Snit
Posts:
25
Registered:
6/15/12
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Re: Visualizing where to draw the standard deviation line
Posted:
Jun 15, 2012 12:27 PM
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On 6/15/12 9:01 AM, in article
f011e6ae-88bc-4763-9670-3b5f86395188@s9g2000vbg.googlegroups.com, "Onion
Knight" <onionknightgot@gmail.com> wrote:
> On Jun 15, 11:43 am, Kaba <k...@nowhere.com> wrote:
>> 15.6.2012 6:29, Onion Knight kirjoitti:
>>
>>> There has been a debate in COLA as to if the distance from the mean to
>>> the inflection point is where the standard deviation should be. One
>>> person is saying that this distance is where the line should always be
>>> drawn while one other is saying the distance from the mean is
>>> irrelevant and it is only the area under the curve that matters. The
>>> first agrees the area under the curve is also always the same but
>>> insists the inflection point is where the line should be drawn. He
>>> even produced a video to show his
>>> ideashttp://www.youtube.com/watch?v=MoW3hMq-eIc
>>> and he showed what he claimed was an incorrectly depicted image and
>>> showed where he says it should behttp://tmp.gallopinginsanity.com/sd.png
>>> I admit this goes over my head. Is he correct? Is it really that easy
>>> that you can just look at the inflection point and see where the
>>> standard deviation should be drawn? I was never taught that in school.
>>
>> Hi,
>>
>> That's correct. We are given the probability density function of the
>> normal distribution
>>
>> f : R --> R : f(x) = C exp(-(x - m)^2 / (2s^2)),
>>
>> where C in R is the normalization constant which makes f integrate to 1,
>> m is the mean, and s is the standard deviation. The claim is that the
>> inflection points of f are exactly at a distance of one standard
>> deviation from the mean, i.e. at m +- s. To prove this claim, compute
>> the first and second derivative of f:
>>
>> f'(x) = C exp(-(x - m)^2 / (2s^2)) (-(x-m)/s^2), and
>>
>> f''(x) = (C / s^2) exp(-(x - m)^2 / (2s^2)) [(x - m)^2 / s^2 - 1].
>>
>> Then the inflection points of f are given by solving the equation
>>
>> f''(x) = 0.
>>
>> This simplifies to
>>
>> (x - m)^2 / s^2 - 1 = 0
>> <=>
>> (x - m)^2 = s^2
>> <=>
>> |x - m| = s.
>>
>> QED :)
>>
>> --http://kaba.hilvi.org
>
> While a lot of that still goes over my head, if I get the gist of it,
> the person who said you can visualize the standard deviation based on
> the distance from the mean (to the inflection point) was correct at
> least in the case of a normal distribution. That is what I assumed
> but wanted a different opinion.
>
> Do you know much about linear trendlines? The same debate included the
> drawing of those in Excel. The same person who spoke of the standard
> deviation also showed how to make a linear trendline,
> http://tmp.gallopinginsanity.com/LinearTrendLineCreation.mov
And to be clear, as the name of the video suggests, the goal here was to
create a linear trend line in Excel (and Numbers). It was not to do other
forms of analysis or create other forms of trend lines... which I do know
exist.
> Others in the same group insisted he was missing steps but if you look
> at the Microsoft site it offers instructions and it seems his process
> is just fine. What steps if any did he skip? Would love to get some
> other input from people who are not involved.
I clearly missed no steps - but the folks arguing against us on this will
never admit they were wrong to claim I did.
--
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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