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Why Standard Deviation Should Be Retired From Scientific Use

Soulskill posted about 6 months ago | from the hope-it-gets-a-good-pension dept.

Stats 312

An anonymous reader writes "Statistician and author Nassim Taleb has a suggestion for scientific researchers: stop trying to use standard deviations in your work. He says it's misunderstood more often than not, and also not the best tool for its purpose. Taleb thinks researchers should use mean deviation instead. '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. The idea stuck: 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. 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.'"

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312 comments

Statistics add plausibility - maybe not meaning. (1)

Anonymous Coward | about 6 months ago | (#45969849)

And, in a word full of highly numerate simpletons, one must never forget this.

Would those data scientists with PhDs (-1, Troll)

Spy Handler (822350) | about 6 months ago | (#45969851)

happen to climate scientists? That would make a lot of sense.

Re:Would those data scientists with PhDs (0)

Anonymous Coward | about 6 months ago | (#45969933)

Not even close. As someone just a field or two over from climate science, I gotta say that I've never heard of a data scientist [wikipedia.org] before. They have nothing in common.

Re:Would those data scientists with PhDs (0)

Daniel Dvorkin (106857) | about 6 months ago | (#45970101)

Given that most of the buzz about "data science" seems to be in the business world, I'd say it's more lilkely they're corporate hacks working for the propaganda machine that's so effective on suckers like you.

Re:Would those data scientists with PhDs (1)

ISoldat53 (977164) | about 6 months ago | (#45970341)

They are vital to getting meaningful information out of a sea of data. Cancer research and particle physics use data scientists. Unfortunately so does amazon.com.

Re:Would those data scientists with PhDs (2, Interesting)

Daniel Dvorkin (106857) | about 6 months ago | (#45970685)

Cancer research and particle physics use data scientists. Unfortunately so does amazon.com.

Okay, since cancer research is a very large field, I can't say for sure one way or the other ... but I do know that working in bioinformatics at a major academic research center, I've never known a single person in medical research of any kind who called themselves a "data scientist." We have lots of computer scientists and statisticians, most of whom, fortunately, get along well enough to make use of each other's strengths. Regarding particle physics I have no idea, but yeah, I'm willing to bet Amazon or any other large corporation hires more "data scientists" than all the scientific institutions in the world put together--and gets exactly the kind of buzzword bingo they're paying for in return.

Re:Would those data scientists with PhDs (0)

Anonymous Coward | about 6 months ago | (#45970231)

No, it's more likely to be a public relations firm in the guise of a "grass roots" organization in the pockets of big oil. But we digress.

Re:Would those data scientists with PhDs (2)

segedunum (883035) | about 6 months ago | (#45970353)

Well, given that they think it's a great idea to take two different data sets measured in the same units, but measured in completely different ways, and put them together as a comparison over time then I'd say the definition of deviation is the least of their worries.

response (-1)

Anonymous Coward | about 6 months ago | (#45969861)

First!

Re:response (2)

clj (153252) | about 6 months ago | (#45970193)

I don't know which is more foolish, thinking that saying nothing, but saying it first, is a worthwhile goal, or claiming to be first when you're not. No need for you to choose, however: you did both.

Re:response (0)

Anonymous Coward | about 6 months ago | (#45970301)

You forgot making a blatantly late fp just to elicit a reaction from someone, otherwise known as trolling. Someone with only six digits should know better FFS.

Re:response (5, Funny)

flibbajobber (949499) | about 6 months ago | (#45970251)

First!

... to within 0.5 standard deviations.

Actually, the more posts this story attracts, the more accurate your statement is, and the fewer standard deviations you are away from true first. Response times not being distributed in a Gaussian curve perhaps complicates things.

So you want to retire a statistical term... (5, Insightful)

Anonymous Coward | about 6 months ago | (#45969865)

...because people use it incorrectly in economics? Get bent. The standard deviation is a useful tool for statistical analysis of large populations.

Re:So you want to retire a statistical term... (5, Insightful)

Fouquet (753286) | about 6 months ago | (#45970447)

+1 this. The problem here is the author's impression that "social scientists" and economists are scientists. The groups that he excludes in the first paragraph (physicists) are scientists. Anyone attempting to implement a statistical model designed for a large (and Gaussian) data set on a small number of data points (as the article's example does) should expect to get an answer that is at best marginal. Any scientists who ever received even the most basic of statistics and/or data analysis training knows this. Understand the problem first, then take enough data points, then carry out your statistical analysis & formulate conclusions.

Basic Statistics (4, Insightful)

TechyImmigrant (175943) | about 6 months ago | (#45969895)

The meaning of standard deviation is something you learn on a basic statistics course.

We don't ask biochemists to change their terms because the electron transport chain is complicated.
We don't ask cryptographers to change their terms because the difference between extra entropy and multiplicative prediction resistance is not obvious.

We should not ask statisticians to change their terms because people are too stupid to understand them.

Re:Basic Statistics (5, Funny)

Mr D from 63 (3395377) | about 6 months ago | (#45970029)

We should not ask statisticians to change their terms because people are too stupid to understand them.

But doesn't that give an unfair advantage to statisticians? You have to give everyone a chance!

Re:Basic Statistics (3, Insightful)

Fly Swatter (30498) | about 6 months ago | (#45970355)

Someone should tell that to the lawyers!

Re:Basic Statistics (1)

JoeMerchant (803320) | about 6 months ago | (#45970037)

Actually, meaningful and readily understood labels are a considered a good thing, and beneficial to those who work in the field they apply to.

Except programming, there, based on my experience, you should use whatever label happens to be laying around - never change it, even if it means the opposite of what it does.

Re:Basic Statistics (0)

Anonymous Coward | about 6 months ago | (#45970041)

You've misunderstood. Please read the post again.

Re:Basic Statistics (0)

Anonymous Coward | about 6 months ago | (#45970075)

We don't ask biochemists to change their terms because the electron transport chain is complicated.
We don't ask cryptographers to change their terms because the difference between extra entropy and multiplicative prediction resistance is not obvious.

We should not ask statisticians to change their terms because people are too stupid to understand them.

Nuclear Resonance Imaging (NMR) was changed because people were afraid of word Nuclear despite it describing the process, unlike its replacement term.

Re:Basic Statistics (1)

almitydave (2452422) | about 6 months ago | (#45970243)

And yet, everyone refers to the act of cooking in a microwave as "nuking," and no one seems to have a problem with that.

Re:Basic Statistics (0)

Anonymous Coward | about 6 months ago | (#45970375)

Generally speaking, I am not inside the microwave while it is in use.

Inside the microwave? (0)

Anonymous Coward | about 6 months ago | (#45970691)

Have you checked to see if you're oscillating while it is in use? That might be why you're not inside it, I think you're supposed to be both the particle and the wave unless you check.

Re:Basic Statistics (0)

Anonymous Coward | about 6 months ago | (#45970759)

Well some do, there are those that think food cooked in a microwave oven is bad for you (and in a way not connected to the preservation and break down of various nutrients versus other cooking methods) and that water heated in a microwave will kill plants.

Regardless, almost every use of NMR outside of medical imaging still calls it NMR.

Re:Basic Statistics (2)

Fouquet (753286) | about 6 months ago | (#45970561)

Not in actual physics labs, it wasn't. The change to MRI is only in public facing applications.

Re: Basic Statistics (1)

scrote-ma-hote (547370) | about 6 months ago | (#45970727)

Are you sure it wasn't because there was already a nuclear medicine department in hospitals, band that might cause confusion. Cause people don't seem so upset about radionucliotide scanning...

The big picture (1)

Okian Warrior (537106) | about 6 months ago | (#45970127)

We should not ask statisticians to change their terms because people are too stupid to understand them.

I've always wondered about this attitude.

For me, any change requires an analysis of risk/reward versus value. For example, if code contains confusing names, it might be worthwhile to refactor it.

The tradeoff is in the time spent refactoring versus the perceived value - if it's a mature product that largely works with few planned updates and few people will have to deal with the confusion, then the effort outweighs the returned value. If the code is open source, being actively developed and with many eyes looking at it, there may be a great deal of value in making it easier to understand.

The same could be said of English versus Metric measurements. Why should the US change to use the new system when everyone understands the one we have?

If the Federal Reserve sometimes gets it wrong, there may be great value in changing terms. The effort to fix the mistakes people make might be a good deal less effort than changing the terms used by a subset of mathematicians.

You can look at the big picture and see changes that would return a large overall/distributed value, or you can look at small groups and see that making those changes would cost them time and effort.

Is it too much to ask statisticians to look at the big picture?

Re:The big picture (1)

PRMan (959735) | about 6 months ago | (#45970227)

Especially when in Visual Studio you can right-click and Rename throughout the project. I change names that don't make sense and change them to what makes sense all the time.

Re:The big picture (4, Funny)

boristhespider (1678416) | about 6 months ago | (#45970405)

I often change CSensiblyNamedClassThatDescribesItsFunctionWell to bTrue throughout the code for precisely this reason and no-one ever appreciates it :(

Re:The big picture (1)

flyingfsck (986395) | about 6 months ago | (#45970291)

Everyone understands the US Measures? How many pottles are there in a firkin? Or how many nails in a chain?

Re:The big picture (1)

Okian Warrior (537106) | about 6 months ago | (#45970387)

Everyone understands the US Measures? How many pottles are there in a firkin? Or how many nails in a chain?

Everyone else understands what I meant.

What are you going on about?

Re:Basic Statistics (1)

ClintJCL (264898) | about 6 months ago | (#45970151)

If only scientists were statisticians, your comment might have actually been actionable.

Re:Basic Statistics (3, Informative)

ShanghaiBill (739463) | about 6 months ago | (#45970173)

The meaning of standard deviation is something you learn on a basic statistics course.

I took a statistics course in college. The statistics professor taught us to think of the standard deviation as the "average distance from the average". So if you know the average (mean) then any random data sample will be (on average) one SD away. That is simple, neat, and easy to remember.

It is also wrong.

Re:Basic Statistics (1)

TsuruchiBrian (2731979) | about 6 months ago | (#45970573)

All you need to know is SOCATOA, whatever the fuck that means.

Re:Basic Statistics (3, Interesting)

Mashdar (876825) | about 6 months ago | (#45970181)

Didn't you hear? Guassians are so 1893. And so are all of the other distributions with convenient sigma terms...

And TFS calls standard deviation "root mean square error", which is only true if you assume the mean is a constant estimator for the distribution :(

In any case, no one picked Gaussians because they are so easy to integrate... While we're at it, TFA should suggest we round the number e to 3, because irrational numbers are hard, and who cares what natural law dictates.

Re:Basic Statistics (5, Funny)

gninnor (792931) | about 6 months ago | (#45970311)

Then it would be the same as pi, and that would just be silly.

Re:Basic Statistics (1)

boristhespider (1678416) | about 6 months ago | (#45970425)

Not at all. If e^pi = pi^e then a common interview question would be a hell of a lot easier to answer.

Re:Basic Statistics (2)

wonkey_monkey (2592601) | about 6 months ago | (#45970553)

Mmm, pi^e.

Re:Basic Statistics (1)

MobyDisk (75490) | about 6 months ago | (#45970267)

We should not ask statisticians to change their terms because people are too stupid to understand them.

The author didn't ask anyone to change any terms. They asked people to stop using the wrong statistic. Ex: Don't use mean if you needed the median.

Re:Basic Statistics (1)

fermion (181285) | about 6 months ago | (#45970649)

I can't really get to the article right now, but one this that is true is that Standard deviations only make sense if a sample results in a normal distribution. Normal distributions has certain qualities, one is that the mean=median=mode. If this is not true then one can still have a skewed normal curve. Many distributions a skewed normal curves, which means that a standard distribution is not necessarily the best model. Yet they are still used. This can be a problem. Here is why standard deviation is so important as a statistic. If one has a normal distribution, and one knows, for example that that a part has a nominal length of 1 cm and historical data shows that the machine makes the part with a standard distribution of 0.05 cm, then one has some confidence that almost 70% of the parts will be between 0.95 cm and 1.05 cm. Such knowledge is critical when putting things together and warranty issues. Over time if the parts are out of this range, or if the average changes, then one knows the machine is broken. There are distibutions that are normal. There are many that are not, like distribution of wealth. As far as I can tell stating an average and a distribution in that is pretty silly.

Re:Basic Statistics (1)

Daniel Dvorkin (106857) | about 6 months ago | (#45970705)

The replacement the article proposes (mean absolute deviation or MAD) is also only particularly meaningful if you're dealing with a symmetric distribution, so it really doesn't address the problem you identify.

Re:Basic Statistics (2)

gninnor (792931) | about 6 months ago | (#45970733)

Honestly, of the different things I have studied all had jargon that could have been explained in simpler terms, often in shorter common words. So much of it is a wall to the "stupid" people and their understanding.

Other times there are specific concepts with only one word. These need to be simplified and taught to when it is being introduced in journals, but that would be work and very few people have been trained to speak to laymen.

Even within the sciences some shorthand jargon means one thing in chemistry and another in in biochemistry.

Issues (5, Informative)

Edward Kmett (123105) | about 6 months ago | (#45969913)

On the other hand, you also need to use 2-pass algorithms to compute Mean Absolute Deviation, whereas STD can be easily calculated in one pass. And you still need standard deviation as it relates directly to the second moment about the mean.

Also, annoyingly, Median Absolute Deviation competes for the MAD name and is more robust against outliers.

Re:Issues (2)

Animats (122034) | about 6 months ago | (#45970007)

On the other hand, you also need to use 2-pass algorithms to compute Mean Absolute Deviation, whereas STD can be easily calculated in one pass. And you still need standard deviation as it relates directly to the second moment about the mean.

Right. Some common measures in statistics date from the paper and pencil era, back when computation was really expensive. The same issue applies to least mean squares curve fitting, which is cheap to compute but overweights values far from the curve. This is well known, and was recognized decades ago. This is not something Talib "discovered", or even popularized.

(If you want to annoy Taleb and his flunkies, ask hard questions about the actual performance of his funds in years other than 2008.)

Re:Issues (1)

Anonymous Coward | about 6 months ago | (#45970451)

The same issue applies to least mean squares curve fitting, which is cheap to compute but overweights values far from the curve.

Sadly, minimizing MAD leads to multiple solutions and that's why I normally use least means squares instead of least absolute mean.

Re:Issues (1)

Okian Warrior (537106) | about 6 months ago | (#45970155)

On the other hand, you also need to use 2-pass algorithms to compute Mean Absolute Deviation, whereas STD can be easily calculated in one pass.

Okay, just to be clear: you're saying that we should use STD because (in part) it's faster and easier to calculate?

Isn't that like the drunk looking for his keys under the lamppost - instead of where he dropped them - because the light is better?

Re:Issues (0)

Jane Q. Public (1010737) | about 6 months ago | (#45970497)

"On the other hand, you also need to use 2-pass algorithms to compute Mean Absolute Deviation"

Since when?

Pseudo-code:

1) Start with S = 0 and I = 0.

2) For each data point starting with the second:

3) Add 1 to I. S = S + absolute value of (this data point - previous data point).

4) When all the data points are collected, MAD = S / I

Where's the difficulty?

Re:Issues (1)

Edward Kmett (123105) | about 6 months ago | (#45970679)

Sadly, the problem is your proposed algorithm doesn't work.

Consider the sequence [1,2..100], The real mean absolute deviation is 25.

Your algorithms yields er.. something around 1?

Mean absolute deviation requires you to sum over a bunch of absolute values of differences to a number you don't know a priori.

Unlike stddev's use of x^2, abs doesn't have a continuous derivative and can't be split out into calculations in terms of the moments around 0, and you can't borrow Chan's algorithm.

Basically, to my knowledge, there isn't a sufficient statistic you can accumulate for MAD (either version of MAD) that takes less space than the original data.

Re:Issues (1)

wonkey_monkey (2592601) | about 6 months ago | (#45970687)

Data points: 1 2 10

First pair: (1,2). S = 0+abs(1-2) = 0+1 = 1
Second pair: (2,10). S = 1+abs(2-10) = 1+8 = 9
MAD=9/2=4.5
----
Data points: 1 10 2

First pair: (1,10). S = 0+abs(1-10) = 0+9 = 9
Second pair: (10,2). S = 9+abs(10-2) = 9+8 = 17
MAD=17/2=8.5
----
Two different results from the same data points. Have I misunderstood something?

That's not the problem. (4, Insightful)

khasim (1285) | about 6 months ago | (#45969919)

The problem is that people think they understand statistics when all they know is how to enter numbers into a program to generate "statistics".

They mistake the tools-used-to-make-the-model for reality. Whether intentionally or not.

Re:That's not the problem. (4, Interesting)

Deadstick (535032) | about 6 months ago | (#45969987)

Three characterizations of statistics, in ascending order of accuracy:

1. There are lies, damned lies, and statistics.

2. Figures don't lie, but liars figure.

3. Statistics is like dynamite. Use it properly, and you can move mountains. Use it improperly, and the mountain comes down on you.

Re:That's not the problem. (2)

dcollins (135727) | about 6 months ago | (#45970493)

In Soviet Russia, improper statistics puts you up on mountain.

Re:That's not the problem. (5, Insightful)

JoeMerchant (803320) | about 6 months ago | (#45970107)

The problem is that peoples' attention spans are rapidly approaching that of a water-flea.

Up until the past 50 or so years, people who learned about Standard Deviation would do so in environments with far less stimulation and distraction. Their lives weren't so filled with extra-curricular activities and entertainments that they never sat for a moment from waking until sleep without some form of stimulus based pastime. When they "understood" the concept, there was time for it to ruminate and gel into a meaningful set of connections with how it is calculated and commonly applied. Today, if you can guess the right answer from a set of 4 choices often enough, you are certified expert and given a high level degree in the subject.

Not bashing modern life, it's great, but it isn't making many "great thinkers" in the mold of the 19th century mathematicians. We do more, with less understanding of how, or why.

Re:That's not the problem. (0)

Anonymous Coward | about 6 months ago | (#45970309)

Ha! My squirrel ate your water-flea

Re:That's not the problem. (1)

khasim (1285) | about 6 months ago | (#45970343)

Up until the past 50 or so years, people who learned about Standard Deviation would do so in environments with far less stimulation and distraction.

They also did so in an environment where they had to do all the math by hand (or with a slide rule).

The math is not difficult. But it is repetetive in the extreme. So unless you were a savant you learned to pay very close attention to the numbers and what they represented. For those of you who didn't take statistics, here's a link to show you how standard deviation is calculated. With only 6 items:
http://www.wikihow.com/Calculate-Standard-Deviation [wikihow.com]

Imagine doing that, by hand, with a hundred items. And that is just finding the standard deviation.

Now you can get the "answer" with nothing more than copy-paste. And if that "answer" doesn't suit you then you tweak the input and get another "answer" a second later.

Re:That's not the problem. (1)

Nemyst (1383049) | about 6 months ago | (#45970725)

I really, really wish I could finish my Master's just by guessing the right answer on a multiple-choices exam. Sadly, it would appear that either you're wrong, or I've picked a subject where that gross oversimplification does not apply. Either way, I think you're being blinded by your nostalgia goggles.

Re:That's not the problem. (3, Informative)

TsuruchiBrian (2731979) | about 6 months ago | (#45970747)

Not bashing modern life, it's great, but it isn't making many "great thinkers" in the mold of the 19th century mathematicians. We do more, with less understanding of how, or why.

The easier math problems are lower hanging fruit. As time goes on, the problems that are left become increasingly hard. Even when they get solved, average people can't understand what it means, and that makes it hard to care about, and hward for newspapers to make money covering that story.

Also when you read about the history of mathematics, it's easy to feel like these breakthroughs were happening all the time, compared with now, when in fact they were very slowly, and the pace of discovery is probably higher now than at any point in the past.

It's easy to say music was better in the 70's than now when you condense the 70's down to 100 truly great songs, forgetting all the crap, and compare it to whats playing on the radio today.

because we're so perfect (0)

Anonymous Coward | about 6 months ago | (#45969939)

error free written right in to our scriptdead pretense.

Useful in some situations but nonsense in others (0)

Anonymous Coward | about 6 months ago | (#45969983)

If the value being measured is a voltage or current the square is proportional to energy (or power) so standard deviation has an important physical interpretation. In other applications it could be worthless. No one measure works for all cases - apply the correct tool for the job.

Standard Deviation is Important (5, Informative)

njnnja (2833511) | about 6 months ago | (#45970005)

Standard Deviation is the square root of the second moment about the mean [wikipedia.org] , an important fundamental concept to probability distributions. Looking at moments of probability distributions gives us lots of tools that have been developed over the years and in many cases we can apply closed form solutions with reasonably lenient assumptions. Then we apply the square root in order to put it in the same units as the original list of observations and get some of the heuristic advantages that he attributes to the mean absolute deviation.

But it is a balance, and any data set should be looked at from multiple angles, with multiple summary statistics. To say MAD is better that standard deviation is a reasonable point (with which I would disagree), but to say we should stop using standard deviation (the point made in TFA) is totally incorrect.

Re:Standard Deviation is Important (1, Informative)

Anonymous Coward | about 6 months ago | (#45970103)

This.

Standard Deviation is the square root of the second moment about the mean [wikipedia.org] , an important fundamental concept to probability distributions.

More generally, it is the L^2-norm of deviation from the mean which will open up theory for Hilbert spaces and functional analysis in general. Try to beat that. You shouldn't discard anything because people use it wrong. You should teach students today to use it right instead. p-value has been as big, if not bigger, a problem.

Re:Standard Deviation is Important (2)

JanneM (7445) | about 6 months ago | (#45970287)

What he is saying is not that statisticians should stop using SD in statistical theory or anything. What he's saying is that non-statisticians should stop using SD as a measure of variability when describing their data to each other. And since everybody (except statisticians) think SD is the average deviation from the mean, then people should perhaps use that instead, and reduce confusion for everyone.

Re:Standard Deviation is Important (0)

Anonymous Coward | about 6 months ago | (#45970433)

I'm not a statistician and I knew what standard deviation is. Granted, I'm a mathematician.

Re:Standard Deviation is Important (0)

Anonymous Coward | about 6 months ago | (#45970519)

We have so much theory on second moment distributions because those happen to be mathematically convenient --- you can calculate all sorts of useful properties from first principles using pencil and paper. However, most work today is done with different tools from pencil and paper; it's easy to use a computer to numerically calculate all sorts of stuff that would be prohibitatively difficult without analytical shortcuts "by hand."

Since few people bother to understand the analytical theory anyway, perhaps there are good reasons to switch to more "brute force" computationally intensive methods (which may be easier to explain/understand, even if they take more arithmetical operations to carry out). Instead of approximating everything as Gaussian distributions (because they're analytically tractable), researchers can now numerically manipulate arbitrary probability distributions and carry them all the way through calculations. Performing statistics on arbitrary probability distributions will prevent people from making bad simplifying assumptions because they don't understand how the magical analytical tricks work --- it's computationally harder, but, in a sense, conceptually clearer.

Re:Standard Deviation is Important (3, Insightful)

neonsignal (890658) | about 6 months ago | (#45970677)

I'm a little surprised at Nassim Taleb's position on this.

He has rightly pointed out that not all distributions that we encounter are Gaussian, and that the outliers (the 'black swans') can be more common than we expect. But moving to a mean absolute deviation hides these effects even more than standard deviation; outliers are further discounted. This would mean that the null hypothesis in studies is more likely to be rejected (mean absolute deviation is typically smaller than standard deviation), and we will be finding 'correlations' everywhere.

For non-Gaussian distributions, the solution is not to discard standard deviation, but to reframe the distribution. For example, for some scale invariant distributions, one could take the standard deviation of the log of the values, which would then translate to a deviation 'index' or 'factor'.

I agree with him that standard deviation is not trustworthy if you apply it blindly. If the standard deviation of a particular distribution is not stable, I want to know about it (not hide it), and come up with a better measure of deviation for that distribution. But I think the emphasis should be on identifying the distributions being studied, rather than trying to push mean absolute deviation as a catch-all measure.

And for Gaussian distributions (which are not uncommon), standard deviation makes a lot of sense mathematically (for the reasons outlined in the parent post).

Education!! (2)

RichMan (8097) | about 6 months ago | (#45970057)

There is a great difference between a mean value and an RMS value. Scientific people can work with the appropriate version so I don't see a problem with using the correct one for the correct occasion. And certainly science should stay with the correct term as appropriate.

What I believe the person is calling for here is the most appropriate use when communicating to the non-scientific person. This is an education issue in that the communication really should not use either term as a shorthand but should explain in full the effect of the distribution. Science uses mean and standard deviation (often also requiring a named distribution) because they are shorthands that describe the random behavior and have full meaning without any other explanation needed. So I say use neither term when communicating to the non-scientific as they do not fulfill the communication role to which they are intended.

What I believe should actually be done is proper education of all so that they understand the differences between various random distributions and move totally away from a "it is cold today, so global climate change based on heating must be a lie".

Re:Education!! (1)

ZombieBraintrust (1685608) | about 6 months ago | (#45970125)

He isn't talking about Non Science people. He is talking about Social Science people and Science Journalist people. Both of whom have educations.

Re:Education!! (1)

Obfuscant (592200) | about 6 months ago | (#45970179)

He isn't talking about Non Science people. He is talking about Social Science people and Science Journalist people. Both of whom have educations.

So he is talking about Non Science people. Have you never read the output of a Science Journalist when they write about something you are familiar with?

"Hav[ing] an education" doesn't make one a scientist. Doing things the scientific way makes one a scientist.

Re:Education!! (2)

bunratty (545641) | about 6 months ago | (#45970143)

The problem with people accepting anthropogenic global warming is not a matter of understanding. It's a matter of people believing what they want to believe. If people want to believe in God and think that evolution diminishes the importance God or think that evolutions are saying that God doesn't exist, they look for any evidence that evolution doesn't happen, no matter how flimsy it is, to prevent having to feel uncomfortable emotions. If people believe that they have to give up a comfortable lifestyle to reduce carbon dioxide emissions, they will look for any evidence that AGW is incorrect, no matter how flimsy it is. You can see this behavior for what it is when people cling to a mistaken idea for dear life. In a way, they feel that their way of life does depend on that belief, because that belief is their way of comforting themselves.

Re:Education!! (2)

onkelonkel (560274) | about 6 months ago | (#45970765)

It is even worse than that with religious folk. All sorts of people will go into "Cognitive Dissonance" mode when their strongly held beliefs are challenged and some will refuse to change their beliefs no matter what evidence is presented. With religious people you get this plus also they are convinced that it is their faith (how strongly they cling to their beliefs - no matter what) that determines their reward in the afterlife. There is no point in attempting logical or evidence based discussions with someone like that.

WTF (0)

Anonymous Coward | about 6 months ago | (#45970079)

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

First, when the media reports on a scientific discovery, they report the researcher's stats - not they're own. So, if there's an error with the interpretation of STD, then it's the original researchers'.

Do you take every observation: square it, average the total, then take the square root? Or do you remove the sign and calculate the average? For there are serious differences between the two methods.

I suggest he publishes in a peer review journal instead of ... WTF is 'edge.org'???

"many with PhDs" (1)

Daniel Dvorkin (106857) | about 6 months ago | (#45970083)

If there are "data scientists" who don't understand what the standard deviation is, then they certainly shouldn't be calling themselves "data scientists," and quite possibly not scientists at all. What subjects are their PhDs in, I wonder? This doesn't do anything to reduce my skepticism that such a thing as "data science" really needs to exist.

Roadway Intersections (1)

Okian Warrior (537106) | about 6 months ago | (#45970247)

If there are "data scientists" who don't understand what the standard deviation is, then they certainly shouldn't be calling themselves "data scientists," and quite possibly not scientists at all. What subjects are their PhDs in, I wonder?

The problem isn't with highly-educated people, it people who are not highly educated, or who are highly educated but in a different field.

If a particular intersection attracts a lot of accidents, we consider the accidents to be the fault of the drivers involved. But at the same time, we recognize that aspects of the intersection might be a contributing factor as well.

Expert drivers would never have such accidents, but if we spend some effort reblocking the intersection we could get improved safety, and sometimes there is value in doing this.

Like the roadway intersection, if a term is so confusing that average people make mistakes because of it, there may well be value in changing to easier-to-understand terms.

Re:Roadway Intersections (0)

Anonymous Coward | about 6 months ago | (#45970435)

"...Expert drivers would never have such accidents..."

A completely ridiculous assumption.

Re:"many with PhDs" (0)

Anonymous Coward | about 6 months ago | (#45970305)

Sociologists are notorious for misusing statistics. I've perceived this for a long time. I'd love to see a citation for Taleb's claim that it's been shown that the majority of sociologists misuse statistics, because there are lots of people who need it thrown in their face.

Re:"many with PhDs" (1)

Anonymous Coward | about 6 months ago | (#45970407)

Hi. Ph.D. in data science and network analysis here. First, I consider my statistics background among my peers to be somewhat lacking, because I have chosen to specialize more in graph theory. Even so, I understand at a very deep level a concept as simple as standard deviation, and I doubt very much anybody with a Ph.D. who would call himself a data scientist does not. This article is offensive, frankly.

Second, you may have skepticism, but data scientists operate at an interesting and challenging intersection of hardware and parallelism challenges in processing huge data sets, hardcore statistics, data mining principles and machine learning algorithms, and often network science to name a few skills. What other existing specialization in computer science, physics, etc,. do you feel is qualified to use Hadoop to process trillions of triple stores into a network and subsequently build highly multivariate link prediction models and evaluate their output statistically with respect to ground truth, to name but one trifling task?

Re:"many with PhDs" (3, Interesting)

Daniel Dvorkin (106857) | about 6 months ago | (#45970619)

What other existing specialization in computer science, physics, etc,. do you feel is qualified to use Hadoop to process trillions of triple stores into a network and subsequently build highly multivariate link prediction models and evaluate their output statistically with respect to ground truth, to name but one trifling task?

As it happens, one of my colleagues runs a project which, among other things, does exactly that. His PhD is in computer science. I'm a bioinformaticist with a background primarily in biostatistics; I couldn't develop a tool like that, but I can certainly see the value in it. In general, I'm not arguing that the tasks currently getting lumped together under "data science" aren't valuable. I'm just saying that I'm not convinced they fit together into a coherent field that can meaningfully be studied in a single degree program, and attempts to make them so may well run into the problem of "jack of all trades, master of none."

Yes, use the interquartile range instead (1)

G3ckoG33k (647276) | about 6 months ago | (#45970105)

Yes, use the interquartile range instead https://en.wikipedia.org/wiki/Interquartile_range [wikipedia.org]

It is like the median a very robust method, not readily influenced by outliers. https://en.wikipedia.org/wiki/Median [wikipedia.org]

The median is wickedly robust, with a breakdown point at 50%, meaning that you can throw a huge a mount of junk data at it and it still doesn't care.

The arithmetic mean and the standatd deviation are both junk, often worse than the too-often-assumed-normal data thrown at it.

Circular error probable. (0)

Anonymous Coward | about 6 months ago | (#45970651)

Cep of 50% and 10 meters means half the missiles land on your house, and half on your neighbors. A fine measure

FRIST SToP (-1)

Anonymous Coward | about 6 months ago | (#45970131)

posts. TherefoRe

How about "somewhere in the middle" (1)

sandbagger (654585) | about 6 months ago | (#45970133)

That's a good enough replacement term.

Why eliminate it? (0)

Anonymous Coward | about 6 months ago | (#45970147)

Properly educating the world on this problem would likely take no more effort than convincing everyone to stop using standard deviation. To that end, why eliminate something that (apparently) has widespread use?

Same trick, different pony (1)

Blackajack (1856892) | about 6 months ago | (#45970169)

My college math teacher made a special point of warning us that journalists almost always mix up pct and pp. Sometimes they even do that on purpose!

Re:Same trick, different pony (0)

Anonymous Coward | about 6 months ago | (#45970241)

Ooh, you took college "math"? Did you take college "history" and "gym," too?

Use "Margin of error" (1)

sinequonon (669533) | about 6 months ago | (#45970171)

If you don't like the term "standard devation", use "margin of error" instead.

Standard deviation BAD, but mean GOOD? (4, Interesting)

PacoSuarez (530275) | about 6 months ago | (#45970275)

Perhaps non-mathematicians don't have a problem with this, but it rubs me the wrong way.

What makes the mean an interesting quantity is that it is the constant that best approximates the data, where the measure of goodness of the approximation is precisely the way I like it: As the sum of the squares of the differences.

I understand that not everybody is an "L2" kind of guy, like I am. "L1" people prefer to measure the distance between things as the sum of the absolute values of the differences. But in that case, what makes the mean important? The constant that minimizes the sum of absolute values of the differences is the median, not the mean.

So you either use mean and standard deviation, or you use median and mean absolute deviation. But this notion of measuring mean absolute deviation from the mean is strange.

Anyway, his proposal is preposterous: I use the standard deviation daily and I don't care if others lack the sophistication to understand what it means.

Re:Standard deviation BAD, but mean GOOD? (0)

Anonymous Coward | about 6 months ago | (#45970575)

Ah, thank you! The most intelligent comment I've read here. I just hope everyone reads it. Most importantly:

The constant that minimizes the sum of absolute values of the differences is the median, not the mean. So you either use mean and standard deviation, or you use median and mean absolute deviation. But this notion of measuring mean absolute deviation from the mean is strange.

I hate averages (5, Interesting)

tthomas48 (180798) | about 6 months ago | (#45970337)

I also think averages should go away. Most people think they are being reported the median (the number in the middle) when people tell them the average. It's great for real estate agents, and people trying to advocate for tax reform, but the numbers are not what people think they are.

Revisiting a 90-year-old debate: Advantages of MAD (1)

Anonymous Coward | about 6 months ago | (#45970359)

Food for thought: "Revisiting a 90-year-old debate: the advantages of the mean deviation"

http://www.leeds.ac.uk/educol/documents/00003759.htm

SD in life sciences (0)

Anonymous Coward | about 6 months ago | (#45970397)

When taking measurements (such as protein concentration in blood) we are forced by the magazine editors to inform SD as an error estimate. That is in my view plainly wrong, as the SD is an estimate of the population variance. I try to use what is known as standard error of the mean (SEM) (mean deviation in TFA).

Confused Taleb (1)

Anonymous Coward | about 6 months ago | (#45970403)

Didn't Taleb warn us about the perils of modeling things with normal distributions that fail to capture outliers ("Black Swans") and yet now he advocates the use of a stastical measure that conceals^H^H^H^H^H is robust with respect to outliers?

Oh well, next year he'll probably come up with something along the lines of "Monte Carlo methods major cause of global warming, return to analytic methods and moments unavoidable truth"...

Incorrect identification of the problem. (0)

Anonymous Coward | about 6 months ago | (#45970411)

The problem is not that standard deviation is confusing. The problem is that sociologists need to learn how to apply statistics. Either the majority of sociology PhDs are ignorant of statistics, or they've mastered the art of selecting a politically desirable conclusion and misapplying statistics to support it.

Bell Curve (1)

samwhite_y (557562) | about 6 months ago | (#45970421)

I find this article quite confusing. Is the actual suggestion that we should be going around using the mean deviation as a way of capturing the general variance of our data sets? Or to put it another way, does he want "deviation" measures not to give us a real sense of the larger deviations that might occur with some real probability. For example, with temperatures, standard deviation is more likely to suggest that we can have periods of significantly higher and lower temperatures than a simple "mean deviation".

Adding to my confusion is that there is no reference to articles, books, or other subject material that supports the general thesis. If the "mean deviation" is better than the "std deviation", give some real concrete examples and supporting mathematics.

Also, there seems to be no reference to "bell curve" distributions and "non bell curve" distributions. Standard deviation computations are built around bell curve distributions for their mathematical soundness. For example, if I were to take every number and raise it the fourth power, standard deviation would not work so well on this new set of numbers. Is the author suggesting that typical sampling distributions of sampled events tend not to be "bell curve" like?

Standard deviation is taught in 7th grade in my local school. It shows up constantly in any standard K-12 curriculum. To challenge this, you really should bring a lot more substance to any argument that we should do things differently.

For example, I could argue that we should use 1:2 to represent 1/2 because the slash (/) should be used for logical dependency arguments instead. I could create lots of examples and go into a diatribe about how people constantly misuse fractions and ratios because they use a slash in their construction. But I would still be spouting nonsense.

Mean Deviation is Always Zero (3, Interesting)

dcollins (135727) | about 6 months ago | (#45970423)

Well... first of all, summary has it wrong. It's not "mean deviation", it's "mean absolute deviation", or just "absolute deviation" from the literature I've seen. (Mean deviation is actually always zero, the most useless thing you could possibly consider.)

Keep in mind that standard deviation is the provably best basis if your goal is to estimate a population *mean*, the most commonly used measure of center. Absolute deviation, on the other hand, is the best basis to use for an estimate of a population *median*, which is maybe fine for finances, which is what the linked paper seems mostly focused on. (Bayesian best estimators, if I recall correctly.)

If the main critique is that economists and social scientists don't know what the F they're doing, then I won't disagree with that. But no need to metastasize the infection to math and statistics in general.

The example is flawed (1)

Glires (200409) | about 6 months ago | (#45970455)

The example in the article isn't even an example of a standard deviation. He may have plugged his five values into the RMS formula, but what it produced isn't an actual standard deviation because five values is too small of a sample size.
This article is really a demonstration of why people should stop misusing the term "standard deviation" than it is an argument of why people should stop using standard deviation.

Know it, use it. (2)

ExXter (1361251) | about 6 months ago | (#45970517)

I studied geodesy in germany as diploma on a technical university. Standard deviation has its right to exist and to be there and to be used. If this man really means what he says he should not say to abandon standard deviation but to write BOOKS that teach people correctly what it is and how it is calculated on the data which you have. Yes I also meet people (talking of themselves as scientists and researchers) who have no fucking clue how to work with data and standard deviation, but on the other hand I also meet alot who know and also derive the right conclusions, formulars or algorithms out of these. For me this guy sounds like a mad panda who just didn't get it right...

Using MAD moves in the wrong direction (0)

Anonymous Coward | about 6 months ago | (#45970577)

He says that standard deviation gives too much weight to tail events.

But I think the bigger problem in finance is under weighting tail events.

Taleb doesn't live in a normal world (1)

Yoik (955095) | about 6 months ago | (#45970611)

When I was in school, they still taught the central limit theorem which explains why so many error distributions are "normal". Our world provides us with millions of examples in everyday life where the standard deviation of our experiences is the best statistic to estimate the probability of future events.

What you do with a statistic is what counts. It's easy to look at the standard deviation and estimate the probability that the conclusion was reached by chances of the draw, though it takes some practice to develop your intuition. It is imbedded in our language when we talk of "6 sigma" reliability or " 4 sigma" thinkers. Anyone who thinks he is a scientist should understand this!

Mr. Taleb may be working in a field where normal distributions are rare, but the probability is he is either lying or poorly educated.

he does have a point, but maybe goes too far (1)

dsoodak (3022079) | about 6 months ago | (#45970627)

I agree that mathematicians may become imprinted on standard deviation and forget that it is only used because it is easier to work with than average absolute deviation (ex: the derivative of x^2 is continuous, unlike abs(x)), and that less technically inclined readers might not realize there is a difference. However, they ARE usually pretty close (I don't have a reference, but I once ran a simulation comparing the 2 using random data with a Gaussian distribution and the curves matched exactly), and its harder to find exact solutions with average absolute deviation. On the other hand, it wouldn't hurt to use "MAD" occasionally on a data set to make sure that the standard deviation gives results that are meaningful as a measure of "deviation".

. . . in Social and Biological Sciences (1)

dmatos (232892) | about 6 months ago | (#45970665)

That's what he concludes at the bottom of the article. He starts the article by saying that standard deviation should only be used by physicists, mathematicians, and mathematical statisticians. If I'm not mistaken, "physics" and "math" covers a whole lot of different fields, including most of the STEM fields that (largely) define the users of this site.

I know in my particular field (physics based), standard deviation is a hell of a lot more useful than mean average deviation. And easier to use.

Bah. I call poor summary.

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