you decide what % of yoru bankroll to bet on perceived edge for example.

Ok so he asserted that people should just use mean deviation instead of mean of squares. Guess what though, taking the squares have a purpose: it penalizes big deviations so two situations which have the same mean deviation but one is more stable have different standard deviations. THis information is useful for many things: risk estimation or calculating sample size needed for required confidence (if you need more experiments, how careful should you be with conclusions and predictions etc). He didn't mention how are we going to achieve those with his proposal. Meanwhile he managed to throw insults towards various groups without giving one single example of misuse he describes.

This is not the first time he writes something this way. His whole recent book is like that. It's anti-intellectual bullshit with many words and zero points. He doesn't give any arguments, he throws a lot of insults, he misues words and makes up redundant terms which he then struggles to define. The guy is a vile idiot of the worst kind: ignorant and aggressive. Him gaining so much following by spewing nonsense like this article is for sure fascinating but there is no place for him in any serious debate.

tptacek3• 13 years ago

This comment was great fun to read, and I suspect that I share some of your opinions about Taleb (although mine are decaying with each day that passes since I last finished reading any of his books), but it would have been stronger as an argument if you had left off the part about him being a "vile idiot".

bluecalm12• 13 years ago

I just can't pass it. I gave my best at reading his book. The guy is unable to write one paragraph which doesn't contain some nonsense or serious misuse of established terms. He is insulting whole groups of people and institutions without giving any examples or research. I am pretty sure that if his stuff were posted without his name the conclusion would be obvious: it's just nonsense and very offensive at that.

I realize calling people idiots are frown upon here but I am ready to defend it. There isn't one other author which infuriates me with his ignorance and inability to make specific point without throwing condescending remarks. If there is anybody who deserve the term it's him. I mean "we should retire standard deviation because everybody misues it and it's not useful for real life" without any examples ? He just called out thousands of scientist, risk managers and statisticians without giving one single argument. His suggestion to just use mean deviation is laughable and obviously doesn't work for many purposes which he didn't address while being condescending in the process.

It's worse than saying: "we should retire Java and just use Python because it has dynamic typing and seemingly developers at even serious companies fail to see this!". Remark of this kind would gain me "idiot" badge pretty quickly. This article is on this level (well, actually lower as remark about Python actually contains an argument) and his book is worse. If that doesn't qualify him as an idiot I don't know what else could.

MaysonL3• 13 years ago

I particularly like Noah Smith's take on him[0]:

"Nassim Taleb is a vulgar bombastic windbag, and I like him a lot. His books do a good job of explaining some deep, important finance ideas for a general audience. He has helped popularize the notion of "skin in the game". His trolling of economists is also good for some lulz (I particularly enjoyed his coinage of the term "macrobullshitters")."

[0]http://noahpinionblog.blogspot.com/2014/01/of-brains-and-bal...

RivieraKid2• 13 years ago

Standard deviation tells you how volatile measurements are not what mean deviation is.

Why would you use sd to convey the amount of volatility? Isn't the mean deviation much more easily understood?

ThomPete6• 13 years ago

Context I think

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=970480

And I think you should pay more attention to this:

"...as it does more harm than good—particularly with the growing class of people in social science mechanistically applying statistical tools to scientific problems..."

if you want to understand where he is coming from.

dworin• 13 years ago

Definitely more context, but I don't think that paper really backs up the assertion. He asked finance professionals or students, not social scientists. And he asked them at a seminar where I'm guessing they didn't have access to a calculator or computer, so it looks like a lot of them just used a rule of thumb.

The question they asked reads like a trick question to me. And coming up with the right answer would have required working backwards through statistical formula It's the type of thing you do an "Introduction to Statistics" class and then don't think about too often because it doesn't have a ton of practical applications. It seems a lot easier to just ballpark it.

bluecalm12• 13 years ago

>"...as it does more harm than good—particularly with the growing class of people in social science mechanistically applying statistical tools to scientific problems..."

Well, for sure there are problem with people applying tools without fully understanding them. It's not very interesting statement. As obviously many things in nature form normal distribution and standard deviation describes those distributions well while mean deviation loses information about volatility. If you are going to propose abandoning of standard deviation it would be nice to give some alternative ways for handling those distributions and maybe show how using mean deviation in place where "many scientists" these days use standard deviation improve things. His study shows that people weren't able to answer his question. That could be for various reasons, like reading it too fast. It doesn't really matter. What matter are example of decisions/measurement which could be better handled by "abandoning standard deviation" or maybe showing that those people actually make financial mistakes due to not understanding the difference.

Even if he is right that many traders misuse or don't understand the term it's a problem with education and not with tools being wrong. "We should abandon standard deviation" is wider claim and to defend it you need to show how problems currently handled by using the measure should be handled in better way.

tlarkworthy• 13 years ago

Yeah. Eliminating stdev so social scientists don't get confused is the tail wagging the dog.

jpwagner• 13 years ago

maybe in an intellectual sense, but a lot more people read http://www.huffingtonpost.com/science/ than http://arxiv.org/

sliverstorm3• 13 years ago

The funny thing is I've never used absolute deviation before, so I'm slightly confused by absolute deviation right now as I wrap my head around what it means relative to sigma (which I have used, lightly, for years) and why anyone would want to use it instead...

edit: apparently MAD can refer to either "mean absolute deviation" or "median absolute deviation". Yup, this sure isn't going to confuse anybody.

yen223• 13 years ago

MAD can also refer to Mutually Assured Destruction, which seems fitting given this thread.

drewblaisdell• 13 years ago

I agree with some of what you wrote, but I think you should reread your reply to Taleb with as much scrutiny as you read Taleb.

corresation6• 13 years ago

Standard deviation tells you how volatile measurements are not what mean deviation is. Those are both very real life things just not the same thing."

While I am not a Taleb fan (he had his own black swan and became exactly the reviled expert his own books warn us about), your hostility in this case seems out of place.

The root of his seemingly casual contemplation is that standard deviation is simply misnamed. That this misnaming causes a cognitive dissonance that confuses even knowledgeable practitioners to mentally conflate it with the mean deviation. Which -- as someone in the financial industry -- I can absolutely confirm. It seems like such a minor thing, but the name has tremendous influence on how we parse these things, and the shortcuts we take in understanding things.

marvin• 13 years ago

What is Taleb's own black swan?

bluecalm12• 13 years ago

Well, I read his article as "let's abandon standard deviation and use average mean deviation instead". I think that's what he claims. It's not: "some people are sometimes confused by the concept and in some places mean deviation would serve better, for example here and here". It has way more aggressive tone and way wider assertions about people misusing standard deviation. Remarks about "real life" doesn't help either, especially if you don't provide even one example where standard deviation is commonly used but mean absolute deviation would serve better.

> Which -- as someone in the financial industry -- I can absolutely confirm.

This is what he is doing: he takes common sentiment often and makes into war. "Abandon standard deviation", "the confusion started", "PhD's are confused" It's easy to like him and nod in agreement while omitting that he took it way too far, proposed things way too radical and again: didn't give one single example of stuff not working because of it.

lisper• 13 years ago

One example please ? I can give hundreds when std dev is useful and mean deviation isn't.

It is ironic that you take Taleb to task for not providing an example, and then you do exactly the same thing that you are excoriating him for. Claiming that you have hundreds of examples is not the same as actually presenting one.

raverbashing• 13 years ago

I understand your point, and I agree mostly with it

But I think the headline was sensationalised.

Taleb doesn't seem to be against "standard deviation" mostly, but calling it "standard deviation" (which should be called something else), and providing a more "user friendly" number.

The positive square root of the second central moment of the density distribution function will keep being that.

shas32• 13 years ago

You conveniently leave out the reasonable portions of his article. I read your comment before I read the article, and guess what, you have cherry picked specific parts of the article such that Taleb comes off as stupid.

It took me ten seconds to figure out what 'Goldstein and Taleb' refers to: http://www-stat.wharton.upenn.edu/~steele/Courses/434/434Con...

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=970480

He specifies that SD is reasonable as a mathematical tool, but not for inference about society, finance, etc.

Your comment appears to have an agenda or ideology underlying it.

Further you don't seem to have read the article fully.

Ok so he asserted that people should just use mean deviation instead of mean of squares. Guess what though, taking the squares have a purpose: it penalizes big deviations so two situations which have the same mean deviation but one is more stable have different standard deviations. THis information is useful for many things: risk estimation or calculating sample size needed for required confidence (if you need more experiments, how careful should you be with conclusions and predictions etc). He didn't mention how are we going to achieve those with his proposal. Meanwhile he managed to throw insults towards various groups without giving one single example of misuse he describes.

That is pretty much what his entire article is about: taking squares may not be the best idea universally.

bluecalm12• 13 years ago

He specifies that SD is reasonable as a mathematical tool, but not for inference about society, finance, etc.

Yes, and as SD is widely used in those so this is quite a bold statement to make an Taleb doesn't give one example of things going wrong with it and his proposal working better. This observation is also wrong and I pointed out some areas where standard deviation is useful.

Your comment appears to have an agenda or ideology underlying it.

Yes it's ideology of calling people out when they assert incorrect things in condescending tone without any arguments while insulting whole groups of scientists and statisticians.

That is pretty much what his entire article is about: taking squares may not be the best idea universally.

No, article isn't about it. It was in my comment. Taleb doesn't mention how MAD works better than SD in some situations and why or why it should be substituted. Taleb doesn't point one situation when MAD works better than SD (I pointed out some where SD works better than MAD) he also doesn't address obvious problems which such substitutions create. Heck, he doesn't even discuss how nature of SD is different than MAD, he just says they are different and the latter is more applicable for "real life". Also he doesn't argue that MAD is sometimes more useful than SD. He argues that the latter should be disposed of outside some very narrow theoretical applications.

tel2• 13 years ago

He's inflammatory. Really, really inflammatory. He also tends to write about obvious technical points so if you do pick through the morass and find the gem you'll be a bit underwhelmed. In this instance, standard deviations are obviously important statistics to compute and have many, many useful properties, sure, but Taleb rightly points out that they can be misused and I agree with him that their misuse is endemic in science and a downright travesty outside of it.

But to just say that some tool is both useful and misusable is boring and wouldn't cause people to talk about this nearly as much.

I don't really like Taleb's style, but I can't deny that it causes conversation about things that people often would not give a second thought. In that way, I can see the outlines of a really great point underlying his inflammatory rhetoric.

Don't hate the player? At least he's arguing that people ought to be smarter and worry about what data really means.

Fomite4• 13 years ago

I think that's my problem. By the time I've waded through the insufferable smugness, the anecdotes and the random and meaningless attention to things I've never encountered in practice, what is left is interesting, but not nearly worth the effort.

marcosdumay• 13 years ago

Don't hate the player? At least he's arguing that people ought to be smarter and worry about what data really means.

Are you still talking about the inflamatory style, or is that about the contents of the article?

Helianthus6• 13 years ago

Having the reputation of 'provocative' can become about being provocative more than being on point.

azakai3• 13 years ago

> The notion of standard deviation has confused hordes of scientists
What an assertion! It also proved to be very useful for hordes of scientists... what about some examples of confused scientists ?

He is exaggerating, for sure. But the point is valid: the mean average deviation (MAD) is often very different than the standard deviation (STD), and the MAD is more intuitive, it has a natural geometrical interpretation - STD's usage of squaring the distance makes it more complex.

And yes, this confuses people in some cases, including scientists. Many scientists are not statistical experts, they use tools as they were taught, and they often assume MAD is approximately the STD, because it usually is, except in rare cases when it is not. I've seen examples of those people in grad school, he is not making this up.

The STD is far more easy to analyze in a mathematical way. That is the huge value it brings - squaring is an operation you can take the derivative of, but absolute value you cannot. STD gives us nice properties like easily provable sum of variances is the variance of the sum, for independent variables.

MAD, however is nicer for reporting data since it is more intuitive. I think he makes a valid point that STD is used more frequently than it should be.

Ok so he asserted that people should just use mean deviation instead of mean of squares. Guess what though, taking the squares have a purpose: it penalizes big deviations so two situations which have the same mean deviation but one is more stable have different standard deviations.

His point is that many people are not aware of that property and do not want it.

sliverstorm3• 13 years ago

the MAD is more intuitive

Which one, the mean average deviation or the median average deviation?

elipsey2• 13 years ago

I'm relieved to hear from others who didn't love his book, now I don't feel so left out. I checked out Black Swan from the library a while back. It seemed like Taleb's smug prose and mudslinging were writing a check his evidence couldn't cash, but I couldn't stand more then the first 50 pages, so I never got to find out. My girlfriend read it all of it and sort of gave me the cliff notes; she thought I wasn't missing much.

If I ever met anyone in real life who was as impressed by his book as as much as the inexplicably fawning blogs and reviews I have seen, I would give it another try, but I sorta feel like I've been had. At least it was a library book, so I didn't give him 12 bucks.

Anybody here love his stuff, wanna convince me to try again?

Daniel_Newby2• 13 years ago

MAD, however is nicer for reporting data since it is more intuitive.

I have a hard time fathoming how anyone could think such a thing. This is math: we should be using things because they map to reality in some way, not because they are aesthetically pleasing.

The standard deviation maps to processes where the "importance" of changes is proportional to their square. For example, electrical power is proportional to the square of voltage, so AC power systems are conventionally rated by standard deviation. My 120 V power outlet has a standard deviation of its potential of 120 volts.

Standard deviation is also commonly used in situations where we cannot put a number on the importance of the deviation but we know it is big.

The mean average deviation is useful for numbers that are directly proportional to their importance. For example, if we have a hundred lamps and we measure their optical power outputs, the MAD would be a useful measure of their variation. Optical power is already in units of oomph.

klodolph7• 13 years ago

and the MAD is more intuitive, it has a natural geometrical interpretation

It's less intuitive, not more intuitive, at least for me. And the standard deviation definitely has a more geometric interpretation than MAD. If you measure a hundred samples, and you want to figure out how much they differ from the expected values, what could be more intuitive than Euclidean distance? But most people never bother to try and extend their intuition about ℝ^3 to ℝ^100 to realize how simple standard deviation truly is.

What is being advocated here is the use of the L_1 norm (MAD) over the familiar L_2 norm (standard deviation). Everybody knows and understands L_2, and L_2 has a lot of desirable properties.

thaumasiotes4• 13 years ago

The STD is far more easy to analyze in a mathematical way. That is the huge value it brings

This is also what I have read (I have essentially no experience with statistics).

squaring is an operation you can take the derivative of, but absolute value you cannot

We can talk without wild, obviously false hyperbole. It's trivial to take the derivative of the absolute value function. Working with it is more difficult, but taking the derivative is as easy as anything in math:

    f'(x) = -1 (when x < 0); 1 (when x > 0)

bnegreve• 13 years ago

The guy is a vile idiot of the worst kind: ignorant and aggressive.

Your comment is a bit irritating. I don't know the author of this blog post but I think he has a couple of valid points. You seem to dislike him for some other reasons. Feel free to share them. The blog post is still perfectly reasonable.

Anyway, I agree some of your comments as well, namely this:

I can give hundreds when std dev is useful and mean deviation isn't. Anything when you decide what % of yoru bankroll to bet on perceived edge for example.

and this:

Guess what though, taking the squares have a purpose: it penalizes big deviations so two situations which have the same mean deviation but one is more stable have different standard deviations.

But I don't see why this comment from N.T. is stupid:

>>It is all due to a historical accident: in 1893, the great Karl Pearson introduced the term "standard deviation" for what had been known as "root mean square error". The confusion started then: people thought it meant mean deviation.

I actually agree that standard deviation is a confusing name, why do you think that's a stupid comment?

bluecalm12• 13 years ago

Your comment is a bit irritating. I don't know the author of this blog post but I think he has a couple of valid points. You seem to dislike him for some other reasons. Feel free to share them. The blog post is still perfectly reasonable.

Really ? You think call for substituting one of the most common use measures in science, finance, gambling etc. with some other measure which doesn't have the same crucial properties without giving any examples of one going wrong and the other being better is reasonable ? He also threw some assertions about general confusion and scientist using it because of misunderstanding in 1893. Again without any example while giving condescending analogy of someone asking you to calculating average and realizing it's not standard deviation. It's not reasonable by any standard. The reason I have very low opinion about his writing and him are his books, especially Antifragile.

I actually agree that standard deviation is a confusing name, why do you think that's a stupid comment?

He claimed that "the confusion", things he described in previous paragraphs about scientists, PhD's and statisticians is caused by misleading name. I am not saying the name is good but implying that so many people are using it just because the name given to it in 1893 is insulting. It's basically Taleb telling scientists: "hey guys, you use this standard deviation thing because of randomish reason and not because you know what you are doing". It's very strong bold statement which undermines credibility of whole groups of scientists which he again didn't even begin to argue for. He just asserts it and continue.

edw519• 13 years ago

Counterexample:

  |                           ..
  |                         .    .                 
  |    waste      |       .        .       |     stuff
  |     of        |      .          .      |       I
  |     my        |     .            .     |     don't
  |    time       |   .    stuff I'll  .   |     grok
  |               | .        read        . |       
  |(Nassim Taleb) |                        | .       
  |       .       |                        |       . 
  |______________________________________________________
          -3     -2     -1     0     1     2     3
                       standard deviations

avenger1233• 13 years ago

Very nice! I did have his books on my reading list. But this whole discussion definitely puts me closer to the "waste of my time" side of the distribution.

NAFV_P• 13 years ago

I know this might be shooting the argument in the wrong direction...

Correct me if I am wrong, but I thought that the term inverse square law was erroneous, and I have yet to come across a complaint from anyone.

canvia• 13 years ago

Take this with a grain a salt. Taleb has made a lot of enemies with his writings about the bank bailouts and gov inefficiency. There are a lot of reasons for people to attack him, especially anonymously on the internet.

I am not saying that the arguments are without merit, just to be cautious in forming an opinion on the man.

justin662• 13 years ago

There are a lot of reasons for people to attack him, especially anonymously on the internet.

On the positive side, if you're going to judge the guy by the insights of his critics, his supporters have included the likes of Benoit Mandelbrot and Jack Bogle.

msellout• 13 years ago

> There is no scientific reason to use it in statistical investigations in the age of the computer
As someone who uses it daily I am eagerly awaiting his argument.

The use of root mean square error|deviation comes from the ease of calculation in the days before computers. Now that we have computers we can just use mean absolute error|deviation. Before computers, we needed calculus to find the "best fit line" -- parameters that create the least distance between predicted and actual values. Calculus plays well with parabolas but not so great with absolute value functions. Now that computers are around, we don't need calculus (as much).

wglb• 13 years ago

I am wondering if you have a lot invested in concepts and techniques that Mr Taleb is suggesting are broken. There is certainly a tone of defensiveness about your post.

I think it is still unexplained why the financial community is sticking to things that are known to be broken. It is like trying to use newtonian mechanics to describe chaotic phenomena. Standard deviation does not properly describe fractal stuff.

Feels like the industry is looking for the lost set of keys on a dark street, not where they were last seen but rather under the lamptpost, cause that is where the light is.

washedup• 13 years ago

His point has always been to cut off the tails. The MAD actually allows you to cut off the tails sooner, and that moves outside of your chosen confidence interval will be seen as tail risk much sooner than if you use STD. For example, think about the following example of normal returns versus S&P returns:

http://managed-futures-blog.attaincapital.com/wp-content/upl...

A distribution built from MAD will more closely resemble the reality of the S&P returns, and will create more robust models. There are many examples of this.

altrego99• 13 years ago

I am so glad that this comment is at the top!

Some other points - std.dev shows up in nature and is easier to understand, and analyze, simply because variances from independent sources add up. That's why something called ANOVA exists.

In OLS regression, we minimize the std. dev. of the error, not the MAD. (It is not because statisticians "thought" std. dev is actually MAD, it's because minimizing std. dev or square error has very nice properties that we use it even though the solution to MAD minimization is also known.)

Lastly, I don't follow who he proposes to be using MAD - if he decrees statisticians and physicists should still use Std. Dev?

Often it is that I find these articles, and I let them pass by. But sometimes, they have a potential to come back - and I stand a chance to be quoted this article, by someone else, who I then have to drain my energy to make the point that it's not really worth reporting MAD from now on.

dnc• 13 years ago

You will find example here: http://www-stat.wharton.upenn.edu/~steele/Courses/434/434Con...

There is relatively simple, yet illustrative problem described on the first page. The solution is on the second page. Try to solve it w/o looking the solution.

bravura• 13 years ago

>>There is no scientific reason to use it in statistical investigations in the age of the computer
> As someone who uses it daily I am eagerly awaiting his argument.

Compute-intensive statistical tests, which are data-driven and make fewer assumptions about the underlying distribution, can give tighter confidence intervals and detect statistical significance better.

For example, stratified shuffling.

upquark• 13 years ago

This guy sounds like a complete joke. Standard deviation is an immensely useful tool in stats. It's not a historical accident we use it everywhere, for example it naturally appears in the very useful Chebyshev inequality, and a million other contexts.

giardini• 13 years ago

bluecalm says:

"What an assertion! It also proved to be very useful for hordes of scientists... what about some examples of confused scientists?"

How about every single economist and financial analyst who failed to predict the financial crashes of the last 50 years? Did you realize how much money was lost over the last 50 years by the financial industry's reliance on models that improperly use the standard Gaussian bell curve? Taleb pointed out why the Gaussian is not usually an appropriate model for financial analysis and suggested a return to more conservative models. Yet today Modern Portfolio Theory and the Black-Scholes models (which use the Gaussian) dominate in financial schools and institutions despite the fact that they absolutely utterly failed, not badly, but catastrophically in every financial crisis when they were most needed.

You state that "Standard deviation tells you how volatile measurements are". But Taleb shows how financial markets are non-Gaussian and have "fat tails" and gives the data and the supporting arguments.

bluecalm says:

"As someone who uses it daily I am eagerly awaiting his argument."

You're late! Taleb began publishing his arguments years ago and continues to publish. You're way behind. Read his papers and read his books in the following order:

Fooled by Randomness http://www.amazon.com/Fooled-Randomness-Hidden-Chance-Market...

The Black Swan http://www.amazon.com/The-Black-Swan-Improbable-Robustness/d...

Antifragile, http://www.amazon.com/Antifragile-Things-That-Gain-Disorder/...

BTW simply because someone's writing style is different does not mean that he is wrong. To me, complaining about a writing style is a form of ad hominem argument. People are different and Taleb is one-of-a-kind. Initially I didn't see where he was going, but once I realized that he was presenting ideas that were absolutely, utterly novel and had real explanatory power I sat up and paid attention. If you read for the facts and the valid arguments you will see that Taleb delivers the goods.

truthteller3• 13 years ago

This whole post is a perfect example of the danger of Taleb's work. Someone with no knowledge of finance or statistics has read his books and now feels able to make extremely strong statements about a link between financial theory and financial crises. :(

Eliezer• 13 years ago

The true case against the standard deviation is more or less impossible to make without going into the math. For a mathematically advanced Bayesian, the idea is straightforward if you've already been through the lawful derivation of Gaussians from their underlying assumptions: Using standard deviations in your thinking makes sense if you think that an increasingly large error has a decreasing log-probability that goes as the square of the size of that error. The distribution that you get from the sum of independent variables is the classic example. Basically, if you think in standard deviations, then all postulates of the form "The error was that size" will come with probability penalties that you trade off against each other in proportion to the square of the size of that error. Thinking in standard deviations similarly corresponds to models where exceptional events become unlikely in proportion to the square of the size of that exception, only by "unlikely" you have to read log probability rather than probability, and log probability is (always) the right way for Bayesians to think about it anyway for reasons I won't go into.

And then the critique of "standard deviation" is that people got taught SD as a statistical tool that you just pull out any time you feel like it, and they don't know what it means in underlying probability-theoretic terms as an assumption about either the world or our own uncertainty, and so it's misused horribly on all sorts of occasions.

I'd guess that SDs are appropriate 40-90% of the time depending on which field you work in, but without a lot of Bayesian background with fairly advanced math people will not be able to really appreciate what the other 60-10% of times look like. And the state of education is not anywhere near like that. It's just people being taught to calculate the standard deviation cause, like, that's something you do. They don't know what assumptions it corresponds to even in the cases where SD does apply.

Burning SDs to the ground and starting over would not be very much amiss in one of the fields where SDs only make sense 40% of the time, but the practitioners are using them all the time. (Machine learning is one of the fields where SDs make sense maybe 40% of the time, and if I found an ML practitioner who had been taught to think in terms of squared error I'd send them off to learn the underlying probability theory until their entire worldview had been translated into likelihood functions instead.)

aet• 13 years ago

You remind me of NNT - hyperbole and extremes. "vile idiot"?

RivieraKid2• 13 years ago

I was just wondering about a very related problem. I do 5 measurenments of some random variable (let's say execution time) and average them. How should I report the variability of that average?

State the sample size and standard deviation?

darkhorn• 13 years ago

90% of the data fall between this point and this point. 50% of the data fall between this point and this point. etc.

MAD is more accurate than Standard Deviation to me, if you ask me.

perlgeek• 13 years ago

If it were 10 or more measurements, I'd use average, standard deviation and sample size if we can expect that variable to be normally distributed.

I don't know how to make meaningful statistics with fewer data points.

bayesianhorse3• 13 years ago

Citing 10 measurements in a table or plot is probably easier than explaining how and why you are taking mean and standard deviation (or anything else for that matter...)

JASchilz• 13 years ago

The central limit theorem shows us that unimodal data with lots of independent sources of error tends towards a normal distribution. That description is a good first-pass, descriptive model for lots and lots of contexts, and standard deviation speaks well to normally distributed data.

Squaring error isn't just a convenient way to remove sign, it's driven by a lot of data-sets' conformance to the central limit theorem.

dj-wonk• 13 years ago

Thank you. I don't think it is intellectually honest for Taleb to omit this fact.

lambdasquirrel• 13 years ago

I think we'd be better off if we recognized that there are statistical distributions in the world besides the plain old Gaussian. For example, wealth does not follow a Gaussian, so why the heck do we throw around ideas like "above average wealth"?

Is MAD any better? Definitely. But I'd like to see a visual demonstration of how well it models exponential-based distributions. How well does it describe their "shape", the skew of the tail?

chilldream• 13 years ago

In that specific case, I'd submit that the word "average" doesn't belong in a conversation attempting any level of rigor. It only encourages the confusion between median and mean.

vorg• 13 years ago

Medians and means are interrelated. Averages are best thought of as being on a scale from meanlike to medianlike: a median requires a mean of the middle 2 values when there's an even number of them, and a mean can have outliers on each side to be eliminated before calculation. The word average abstracts away this detail. (I guess there'd be another scale from meanlike to medianlike absolute deviation, but that's another story.)

programminggeek• 13 years ago

I think because it's called "standard deviation" that it sounds like the thing to use or look for. It sounds more correct because of the word standard.

I feel like it is the same kind of failing due to human perception of language that programmers have with the idea of exceptions and errors, especially the phrase "exceptions should only be used for exceptional behaviors". That's a cool phrase, but people latch on to it because of the word exception sounding like something extremely rare and out of the ordinary whereas we see errors as common, but they are in fact the same thing. Broke is broke, it doesn't matter what you call it, but thousands of programmers think differently because of the name we gave it.

We are human and language absolutely plays a role in our perception of things.

klodolph7• 13 years ago

I think because it's called "standard deviation" that it sounds like the thing to use or look for.

Yes! Because it's an awesome trick and lets you do good estimates on napkins.

The other day I was buying lunch at a food cart and thought about how much change the food carts had to carry, as a function of how many customers they have, under the assumption that they want to be able to provide correct change to 99% of their customers.

Let's say that the average amount of change a customer needs is $5, and a 99-th percentile customer needs $15 in change. If we pretend that the distribution is approximately Gaussian we can calculate that 1,000 food carts with 1 customer each would need $15,000 in change, but 1 food cart with 1,000 customers would need $5 x 1,000 + ($15 - $5) * sqrt(1,000) ≈ $5,320. That's math you can do in your head without a calculator (being a programmer, 1,000 ≈ 2^10 so sqrt(1,000) ≈ 2^5).

The standard deviation and assumptions of normality are so useful because of the central limit theorem. That is, if you have many iid variables which have finite standard deviation the sum will converge to a Gaussian distribution as the number of variables increases.

Then you say "Well, the standard deviation weighs the tail too heavily" and the response is "well use higher order moments then, that's what they're they're for".

skybrian3• 13 years ago

It's a neat math trick, but it seems more accurate to say this lets you calculate bad estimates on the back of a napkin. Unless you really think food carts carry $5000 in change.

The quantitative work I do has to do with measuring latency, where the minimum, median, 90%, and 99% values are more meaningful than the mean or standard deviation. Programs typically have a best-case scenario (everything cached) and a long one-sided tail.

roywei• 13 years ago

four-day returns of stock x: (-.3, .3, -.3, .3) -> MAD = 0; four-day returns of stock y: (-.5, .5, -.5, .5) -> MAD = 0.

andrewcooke2• 13 years ago

nope. look at what the "A" in MAD stands for.

michaelhoffman3• 13 years ago

No, it's the median absolute deviation. Absolute deviation is the absolute difference between an average and a data point. So (-.3, .3, -.3, .3) -> MAD = 0.3; (-.5, .5, -.5, .5) -> MAD = 0.5.

jameshart• 13 years ago

The A in MAD stands for 'absolute', so no, the MAD for those two stocks is .3 and .5 respectively - versus standard deviations of 0.35 and 0.58.

spikels2• 13 years ago

You have calculated the mean. This is only the first step in calculating the MAD (mean absolute deviation). You then need to take the absolute value of the difference (deviation) of each datapoint from this mean - for your x you get (.3, .3, .3, .3) and for your y (.5, .5, .5, .5). Finally you take the mean of these absolute deviations to get MAD(x)=0.3 and MAD(x)=0.5.

cheald3• 13 years ago

I really tried to get through "The Black Swan" and Taleb's writing struck me as so pretentious and self-involved that it made it impossible for me to finish.

He strikes me as someone who is so desperate to be important and recognized that an assertion like this doesn't really surprise me.

andrewcooke2• 13 years ago

fascinating.

Alex_MJ• 13 years ago

His facebook doesn't inspire a lot of confidence. It's full of vague availability-heuristic-targeting generalities.

"Virtue is when the income you wish to show the tax agency equals what you wish to show your neighbor"

"The problem is that academics really think that nonacademics find them more intelligent than themselves",

etc

I've read black swan as well, and there were parts I didn't quite grok at the time (You cannot predict a black swan! etc)

My take is that he's a Malcolm Gladwell with numbers and therefore less easily takedownable but has the same model of "hold prestigious academic position, appear wise, publish book with simple principle, be easily referenceable by people who want to sound well-read" except he has lots of math and charts to point at lest anyone call him out on it.

calroc2• 13 years ago

I started reading that book and I thought he was a genius, but then, right abut the point where he starts bagging on the Uncertainty Principle, I realized that he's actually kind of an idiot.

The book does make a good point though.

cheald3• 13 years ago

Maybe I'm the idiot, but I found the book's point to be pretty trivial. "Sometimes unexpected things happen, and people are bad at expecting the unexpected" seems pretty damn trivial to me.

Maybe it's because I think like a programmer rather than a finance guy, but a large portion of what I do on a daily basis is about mitigating risk from the unknown. A programmer who only guards against known risks is going to get his ass handed to him sooner rather than later (these are the sorts of people who use blacklists and regexes to sanitize SQL). A finance guy who only guards against known risks is just playing the averages. My experience with traders is that they tend to be pretty abstracted from reality and like to impose rules and patterns where there are none. I can see why those sorts of people would find Taleb's work groundbreaking.

Taleb's undoubtedly intelligent, but I feel like he woke up one day, decided that he wanted to be a philosopher who brings wisdom to the masses, and built his temple on a mind-searingly obvious principle, which he now proclaims to be his great gift to humanity, for which he should be praised, hallowed be his name. The impression I got off of him was that he considers himself a prophet, imparting a word to the masses that the rest of us are just too stupid to recognize. Gag me.

triplesec2• 13 years ago

Talebs problem is an intense narcissism, allied with strong intelligence, but not as strong as his narcissism would leave him to believe. So, we have to listen carefully to find his useful insights, while wading through the bombast.

Don't try to engage with him critically, but constructively, directly on the internets though, because he prefers acolytes to arguments!

olifante• 13 years ago

Not really a surprise for someone who was so in thrall to Benoît Mandelbrot, another world-class narcissist.

Here's Taleb on Mandelbrot: "[He] had perhaps more cumulative influence than any other single scientist in history, with the only close second, Isaac Newton."

That quote really says it all.

Homunculiheaded• 13 years ago

I sometimes think that progress in the 21st century will be summed up as: "The realization that the normal distribution is not the only way to model data".

Taleb's favorite topic is the "black swan event" which is something that the normal distribution, and the idea of standard deviation, don't model that well. In a normal distribution very extreme events should only happen once in the lifetime of several universes. Of course assuming variation inline with a Gaussian process is at the heart of how the Black-Sholes model calculates risk/volatility/etc.

Benoit Mandelbrot argued that financial markets follow a distribution much more similar to the Cauchy distribution (specifically the Levy distribution) rather than a Gaussian. The problem of course is that the Cauchy distribution is pathological in that it doesn't have a mean or variance, you can calculate similar properties for it (location and scale), but it doesn't obey the central limit theorem so in practice it can be very strange to work with.

The normal distribution is fantastic in that it does appear frequently in nature, is very well behaved, and has been extensively studied. However a great amount of future progress is going to come from wrestling with more challenging distributions, and paying more attention to when assumptions of normality need to be questioned. Of course one of the challenges of this is that the normal distribution is baked into a very large number of our existing statistical tools.

jerf4• 13 years ago

This is actually what I expected to read: "The standard deviation is useful because with the average and the standard deviation, one can fully characterize a normal distribution. However, the standard deviation is less useful a statistical summary the farther away from 'normal' you get, and in reality, there is no such thing as a normal distribution, as a true normal distribution is defined on the entire real number line from negative infinity to positive infinity. Reality always provides some bound, and it's often quite distorted from Guassian. For instance, a 'normal' distribution averaging 2 with a standard deviation of 1.4, bounded by 0, is quite non-Gaussian in many important ways! (Not least of which is that you're going to have to do something to replace the missing probability...)

"People rarely check how closely their data conform to the standard distribution; indeed, many people blindly apply the standard deviation to their data regardless of its distribution! The resulting number is often more obfuscatory than helpful, to the extent that it crowded out more useful summaries.

"It's a useful metric when treated carefully, but it is rare to encounter it treated carefully. Science courses would be well-served to stop teaching it in favor of a stronger emphasis on multiple distributions. (Multiple distributions are usually touched upon, but implicitly our curricula overfavor the Gaussian distribution and end up accidentally implicitly convincing students its the only one.)"

But that's just me.

Helianthus6• 13 years ago

Reality always provides some bound

But... it doesn't. You ever hear about the hypothetical possibility of your atoms lining up and falling through the floor?

It's hypothetical in the sense that it's really ridiculously unlikely, but there is no bound preventing it.

Now the central point about different probability curves stands, but that's not what Taleb was talking about--he seems to think that it's the tool's fault if people are using it wrong--and it's also not what Homunculiheaded argued.

Helianthus6• 13 years ago

"The realization that the normal distribution is not the only way to model data".

Realization by who? If you understand the normal distribution you had damn well better know that there are other probability distributions.

The problem of course is that the Cauchy distribution is pathological in that it doesn't have a mean or variance, you can calculate similar properties for it (location and scale), but it doesn't obey the central limit theorem so in practice it can be very strange to work with.

In other words, we're using the normal distribution as the workhorse because considering other distributions is, well, inefficient/unproductive.

However a great amount of future progress is going to come from wrestling with more challenging distributions, and paying more attention to when assumptions of normality need to be questioned

What exactly is it that you think physicists have been doing for the past half century? The error accounting for CERN's experiments requires actual millions of PhD-hours.

This topic's conversation is at some bizarre intersection of good intentions, concrete knowledge, and woeful ignorance. I guess I tar myself with that brush.

jerf4• 13 years ago

"Realization by who? If you understand the normal distribution you had damn well better know that there are other probability distributions."

See Glyptodon's post: https://news.ycombinator.com/item?id=7065067

If you hang out with mathematicians, yeah, sure, everybody knows there's a ton of distributions. Try hanging out with, say, biologists. The undergrad statistics education is basically "mumble mumble guassian mumble hideous equations mumble mumble YOU MUST DO THE CHI-SQUARED TEST mumble mumble poisson mumble hideous equations mumble YOU MUST DO THE CHI-SQUARED TEST mumble mumble CHI mumble calculus is hard mumble mumble NULL HYPOTHESIS mumble CHI CHI CHI WE WILL DRUM YOU OUT OF THIS DISCIPLINE IN DISGRACE IF YOU DON'T DO THE CHI-SQUARED TEST".

I'm hardly even exaggerating! I remember being asked by someone in their third semester of using the damn test what it actually meant.

Nominally, yes, the Poisson and probably a couple of others were mentioned, but believe me, the ALL CAPS part of the education does not mention them.

Glyptodon• 13 years ago

All I know is this reminds me a lot of high school where we had to always compute std dev in problems, homework, and sometimes labs, but nobody really ever explained how to interpret it. It was always like "This is std dev. This is how you compute it. Make sure you put it your tables and report."

Eventually someone (or something) did explain it, but once I understood it, it became clear that it wasn't always a sensible thing to be asked to calculate but was instead just an instinctive requirement.

afterburner• 13 years ago

I've found MAD a potentially useful measure for monitoring whether something gets out of whack; when using STD I needed to modify it to give less weighting to outliers.

randomsample22• 13 years ago

Standard deviation and mean absolute deviation are both useful, but I think it's silly to suggest that we all adopt exactly one measure of variability to summarize data sets. When in doubt, make a fucking histogram.

michaelhoffman3• 13 years ago

Histograms can be misleading too, especially when the breaks are not set well.

randomsample22• 13 years ago

Anything can be misleading, but in most cases a histogram conveys more information than a single number ever could.

etanazir• 13 years ago

The minimum uncertainty wave equation is ~ e^(-x^2) ergo the standard measure is in terms of x^2. QED.

spikels2• 13 years ago

You gotta love the acronyms: STD versus MAD!

Taleb is definitely mad but his use of the MAD acronym (mean absolute deviation) is actually correct. However the STD acronym (all caps) refers to "sexually transmitted disease" and not generally used for "standard deviation". Most people use SD, Stdev, StDev or sigma.

Once again his ability to coin new terminology outstrips his ability to form coherent ideas that are anything more than trivial (eg. we have known about fat tails in stock returns for 50+ years). Like George Soros[1], Taleb's success says more about the state of the world of finance than their contributions to our knowledge.

[1]-See his book "The Alchemy of Finance"

Fomite4• 13 years ago

STD is also an obsolete term. Epidemiology, Medicine etc. most often now refer to them as STIs, or Sexually Transmitted Infections.

The reasoning for this is that many sexually transmitted infections can be acquired, passed on to others, etc. without causing any clinical symptoms. See: HPV, among others.

vzhang• 13 years ago

I'm seriously questioning some people's reading comprehension - he NEVER said STD is not useful! He's only saying the name "Standard Deviation" is badly chosen.

bluecalm12• 13 years ago

Read the blog post carefully:

it is time to retire it from common use and replace it with the more effective one of mean deviation
Standard deviation, STD, should be left to mathematicians, physicists and mathematical statisticians deriving limit theorems
There is no scientific reason to use it in statistical investigations in the age of the computer, as it does more harm than good

He is saying it's not useful for real world things and people are just confused. What you wrote is reasonable view. What Taleb writes isn't.

puranjay• 13 years ago

NNT is my intellectual superhero but the amount of hate he gets is tremendous.

Please understand that NNT's biggest issues are not so much with the way statistical models are applied to economics and finance, but how social scientists sometimes feel compelled to apply them to social fields as well, which is plain unscientific, dumb, and mostly disastrous.

So when you bear down on his arguments, please keep this context in mind.

triplesec2• 13 years ago

You're making too many gross generalisations here, as does Mr Taleb. He's right that in all fields there are statistically illiterate people making huge errors, and academic theorists have been making such - and more complete - criticisms for a while now. So, there's a real issue. However, there are a good number of competent social scientists too, beyond the mediocre morass, who understand just what variable construction and limitations to statistical operations are.

Fomite4• 13 years ago

Among other things, I've seen way more appalling applications of statistics in finance and economics than I have in social science.

Also, the assertion in your post that the misapplication of statistical models in social science is "disastrous" but somehow giving finance a pass? You've got to be kidding me.

jessaustin6• 13 years ago

NNT, at least, doesn't give finance a pass. He excoriates them at every opportunity.

dxbydt• 13 years ago

The notion of area has confused hordes of scientists; it is time to retire it from common use and replace it with the more effective one of circumference. Area should be left to mathematicians, topologists and developers selling real estate. There is no scientific reason to use it in statistical investigations in the age of the computer, as it does more harm than good.

Say someone just asked you to measure the area of a circle with radius pi. The area is exactly 31. But how do you do it?

scala> math.round(math.Pi * math.Pi * math.Pi).toInt

res1: Int = 31

Do you pack the circle with n people, count them up and verify n == 31 ? Or do you pour a red liquid into the circle and fill it up, then drain it and measure the amount of red ? For there are serious differences between the two methods.

If instead, you were asked to measure the circumference of a circle with radius pi.

scala> math.round(2 * math.Pi * math.Pi).toInt

res2: Int = 20

You just ask an able-bodied man, perhaps an unemployed migrant, to walk around this circle while another man, an upstanding Stanford sophomore, starts walking from Stanford to meet his maker, I mean VC, well its the same thing...

So by the time the migrant finishes walking around the circle, our upstanding Stanford entrepreneur is greeting the VC on the tarmac of the San Francisco International Airport. This leads one to rightfully believe that the circumference of the circle of radius pi is exactly the distance from Stanford to the SF Airport ie. 20 miles. It corresponds to "real life" much better than the first—and to reality. In fact, whenever people make decisions after being supplied with the area, they act as if it were the distance from their university to the airport.

It is all due to a historical accident: in 250BC, the Greek mathematician Archimedes introduced Prop 2, the Prevention of Farm Cruelty Act ( http://en.wikipedia.org/wiki/California_Proposition_2_(2008) ). No I believe this was a different Prop 2. This Prop 2 states that the area of a circle is to the square on its diameter as 11 to 14 (http://en.wikipedia.org/wiki/Measurement_of_a_Circle ) .The confusion started then: people thought it meant areas had to do with being cruel to farm animals. But it is not just journalists who fall for the mistake: I recall seeing official documents from the department of data scientists, which found that a high number of data scientists (many with PhDs) also get confused in real life.

It all comes from bad terminology for something non-intuitive. Despite this confusion, Archimedes persisted in the folly by drawing circles in the sand, an infantile persuasion, surely. When the Romans waged war, Archimedes was still computing the area of the circle. The Roman soldier asked him to step outside, but Archimedes exclaimed "Do not disturb my circles!" (http://en.wikipedia.org/wiki/Noli_turbare_circulos_meos)

He was rightfully executed by the soldier for this grievous offense. It is sad that such a minor mathematician can lead to so much confusion: our scientific tools are way too far ahead of our casual intuitions, which starts to be a problem with a mad Greek. So I close with a statement by famed rapper Sir Joey Bada$$, extolling the virtues of the circumference: "So I keep my circumference of deep fried friends like dumplings, But fuck that nigga we munching, we hungry." (http://rapgenius.com/1931938/Joey-bada-hilary-swank/So-i-kee...)

mekael• 13 years ago

Possibly the best thing I've read all week. Thank you sir.

eruditely2• 13 years ago

Except the difference here is that generally Taleb is right and has a point. You know the b difference between the probabilistic hacker news titles generator and the actual titles found here are that even though they sound the same and have like weight same style. .. one is actually real.

al2o3cr• 13 years ago

Shorter social scientists: "Gaussian distribution sez wut?"

notastartup• 13 years ago

I've been a long time fan of Dr. Nassim Taleb. First book I've read was the one about his time as a day trader and how on the Black Friday market crash, he made a killing and cleared his desk and never had to work again.

There are those that dislike his ideas because it is threatening to their existing assumptions about probability and statistics. He argues that experts and majority of people do not account for the unpredictable but significant impact a single event can have which often shatters the commonly held belief. For example, swans were white until the discovery of black swans in Oceania, too big to fail multi-national corporations going bankrupt like Lehman's brothers and etc.

He's not anti-academic, but he is against teachings in the common academia that is based on naive assumptions that is specifically tailored to serve those that thrives most off the limited quantitative measures, such as market callers, hedge funds selling complicated quantitative algorithm trades, academics seeking fame and fortune by writing the most logical and quantitative paper without questioning any of the tools they are using, it is this hypocrisy and laziness that is apparent and those that try to deny to the point of making ad hominem remarks against a man, who simply observes these things and decides to write it in an entertaining manner (otherwise nobody would give a shit because the topic would be dry without lay man's linguo).

Keep an open mind, a lot of what he says I do find interesting ideas and it has influenced my thinking process quite a bit, however it's no way in anyway, grounds for cracking jokes or ridicule, in fact when I read some of the comments here, it's a bit shameful. We should be embracing new ideas in order to explore them, regardless of who the explosive nature of the claim, because the black swan event is very real and is not captured or understood completely by our current set of statistical tools and methodology based on questionable assumptions about how the real world operates. For example, 1/2500 chance is not what we really think it means in the real world because black swan events are more common than we think, a percentage probability do not fully reflect it's frequency and the magnitude of it's event.

Note the fall of crime rates in the United States following a decision to legalize abortion, economists and experts would come on television and bring up all sorts of random theories and ideas but little did they realize it was a chain effect from a court ruling passed decades ago until two economists came out with a paper that was ridiculed because it suggested that 'killing babies from poor neighbourhoods = lower crime rate' where most poor neighbourhoods is occupied by African Americans. Because such idea was earthshakingly controversial and still denied even to this day. Because Galileo claimed the earth was round instead of flat, he was executed. This is simply the nature of our world, almost all part of life, there exists a hierarchy that people simply do not ask questions either due to blind trust or the fear of reprisal.

jessaustin6• 13 years ago

I think I agree with most of this, but now aren't we supposed to say that the drop in crime is due more to reduced childhood lead exposures than to abortion? Not just because it's a feel-good, humanistic explanation rather than a horrific racist eugenics explanation, but also because recent studies show a pretty strong lagged correlation...

MaysonL3• 13 years ago

How often do "six sigma" events occur in financial markets? A hell of a lot more often then the 0.0000001973% that they would in a normally distributed system.

tsax5• 13 years ago

Exactly. I'm astounded that this basic fact - that financial modelers have been using the wrong distribution for decades IS NOT BEING DENOUNCED. For example, the Capital Asset Pricing Model (CAPM) which assumes that returns fall on a normal distribution.

justin662• 13 years ago

Taleb has a textbook draft up which is more technical than his popular writings:

http://www.fooledbyrandomness.com/FatTails.html

There might be something there for the more rabid critics. At least it will keep them off the internet for a few days...

snake_plissken• 13 years ago

I've always thought his writings were more allegorical than scientific; you can't rely on the standard deviation to never go against you at the worst possible time. But like anything else, it can and it (probably) will.

Also, yes, his writing style is grating and he takes opportunistic character swipes at pretty much everyone.

tn13• 13 years ago

There is nothing wrong with STD or MAD. The real problem is a lot of people apply them without realizing the nature of their data and what kind of analysis they want to do.

In this case what matters in the end is the kind of impact deviation from mean has on the real world variable you have. I agree that in most Gaussian experiments MAD might be more useful than STD.

STD is more useful when the real world impact of the deviation increases exponentially with the magnitude of deviation and hence it is a good idea of magnify the (x-n) by squaring it. In many cases the impact is linear where MAD clearly works better. For example in cricket where n runs are n times better than 1 run. But in case of shooting. Hitting 9 targets out of 10 might be 100 times better than 1 out of 10 so there MAD will be misleading.

Beliavsky• 13 years ago

If data is drawn from a Laplace distribution of the form p(x) = exp(-|x|), the mean absolute deviation is more informative than the standard deviation, but if its form is close to the normal, p(x) = exp(-x^2), the standard deviation is more important. So whether to use the mean absolute or standard deviation depends on the distribution of the data. There is a field called robust statistics that looks at this question.

ChristianMarks• 13 years ago

Climate scientists--among others--have made similar recommendations to use the absolute mean error in place of the standard deviation, depending on the application. Taleb might have cited the extensive methodological literature--for example:

Cort J. Willmott, Kenji Matsuuraa, Scott M. Robeson. Ambiguities inherent in sums-of-squares-based error statistics. Atmospheric Environment 43 (2009) 749–752.

URL: http://climate.geog.udel.edu/~climate/publication_html/Pdf/W...

tehwalrus• 13 years ago

at least he's leaving us physicists alone with it...

thetwiceler• 13 years ago

It is sad that Taleb does not see the value in the standard deviation; standard deviation is far more natural, and more useful, than MAD.

For example, if X has a standard deviation of s, and Y has a standard deviation of t, then the standard deviation of X + Y is sqrt(s^2 + t^2). There is a geometry of statistics, and the standard deviation is the fundamental measure of length.

To retire the standard deviation is to ignore the wonderful geometry inherent in statistics. Covariance is one of the most important concepts in statistics, and it is a shame to hide it from those who use statistics.

Additionally, I will mention that we do not need normal distributions to make special the idea of standard deviations. In fact, it is the geometry of probability - the fact that independent random variables have standard deviations which "point" in orthogonal directions - which causes the normal distribution to be the resulting distribution of the central limit theorem.

bayesianhorse3• 13 years ago

Nassim Taleb somehow likes to beat up on normals...

We Bayesians have similar notions, but we usually try not to overly bully frequentist methods, the poor things. Also, being familiar with Bayesian methods, a lot of what Taleb is saying sounds vaguely familiar...

kylebrown• 13 years ago

Well, frequentist methods are taking the blame for the most recent financial crisis, such as assuming a normal distribution when the empirical one is fat-tailed.

Perhaps the Bayesian methods will take the blame in the next financial crisis. Such as the error in estimating a non-stationary distribution and quantifying the uncertainty.

bayesianhorse3• 13 years ago

Statistical economists or analysts always said that the normal distribution is a simplification and that this simplification has its own problems.

It's just that traders and bankers would fire statisticians who were too vocal about it as wasting their time with unnecessary explanations...

Bayesian methods in general can only take the blame if you can prove some other method being more reliable.

Also they have another advantage: Bayesian methods are so mind blowing and beautiful, that it is hard to blame them for anything!

beloch• 13 years ago

I'm a physicist, so I'm one of the people this guy says standard deviation is still good for. However, despite some "oddities" (pointed out by others here) in his article, I'm more than willing to admit a simpler, easier to understand term would be helpful for explaining many things to the general public. Hell, it would be helpful for explaining things to journalists, who we then trust to explain things to the public!

Look at an reputable news site or paper. Odds are they post articles based on polls several times a day. How many report confidence intervals or anything of the sort? These are crucial for interpreting polls, but are left out more often than not. Worse yet, many stories make a big deal about a "huge" shift in support for some political policy, party or figure, when the previous month's figure is actually well within the confidence interval of the current month's poll!

Standard deviation, confidence intervals, etc. are all ways of expressing uncertainty, and it's become abundantly clear that the average journalist, to say nothing of the average person, has no clue about what the concept means. If the goal is to communicate with the public, then we really need to take a step back and appreciate the stupendously colossal wall of ignorance we're about to butt our heads against. When we talk about the general public, we should keep in mind that rather a lot of people know so little about the scientific method that they interpret the impossibility of proving theories as justification for giving religious fables equal footing in schools. This kind of ignorance isn't a nasty undercurrent lurking in the shadows. It's running the show, as evidenced by many state laws in the U.S.! There is absolutely no hope of explaining uncertainty to most of these people.

There is hope of explaining basic statistics to journalists, if only because they are relatively few in number and it's a fundamental part of their job to understand what they are reporting. Yes, I just said that every journalist who has reported a poll result, scientific figure, etc. without the associated uncertainty has failed to adequately perform their job. We need to make journalists understand why they are failing. If simplifying the way we report uncertainties will assist with this, then I'm all for it. Bad journalism is a root cause of a great deal of ignorance, but it's not an insurmountable task to fix it.

If you are a scientist who speaks to journalists about your work, make sure they include uncertainties. If you are an editor, slap your peons silly if they write a sensationalistic poll piece when the uncertainties say it's all a bunch of hot air. If you are a reader, please mercilessly mock bad articles and write numerous scornful letters to the editor until those editors pull out their beat-sticks and get slap-happy. We should not tolerate this kind of crap from people who are paid to get it right.

latk• 13 years ago

Maybe a solution would be to only communicate the bounds of a value rather than the value itself. E.g. Instead of “party A has 35% with sigma=2%” something like “we expect party A to have 33%–37%”. Providing a range is shorter than explaining the SD, and can be visualized easily, e.g. in a bar chart.

TTPrograms• 13 years ago

There is some argument that MAD is actually better than RMS for a lot of applications. Apparently it predated RMS, but one of the reasons it was switched to was because RMS minimizing linear regression is much, much simpler to calculate. Also consider comparing the robustness of RMS based regression with MAD based regression. See: http://matlabdatamining.blogspot.com/2007/10/l-1-linear-regr...

yetanotherphd• 13 years ago

I had hoped this would be about the revolution occurring in statistics/econometrics where confidence intervals based on strong parametric assumptions (e.g. the confidence intervals you would obtain using the standard deviation) are being replaced by confidence intervals obtained using the bootstrap (and other non-parametric methods) that don't rely on such strong assumptions.

But no, it is just advocating using Mean absolute distance instead of the standard deviation. Which I guess is to be expected from someone whose work focuses mostly on long-tailed distributions.

Still, I think that non-parametric methods are much more valuable as a solution to dealing with non-normal data than what Taleb is proposing.

aredington• 13 years ago

The way I read it he's proposing two things:

1) Refer to the analysis of Root Mean Square Error always by that name. (RMS is already often used in certain jargon instead of stddev).

2) Stop treating RMS as a default measure of variance. Treat Mean Absolute Deviation as the default measure of variance, because the figure it provides is more consistent with people's psychological interpretation.

It's not really retiring RMS, just retiring the idea that it is a good default statistical analysis.

Nassim Taleb: We should retire the notion of standard deviation

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