Electric dipole transition: Difference between revisions

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{{DISPLAYTITLE:Generalized ''p''-value}}
Katie Hopkins has insisted that �peacocking [http://tinyurl.com/pch83be uggs on sale] social media� will not help save the [http://Www.kidnappedNigerian.com/ kidnapped Nigerian] school girls<br><br>
{{Expert-subject|statistics|date=March 2011}}
{{Primary sources|date=October 2010}}
In [[statistics]], a '''generalized ''p''-value''' is an extended version of the classical [[p-value|''p''-value]], which except in a limited number of applications, provides only approximate solutions.


Conventional statistical methods do not provide exact solutions to many statistical problems, such as those arising in [[mixed model]]s and MANOVA, especially when the problem involves many [[nuisance parameter]]s. As a result, practitioners often resort to approximate statistical methods or [[Asymptotic theory (statistics)|asymptotic statistical methods]] that are valid only with large samples. With small samples, such methods often have poor performance.<ref name=WE/> Use of approximate and asymptotic methods may lead to misleading conclusions or may fail to detect truly [[Statistical significance|significant]] results from [[experiment]]s.


Tests based on generalized ''p''-values are exact statistical methods in that they are based on exact probability statements.  While conventional statistical methods do not provide exact solutions to such problems as testing [[variance components]] or [[ANOVA]] under unequal variances, exact tests for such problems can be obtained based on generalized ''p''-values.<ref name=WE>Weerahandi (1995)</ref><ref name=TW>Tsui & Weerahandi (1989)</ref>
The relentless motor mouth wrote about the harrowing issue in her latest Sun column, hitting out at celebrities who have been uploading photos of themselves with posters reading #BringBackOurGirls<br>
�Listen fools,� she said. �You can hold up a sign with a hashtag until your arms drop off, but these girls are not coming back alive unless someone goes in and gets them.<br>


In order to overcome the shortcomings of the classical ''p''-values, Tsui and Weerahandi<ref name=TW/> extended the classical definition so that one can obtain exact solutions for such problems as the [[Behrens&ndash;Fisher problem]] and testing variance components. This is accomplished by allowing test variables to depend on observable random vectors as well as their observed values, as in the Bayesian treatment of the problem, but without having to treat constant parameters as random variables.
High-profile figures to take part in the [http://tinyurl.com/pch83be ugg boots sale] selfie campaign so far have included US First Lady Michelle Obama, prime minister David Cameron and supermodel Cara Deleving<br>.
[http://www.Wikipedia.org/wiki/Prime+Minister Prime Minister] David Cameron joins the campaign to to save the kidnapped schoolgir<br>
But Hopkins has argued that �Obamageddon� would have kicked in to rescue the girls, had they been from Amer<br>a.
�If 276 high school girls had been kidnapped from the US, Obamageddon would have been unleashed,� she wrote. �Instead, Mrs Obama has tried asking nicely, made big puppy dog eyes at the ca<br><br>.


==A simple case==
�David Cameron wasn�t going to be outdone by Mrs Obama and got himself a sign with the same hashtag. Dave knows it is important to be seen to be doing something and, apparently, holding a sign  [http://tinyurl.com/pch83be ugg boots sale] is very much in vogue.�
Hopkins� article has been met with positive responses online - a stark contrast to the usual reception reserved for her often-controversial and always outspoken op<br>ions.
Don't normally agree with @KTHopkins but she's spot [http://tinyurl.com/pch83be uggs on sale] this morning #stopholdingsignsandrescuet<br><br>rls


To describe the idea of generalized ''p''-values in a simple example, consider a situation of sampling from a normal population with mean <math>\mu</math>, and variance <math>\sigma ^2</math>, suppose <math>\overline{X}</math> and <math>S ^2</math> are the sample mean and the sample variance. Inferences on all unknown parameters can be based on the distributional results
- Sonja webster (@webster_sonja) May 16, 2014She's right RT @kthopkins You can hold up a sign until  [http://tinyurl.com/pch83be ugg boots sale] your arms drop off, those girls aren't coming back unless someone goes in and <br>ts em
- Nick Southall (@Nick_Southall) May 16, 2014i don't favour a lot of her opinions but this time i'm agreeing with @KThopkins <br>bsite
- RobK (@6soundmint6) May 1<br> 2014
The former Apprentice star emphasised the need for �giants of men with daggers on their berets and courage in their hearts to teach Mad Dog Boko Bill a <br><br>on�.


:<math> Z = \sqrt{n}(\overline{X} - \mu)/ \sigma \sim N(0,1)</math>
Local residents have started  [http://tinyurl.com/pch83be http://tinyurl.com/pch83be] taking matters into their own hands and forming vigilante groups, after feeling that the Nigerian military was not doing enough to stem attacks by the Boko Haram Islamic mi<br>tants.
and
Hopkins, meanwhile, spoke at the Cambridge Union earlier this week, where she told students she didn't "really like fat people" and "wouldn't like to be ginger in the dark".
:<math>U = n S^2 / \sigma^2 \sim \chi^2 _ {n-1} .</math>
 
Now suppose we need to test the coefficient of variation, <math>\rho = \mu /\sigma </math>. While the problem is not trivial with conventional ''p''-values, the task can be easily accomplished based on the generalized test variable
:<math>R = \frac {\overline{x} S}  {s \sigma} - \frac{\overline{X}- \mu} {\sigma}
    = \frac {\overline{x}} {s} \frac {\sqrt{U}} {\sqrt{n}} ~-~ \frac {Z} {\sqrt{n}} ,</math>
where <math>\overline{x}</math> is the observed value of <math>\overline{X}</math> and <math>s</math> is the observed value of <math>S</math>. Note that the distribution of <math>R</math> and its observed value are both free of nuisance parameters. Therefore, a test of a hypothesis with a one-sided alternative such as <math> H_A : \rho < \rho_0 </math> can be based on the generalized ''p''-value <math> p = Pr( R \ge \rho_0 )</math>, a quantity that can be evaluated via Monte Carlo simulation or using the non-central t-distribution.
 
==Notes==
{{Reflist}}
 
==References==
*Tsui, K. and Weerahandi, S. (1989): [http://www.jstor.org/stable/2289949 "Generalized ''p''-values in significance testing of hypotheses in the presence of nuisance parameters"]. ''[[Journal of the American Statistical Association]]'',  84, 602&ndash;607
 
*Weerahandi, S. (1995) [http://www.springer.com/statistics/statistical+theory+and+methods/book/978-0-387-40621-3  ''Exact Statistical Methods for Data Analysis''  ] Springer-Verlag, New York. ISBN 978-0-387-40621-3
 
==External links==
*[http://www.x-techniques.com/  XPro, Free software package for exact parametric statistics]
 
{{DEFAULTSORT:Generalized P-Value}}
[[Category:Hypothesis testing]]

Latest revision as of 12:06, 28 April 2014

Katie Hopkins has insisted that �peacocking uggs on sale social media� will not help save the kidnapped Nigerian school girls


The relentless motor mouth wrote about the harrowing issue in her latest Sun column, hitting out at celebrities who have been uploading photos of themselves with posters reading #BringBackOurGirls
�Listen fools,� she said. �You can hold up a sign with a hashtag until your arms drop off, but these girls are not coming back alive unless someone goes in and gets them.

High-profile figures to take part in the ugg boots sale selfie campaign so far have included US First Lady Michelle Obama, prime minister David Cameron and supermodel Cara Deleving
. Prime Minister David Cameron joins the campaign to to save the kidnapped schoolgir
But Hopkins has argued that �Obamageddon� would have kicked in to rescue the girls, had they been from Amer
a. �If 276 high school girls had been kidnapped from the US, Obamageddon would have been unleashed,� she wrote. �Instead, Mrs Obama has tried asking nicely, made big puppy dog eyes at the ca

.

�David Cameron wasn�t going to be outdone by Mrs Obama and got himself a sign with the same hashtag. Dave knows it is important to be seen to be doing something and, apparently, holding a sign ugg boots sale is very much in vogue.� Hopkins� article has been met with positive responses online - a stark contrast to the usual reception reserved for her often-controversial and always outspoken op
ions. Don't normally agree with @KTHopkins but she's spot uggs on sale this morning #stopholdingsignsandrescuet

rls

- Sonja webster (@webster_sonja) May 16, 2014She's right RT @kthopkins You can hold up a sign until ugg boots sale your arms drop off, those girls aren't coming back unless someone goes in and
ts em - Nick Southall (@Nick_Southall) May 16, 2014i don't favour a lot of her opinions but this time i'm agreeing with @KThopkins
bsite - RobK (@6soundmint6) May 1
2014 The former Apprentice star emphasised the need for �giants of men with daggers on their berets and courage in their hearts to teach Mad Dog Boko Bill a

on�.

Local residents have started http://tinyurl.com/pch83be taking matters into their own hands and forming vigilante groups, after feeling that the Nigerian military was not doing enough to stem attacks by the Boko Haram Islamic mi
tants. Hopkins, meanwhile, spoke at the Cambridge Union earlier this week, where she told students she didn't "really like fat people" and "wouldn't like to be ginger in the dark".

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