Re: st: Why many things have Normal distribution

[Yuval Arbel <yuval.arbel@gmail.com>]

Thanks David. The paper seems to be very helpful. I agree there is a
possibility that we are making wrong assumptions. That's why we need
to treat statistical analysis with some cautious.



On Thu, Aug 29, 2013 at 7:49 PM, David Hoaglin <dchoaglin@gmail.com> wrote:
> Yuval,
>
> The Central Limit Theorem (CLT) describes the behavior of the
> distribution of the sample mean as the sample size becomes large.  In
> order for the distribution of the sample mean to approach a normal
> distribution, the underlying distribution of the data must satisfy
> some conditions, but those conditions are not very stringent.  The CLT
> provides no information on how the underlying distribution behaves.
> One does, however, expect the behavior of samples to approach that of
> the underlying distribution (whatever that happens to be).
>
> I would have no special expectations of the distribution of heights in
> a large army.  I would look at the actual distribution --- empirical
> evidence, rather than a thought experiment.  Apart from any attempts
> to avoid serving, one would expect recruiters to reject people who
> were too short and people who were too tall.  Also the actual
> distribution might be a mixture of components.  As I recall, in the
> 19th century Quetelet used a frequency distribution of the chest
> circumference of Scottish soldiers to illustrate a method of fitting a
> normal distribution.  In compiling the data he merged several
> components and made a variety of mistakes.
>
> The outcomes of tossing an actual "fair" die depend on how carefully
> the die was manufactured.  Iversen et al. (1971) analyzed the results
> of a large number of throws of various types of dice.
>
> You didn't say how you would use a normal distribution to approximate
> the outcomes of throwing a fair die.  The basic distribution is
> discrete, with six equally likely outcomes.
>
> David Hoaglin
>
> Iversen GR, Longcor WH, Mosteller F, Gilbert JP, Youtz C (1971). Bias
> and runs in dice throwing and recording: a few million throws.
> Psychometrika 36:1-19.
>
> On Thu, Aug 29, 2013 at 5:38 PM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
>> What about the central limit theorem? I was referring to physical
>> human features - such as height - and the example of Napoleon's army
>> candidates for draft. In an army of millions of soldiers - you would
>> expect a normal distribution of heights. The problem is that those who
>> tried to avoid drafting probably bribed somebody to write false
>> heights, which is shorter than the minimal required height. In this
>> case - you might get a skewed distribution of heights
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-- 
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street,
Haifa 33031, Israel
e-mail1: yuval.arbel@carmel.ac.il
e-mail2: yuval.arbel@gmail.com
You can access my latest paper on SSRN at:  http://ssrn.com/abstract=2263398
You can access previous papers on SSRN at: http://ssrn.com/author=1313670
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