[quote=CRGreathouse;175428]I don't agree with that at all. IQ is by definition normal.

There's no reason to avoid negative numbers -- it's just that they'd be very rare. You'd expect a 1.3e-11 fraction of people to have a negative IQ, or about 0.1 people on Earth.[/quote]

The original definition was:

IQ=(mental age)/(biological age)

But even if you take the current definition, then anybody who hasn't been born yet (negative age) essentially leaves all answers blank on the questionnaire, which makes the IQ zero.

[I]Sachlogik vor Zahlenlogik![/I]

[QUOTE=__HRB__;175434]The original definition was:

IQ=(mental age)/(biological age)[/QUOTE]

You're talking about the 1916 Terman IQ definition. We've come a long way since.

Admittedly, IQ isn't really used much in academic circles these days -- psychology has preferred the use of g. But I digress...

[QUOTE=__HRB__;175434]But even if you take the current definition, then anybody who hasn't been born yet (negative age) essentially leaves all answers blank on the questionnaire, which makes the IQ zero.[/QUOTE]

Why would you equate leaving answers blank to an IQ of zero?

[quote=CRGreathouse;175438]Why would you equate leaving answers blank to an IQ of zero?[/quote]
[I]Sachlogik![/I]

[QUOTE=__HRB__;175403]IQs cannot be negative, so the distribution is slightly skewed towards zero[/QUOTE]By definition IQ 100 is 'average'. So if humans get smarter, what it take to get 100 will be higher. You missed to tongue in cheek aspect of my post. I threw in the thing about legs, so that those who may have missed the IQ irony might get it.:razz:

[url=http://en.wikipedia.org/wiki/Lies,_damned_lies,_and_statistics]Lies, damned lies, and statistics[/url]

[quote=Uncwilly;175447]By definition IQ 100 is 'average'. So if humans get smarter, what it take to get 100 will be higher. You missed to tongue in cheek aspect of my post. I threw in the thing about legs, so that those who may have missed the IQ irony might get it.:razz:[/quote]

I sure did, and that's a pretty damn good point, that *almost* took the wind out of my sails. Fortunately for me there is something called the [URL="http://en.wikipedia.org/wiki/Flynn_effect"]Flynn_effect[/URL], which gave me an idea to get me back into sophistic attack mode.

Fact: tests are standardized [I]before[/I] the majority of people take them...

So, if science can make people smarter fast enough, the designers of the IQ tests could simply be too dumb to create tough problems, which means we can actually end up with most people having IQs above 165!

:razz:x2

[quote=philmoore;175424]I consider myself a reasonably intelligent person, but this statement made absolutely no sense to me. Care to explain?[/quote]

On second thought, no.

So, you're still 'it'.

Ok, then I'll respond to your earlier post:

[QUOTE=__HRB__;175430]Since nobody has 1.999 legs, the statistic is meaningless, but e.g. the mode "the most common number of legs a human has is 2" is a meaningful statistic.[/QUOTE]

Let's take another statistic based on discrete data: fertility rates. Supposedly, the U.S. fertility rate is currently 2.1 births per female. According to you, this statistic is meaningless, because there are no women who have had 2.1 births. To me, it is a valid, meaningful statistical assertion that summarizes information that cannot be easily expressed otherwise. Statistics are by nature statements about ensembles, not individuals. To say that the average number of legs is 1.999 is identical to saying that the average "leg rate" in the population at large is 1999 legs per 1000 individuals.

[QUOTE=__HRB__;175423]Sigh.

The arithmetic mean is meaningless for discrete data.[/QUOTE]My maternal grandmother had 1.5 legs for the last decade of her life.

Paul

[quote=philmoore;175475]Let's take another statistic based on discrete data: fertility rates. Supposedly, the U.S. fertility rate is currently 2.1 births per female. According to you, this statistic is meaningless, because there are no women who have had 2.1 births. To me, it is a valid, meaningful statistical assertion that summarizes information that cannot be easily expressed otherwise.[/quote]

IIANM fertility rates are synthetic, so 2.1 is actually some sort of maximum likilhood estimator...ok, that's not really an argument...

[quote=philmoore;175475]To say that the average number of legs is 1.999 is identical to saying that the average "leg rate" in the population at large is 1999 legs per 1000 individuals.[/quote]

Rates have dimension legs/person, but the dimension of the arithmetic mean is legs, so they are not identical.

[QUOTE=__HRB__;175499]IIANM fertility rates are synthetic, so 2.1 is actually some sort of maximum likilhood estimator...ok, that's not really an argument...

Rates have dimension legs/person, but the dimension of the arithmetic mean is legs, so they are not identical.[/QUOTE]

Ok, it is pretty obvious that you are so engrossed in your pedantry and sophistry that you aren't thinking clearly about the issue... Of course fertility rates are synthetic, a projection of what the average fertility rate would be if all women survive past child-bearing age, but we could talk as well about the current average number of children per woman. My point is that these sort of statistics can provide meaningful summaries of the data.

And your statement about the dimension of the arithmetic mean is just nonsensical - sum(data points)/(# of data points), what do you think that number of data points in the denominator represents?

[quote=philmoore;175505]Ok, it is pretty obvious that you are so engrossed in your pedantry and sophistry that you aren't thinking clearly about the issue...[/quote]

I came here to pick a fight, so of course I disagree with this on object- and meta-level.

[quote=philmoore;175505][...]And your statement about the dimension of the arithmetic mean is just nonsensical - sum(data points)/(# of data points), what do you think that number of data points in the denominator represents?[/quote]

In your example, you are actually computing the arithmetic mean of birth rates, which is a continuous variable, so you end up with a meaningful statistic. You must contrast this with the arithmetic mean of births, which is a discrete variable, so the arithmetic mean is a meaningless statistic.

And if you think this is nitpicking, please consider that ignorance of factual logic leads to grave errors in judgment, such as the common belief that one comes out ahead after making a profit of 200% followed by a loss of 100%.