Re: clarify or clogify? re: Why the human race is growing apart

On Apr 10, 1:10 pm, Garamond Lethe <cartographi...@xxxxxxxxx> wrote:
On Fri, 10 Apr 2009 07:42:21 -0700, tgdenning wrote:
On Apr 10, 9:41 am, Kent Paul Dolan <xanth...@xxxxxxxx> wrote:
tgdenn...@xxxxxxxxxxxxx wrote:
Kent Paul Dolan <xanth...@xxxxxxxx> wrote:
tgdenn...@xxxxxxxxxxxxx wrote:
Huh?
   I hope that clarifies the issues a bit rather
  than muddying them still further.  My technical writing tends to
  set saints into frothing fits.
        -- Kent Paul Dolan, kdo...@xxxxxxxx,
             internal email, 2000/11/15
What exactly is a 'group metric'?
A measure of some statistic of a group, in the current case, IQ,
averaged across the group membership.
When you give an IQ test, you are measuring some characteristic of an
individual.
A group, as you are using it, is a subset of the set of humans who
have taken the test. So you are talking about the average of the
individual scores for the selected individuals.  OK.
And why must some 'group' score highest?
We're dealing, conceptually, since IQ isn't really an integer
concept, with real numbers. The real numbers are uncountably
infinite, which makes picking the same one at random
But that has no relationship to the question at hand, since we are
not selecting at random from the set of all integers.

Huh?

1) We are selecting from the set of integers which represents the
range of scores of the entire population that has taken the test.
2) We are not selecting group average scores at random, but from real
data. If we were to divide the population at random into two groups,
for example, the probability would be *extremely high* that the
average of the scores would be identical.
twice in a row really *really* hard to co. Thus, the chance of the
group metrics for the top two groups being identical is an event of
probability zero.
See above.
Thus, in all cases of measuring statistics for groups but a set of
such case of measure zero, among all such cases, one group will
score highest.
You may be saying something that makes sense, but the way you are
saying it doesn't.
And yet it still reads like plain English to me, but then, I'm a
math major, using words I know in their technical senses, so I
suppose it would.
I understand the words in their technical sense, thank you.

Apparently not.

I think you just don't understand the thing you are talking about.

You tell me you understand the words, and then argue against the
selection necessarily being unique as if it were a selection from among
the _integers_. Read what I wrote until you _do_ understand the words,
please. If the concepts are beyond you, that's fine too, but right now
you're arguing from ignorance, and that is very much _not_ fine.

xanthian.

I gave a very clear example of the case. If you randomly select two
groups from a population N, each consisting of N/2 individuals, there is
a high probability that the average score of each group will be
equivalent to IQ=100,

as N approaches infinity

as calculated for the entire population.

Why don't you explain why this is incorrect, since you are a 'math
major'.

When N is smaller, this isn't the case.  In R, you can ask for N elements
of a normal distribution with a specified mean.

mean(rnorm(100, mean=100))
[1] 100.1491
mean(rnorm(100, mean=100))
[1] 99.85304
mean(rnorm(100, mean=100))

[1] 100.2428

For a small number of groups and a small number of individuals in each
group, the difference between 100.2428 and 99.85304 may look
statistically significant (esp. if you're hunting for differences).  Real-
world data will be much noisier.


Sigh. We're talking about IQ tests. Are you saying that the size of
the population that has taken IQ tests is 'small', and that half of
that number is also 'small', in a statistical sense?

BTW, I give you credit for at least having a clue as to what I am
talking about, which the others obviously don't.

-tg







As N goes to infinity, this becomes less of a problem.

mean(rnorm(1000000, mean=100))
[1] 99.99892
mean(rnorm(1000000, mean=100))
[1] 100.0010
mean(rnorm(1000000, mean=100))

[1] 99.9987



-tg

.

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