Here's the story on NPR:
http://www.npr.org/2012/05/03/151860154/put-away-the-bell-curve-most-of-us-arent-average

And the associated research article: http://onlinelibrary.wiley.com/doi/10.1111/j.1744-6570.2011.01239.x/full

Now discuss!

Mmm, is there a statistician in the house? Did a competent statistician review this paper, do you think? I'm not one, but it does strike me that it may be important that in a group of Emmy nominees it isn't possible to have been nominated less than 1 time, and in the whole population it isn't possible to have been nominated less than 0 times! In fact, I don't see how on earth anyone could have claimed with a straight face that they'd expect this to be normally distributed, so finding that it isn't doesn't seem noteworthy to me.

Nevermind the fact that the moment you start talking about Emmy nominees, your entire sample group is outliers. What percentage of SAG cardholders is ever nominated?

DD7 said to us at dinner last month, "Did you know that alamost everyone in the world has more than the average number of legs?" I thought about it for a minute, then agreed that she was right. That article has less insight than she did.

I think it's best to review the actual article (which actually is quite heavy on the stats indeed) before we start taking potshots at the simplistic NPR coverage. I'm distracted at the moment, but I'm not actually grasping the original article that well myself; however, it's definitely occurred to me to wonder why we assume that the bell curve is a constant.

It's very frustrating to see papers like this getting published. Part of the problem, IMO, is that the reviewers are as clueless as the authors.

This paper on "values affirmation" as a way of raising the GPAs of certain students is risible, yet got published in Science!

Because the Central Limit Theoren says that for *any* distribution of an underlying variable, for a large enough value of N, a normal distribution will be observed.

I won't claim to have read the paper exactly, but I did glance through it before I took the potshot :-)

Once you've read the article, the real potshots will begin.

I'll give you a hint: AVN.

I think my favorite potshot so far is the indirect one by the seven-year-old who observed that most people have more than the average number of legs.

The comments at the NPR site echo some of the criticisms made here.

Which is entirely true.

I think ultramarina's question is a good one. The Central Limit Theorem doesn't say that the empirical distribution will be normal. It says that with a large enough N, the distribution of the sample means will be approximate a normal distribution around the population mean. It is about determining whether your sample is representative of the population, not that the empirical data itself is normally distributed.

The assumptions regarding the bell curve come from a different source than the central limit theorem. I don't really have time to read the actual journal article, but I am guessing that it is being described inaccurately by the NPR coverage (as is often the case).

For those that didn't read the article, AVN is "Adult Video News". That must have been "hard" research.

Sorry, couldn't resist.

Ok, I skimmed through the article, and I am puzzled first and foremost about its purpose.

People who deal with stats on a regular basis don't believe that all distributions are normal, so that is not the target. Consider queues, such as the queue for a bank teller or grocery cashier. It's well understood that an exponential distribution provides a good approximation for the time between people joining the queue. Stock returns are well known to approximate a log-normal distribution but with kurtosis (fat tails).

Ok, now I saw the top of the article and saw that it was published in Psychology Today. The PhDs in the subject are hopefully proficient in statistics, so I will generously speculate that the purpose of this article is to inform the practitioners that are less math savvy. It's just not groundbreaking research.

"We revisit a long-held assumption in human resource management, organizational behavior, and industrial and organizational psychology that individual performance follows a Gaussian (normal) distribution."

Apparently the goal of the article is to challenge these beliefs in these particular sub-disciplines. I guess. I find it strange, too, but it seems to be speaking to a very specific audience and wasn't really intended to be picked up more generally, imo. I am not familiar with these specific areas, though, so can't speak to how important this assumption (that performance is normally distributed)is for them.

As a humble social scientist (although not psychologist) myself, I would hope that my colleagues do not believe that all distributions are normal, but who knows?! lol

awesome.

I heard this on npr too, and did the same , 'huh?' SMALL but SIZEABLE kept making me wonder what on earth they MEANT, also.

The study is not published in Psychology Today (btw--Psychology Today has completely lost its credibility, IMO, by allowing all sort of crapola to be printed under its banner by unqualified bloggers). It's in Personnel Psychology, some sort of academic journal about, well, personnel pesychology. It has a pretty low impact rating and seems to be fairly obscure. I have no idea why this got picked up by NPR, truly. I follow social science press pretty closely and it continues to mystify me why some of these stories get hot. This is an example, because it's hard to make sense of and perhaps not all that exciting in the first place.


I went back and looked at it again, and I think you have it right.

Quote from the article.

"If you had a superstar performer working at your factory, well, that person could not do [a] better job than the assembly line would allow," Aguinis said. "If you unconstrain the situation and allow people to perform as best as they can, you will see the emergence of a small minority of superstars who contribute a disproportionate amount of the output."

For example, what this means from a work output perspective is that 10% of your programmers do 90% of the work. The work per individual is highly skewed. And I would suspect that the actual output, due to a detailed knowledge of the domain and very good skills, is actually higher. The low productivity of the others is masked by the team adopting the tools and approaches of the top workers, thus making them more productive.

This assumes that the field is amiable to someone being totally unconstrained. In a lot of cases, it is not. Ie, a superstar maintaining buggy code who cannot also re-architect it.

I just knew someone was going to call me on that - I almost went back and edited the remark out after I made it. You are right, of course. I allowed accuracy to suffer for the sake of a good line.

Test-makers map raw scores to deviation IQs so that the IQs are normally distributed. So I think a statement that IQs are normally distributed is mostly a statement about how IQs are computed.

Originally, IQ stood for intelligence quotient -- the ratio of mental age to chronological age. I wonder how closely the distribution of ratio IQs conforms to the normal distribution.