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Bell curve in human performance questioned
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Bell curve in human performance questioned

  #1 (permalink)
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Bell curve in human performance questioned

Very short NPR article here:

Put Away The Bell Curve: Most Of Us Aren't 'Average' : NPR

If you want to hear the radio broadcast (about 5 minutes) please click on the speaker icon near the
top that says Listen to the Story next to it.

Also at the above link, if you look at the bottom of the page you will find the first page of about
300 comments on the subject. Some are actually interesting.

Excerpt of the article above is here:

"We looked at researchers, we looked at entertainers, we looked at politicians, and we looked at collegiate as well as professional athletes," Aguinis said in an interview. "In each of these kinds of industries, we found that a small minority of superstar performers contribute a disproportionate amount of the output."

These superstars, moreover, accounted for much of the success of the group as a whole. The vast majority of the others in the group, Aguinis said, were actually performing below the mathematical average.

======================================================================

The link below is the research paper that all this started from. It is not an easy or short read.
It is interesting though, like so many things that seriously challenge what we've been taught for so long.

I've excerpted some of it below in blue.





THE BEST AND THE REST: REVISITING THE NORM OF NORMALITY OF INDIVIDUAL PERFORMANCE

ERNEST O’BOYLE JR. , HERMAN AGUINIS

THE BEST AND THE REST: REVISITING THE NORM OF NORMALITY OF INDIVIDUAL PERFORMANCE - O’BOYLE JR. - 2012 - Personnel Psychology - Wiley Online Library

========================================================================

Our results suggest that the distribution of individual performance is such that most performers are in the lowest category. Based on Study 1, we discovered that nearly two thirds (65.8%) of researchers fall below the mean number of publications. Based on the Emmy-nominated entertainers in Study 2, 83.3% fall below the mean in terms of number of nominations. Based on Study 3, for U.S. representatives, 67.9% fall below the mean in terms of times elected. Based on Study 4, for NBA players, 71.1% are below the mean in terms of points scored. Based on Study 5, for MLB players, 66.3% of performers are below the mean in terms of career errors. Moving from a Gaussian to a Paretian perspective, future research regarding performance measurement would benefit from the development of measurement instruments that, contrary to past efforts, allow for the identification of those top performers who account for the majority of results. Moreover, such improved measurement instruments should not focus on distinguishing between slight performance differences of non-elite workers. Instead, more effort should be placed on creating performance measurement instruments that are able to identify the small cohort of top performers.

Along with testing for normality, our results also suggest that the methodological practice of forcing normality through outlier manipulation or deletion may be misguided. Dropping influential cases excludes the top performers responsible for the majority of the output, and doing so creates a sample distribution that does not mirror the underlying population distribution. As such, sample statistics will bear little resemblance to population parameters. Samples that exclude outliers generalize only to those individuals around the median of the distribution. Therefore, our second recommendation for research methodology is to shift the burden of proof from outlier retention to outlier deletion/transformation. That is, influential cases should be retained in the data set unless there is clear evidence that their value is incorrect (e.g., typographical error) or belong to a population to which the researcher does not wish to generalize. Regardless, the handling of influential cases should always be reported.


Last edited by stephenszpak; May 6th, 2012 at 02:19 AM.
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The average performer is a lot worse than average..


This certainly applies to the performance of mutual funds, where most of them underperform relative to their benchmarks.

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Known long time ago. It is the Pareto distribution.

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So is it this ....

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or this .....

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The researchers looked at:
==================================================================
We conducted 5 studies involving 198 samples including 633,263 researchers, entertainers, politicians, and amateur and professional athletes. Results are remarkably consistent across industries, types of jobs, types of performance measures, and time frames and indicate that individual performance is not normally distributed—instead, it follows a Paretian (power law) distribution.
==================================================================

They did not look at the general population. I don't know if you noticed that or not.
Your bell curve is about the entire population. If we took your graph we would have
to look only at the people that had 20 years of education. Apparently if we took only that
group we would NOT find a bell curve there.

This is really all my fault. I should have titled this post as: Bell curve does not fit population of
super-achievers, or something like that.
( S.S. )


=======================================================================

Results reported in Table 1 show that the Paretian distribution yielded a superior fit than the Gaussian distribution in every one of the 54 scientific fields...To interpret these results further, consider the field of Agriculture (see Table 1). A normal distribution and a sample size of 25,006 would lead to approximately 35 scholars with more than 9.5 publications (three standard deviations above the mean). In contrast, our data include 460 scholars with 10 or more publications. In other words, the normal distribution underestimates the number of extreme events and does not describe the actual distribution well.
=====================================================================

Using the U.S. House of Representatives as an example, the normal distribution suggests that of the 8,976 individuals to have served in the House, no more than 13 representatives should be three standard deviations above the mean (i.e., serve more than 13 terms). Contrary to the expectation based on the normality assumption, 173 U.S. Representatives have served more than 13 terms.
========================================================================

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dryg View Post
Known long time ago. It is the Pareto distribution.

They do indeed mention the Pareto distribution. This article is a little above my head.
I don't know if they are adding to his ideas or just restating them. They do have him as
a reference as: Pareto V. (1897). Le cours d’economie politique. London, UK : Macmillan.

If it is only a rehash of a powerful truth that was discovered in the 19th century, one wonders how long
it is going to take before papers like this recent one aren't surprising.

( S.S. )


=================================================================
Beyond concepts of ethics and fairness, a Paretian distribution of performance has many practical implications for how business is done. As we described earlier, a Pareto curve demonstrates scale invariance, and thus whether looking at the entire population or just the top percentile, the same distribution shape emerges. For selection, this means that there are real and important differences between the best candidate and the second best candidate. Superstars make or break an organization, and the ability to identify these elite performers will become even more of a necessity as the nature of work changes in the 21st century (Cascio & Aguinis, 2008b). Our results suggest that practitioners should focus on identification and differentiation at the tails of the distribution so as to best identify elites.
==================================================================

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So is it this ....

Where did you get that second picture from? Thanks.

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stephenszpak View Post
==================================================================

They did not look at the general population. I don't know if you noticed that or not.
Your bell curve is about the entire population. If we took your graph we would have
to look only at the people that had 20 years of education. Apparently if we took only that
group we would NOT find a bell curve there.

This is really all my fault. I should have titled this post as: Bell curve does not fit population of
super-achievers, or something like that.
( S.S. )


=======================================================================

@stephenszpak

I don't know if you noticed or not... I am not edumencated... I posted the chart because I thought it was purdy...


ReaM View Post
Where did you get that second picture from? Thanks.

@ReaM

Google search for IQ images

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Thanks!


Back in 2009 there was a moment I began to think I was retarded. You know how it is when life does not go the way you want it to, so I participated in Mensa test (I took the international) and scored 145. Today that's one of a few if not the only thing that keeps me going. I am retarded when it comes to speech.

I also wanted to take the SAT in 2010 for the same reason, but the train broke on the way to the test so I never took it.

I can't imagine being any more stupid than I think I am. I would then probably rely on feelings to solve problems. That would be a disaster.

I would agree with the article. Einstein, Leibnitz, Newton for example contributed a lot more than 99,99% of the rest of population

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