Snit
Posts:
25
Registered:
6/15/12
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Re: Visualizing where to draw the standard deviation line
Posted:
Jun 15, 2012 12:24 PM
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On 6/15/12 8:44 AM, in article jrfl96$vtq$1@news.cc.tut.fi, "Kaba"
<kaba@nowhere.com> wrote:
> 15.6.2012 17:55, Snit kirjoitti:
>> Thanks. :)
>>
>> I am the one who produced the media and was in the "debate" (if you have
>> ever visited an "advocate" group you know the debates there can be rather
>> silly). I noted the sigma should be depicted a specific distance from the
>> mean and was told:
>
>> So thank you for giving a correct and detailed answer. Maybe it will help
>> him (and his friend) to understand they were wrong - not that they will ever
>> admit to it.
>
> For the mathematically inclined, the proof still needs to be added a
> detail to be valid; Having a zero second derivative is necessary for an
> inflection point, but not sufficient (the second derivative needs to
> change sign!). Let's patch that up.
>
> We already computed that the points of zero second derivative are at
> m +- s. Computing the third derivative of f at these points give
>
> f'''(m +- s) = +- (2 * C)/(s^3 * exp(1/2)).
>
> Since these are both non-negative, the points m +- s must be inflection
> points (that is, the second derivative moves through the zero either
> from positive to negative or negative to positive).
If I understand correctly, though, for a normal distribution the inflection
points will always be at the points where the second derivative is zero -
and there will always be two and only two of those points. And it is at
those points where the first sigma line should be drawn. If you know this
you can see where standard deviation lines are often drawn incorrectly, such
as this one:
<http://www.udel.edu/htr/Statistics/Images/Class12/normal2.gif> From:
<http://www.udel.edu/htr/Statistics/Notes/class12.html>
Which is the example I used for showing how you can make a decent
approximation visually: <http://tmp.gallopinginsanity.com/sd.png>.
I also pointed to some other examples which at least appear incorrect to me
(though they are not as far off as the above example):
<http://www.footballguys.com/shickstandard_1_files/image009.gif> From:
<http://www.footballguys.com/shickstandard_1.htm>
Sigma lines clearly not at a far enough distance from the mean, esp. on the
graph to the right.
<http://www.gsseser.com/images/StandardDeviation2s.gif> From:
<http://www.gsseser.com/Deviation.htm>
Sigma lines clearly not at a far enough distance from the mean.
You would think that such sites would be made by people who knew better. I
openly admit I am not a math wiz (you are clearly far more knowledgeable
than I am) but it is rather silly when sites claiming to be teaching such
things get their depictions wrong (of course, one of the sites above is from
"Footballguys"... and you might not expect them, by stereotype, to be the
most knowledgeable in such areas anyway). :)
Then again, the "Environmental Surveillance, Education and Research Program"
sounds like a group that should know better, and the one that is just
grossly wrong was from the University of Delaware - and while the class is
in the Political Sciences department, the same instructor apparently teaches
classes in the Applied and Social Statistics department
(<http://www.udel.edu/htr>). He certainly should know better!
--
The indisputable facts about that absurd debate: <http://goo.gl/2337P>
cc being proved wrong about his stats BS: <http://goo.gl/1aYrP>
7 simple questions cc will *never* answer: <http://goo.gl/cNBzu>
cc again pretends to be knowledgeable about things he is clueless about.
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