Hi all, this is my way to see the question on
pvalue....
A statistical test it is like a diagnostic test...
his scope is to diagnose the truth. In general the truth is about a
comparison... There is the difference between group or not...
Power (1-b) ( True positive rate= Probability to see the difference when there is
in reality) and Confidence (1-a) ( True negative rate= Probability to see that the
difference does not exist, when really it does not exist) are the
same of Sensitivity and Specificity in a diagnostic test.
So the complement of Power will be
the False negative rate ( Probability to declare that the difference it doesn't
exit when in reality exist...error called II type or Beta-error). The Complement
of Confidence will be the False Positive Rate (or Pvalue or error alpha or I
type error) i.e. the Probability to see a difference when in reality it doesn't
exist!
Again ... Power and Confidence are a measure of
accuracy of statistical test.... like Sensitivity and Specificity are
measures of accuracy in diagnostic field of medicine. When accuracy is high,
the probability to make error.... will bevery low
In a statistical test, we have the advantage
to set as we want the accuracy of our "diagnostic test of the truth" , before
the study start. Anyway we can evaluate this accuracy after we
get the result of an experiment... In fact we have to answer to this question...
how is the probability that this results are truth?? ( accuracy of the
study)... in this sense we cannot focus only on alpha error ... because both
measures of accuracy "Power and Confidence" are important.
I think also that before to consider the accuracy
of experimental results...we have first to evaluate the magnitude of
difference... and ask ourself is the difference it is "important" fo our
study.... we can see large difference ( very important) but low accuracy of the
truth ( probabily small sample size) or.... we can be very closed to the truth (
very high accuracy) but we have very small difference ( not important)... ....
but this is another story ...about the classical question on statistical
significance vs clinical significance ( in biomedical fields)....
very sorry for my bad English
...
Massimo Tranquillo
DVM
Italy
----- Original Message -----
From: "Jay Warner" <[EMAIL PROTECTED]>
To: "Robert Lundqvist" <[EMAIL PROTECTED]>
Cc: <[EMAIL PROTECTED]>
Sent: Wednesday, December 10, 2003 10:34
PM
Subject: Re: P Value for Kids ?
> at base), IF the map is correct. And you read it correctly.....
>
> I like the idea of a map, although it is 2-D and the p value is 1-D.
>
> BTW, what's a chap from Sweden (@sm.luth.se) doing on walkabouts?! :)
>
> Jay
>
> Robert Lundqvist wrote:
>
> > My approach is often to use very loose terms where I try to make
> > connections to other concepts which might be more familiar:
> >
> > *The null hypothesis could be considered as a map
> >
> > *You go out on a walkabout with that map in your hand, i e you take a
> > sample
> >
> > *The p-value tells you the probability of ending where you find yourself
> > in the end
> >
> > *If the p-value is low, then it must be reasonable to question the
> > relevance of the map/the null hypothesis
> >
> > This way you can avoid - for some time - to include more tecnical terms.
> > Any comments on this approach? Any fundamental gaps?
> >
> > --robert
> > ********************
> > Robert Lundqvist
> > Dept of mathematics
> > Lulea University of Technology
> > Sweden
> >
> > On Thu, 4 Dec 2003, VOLTOLINI wrote:
> >
> > > Dear friends,
> > >
> > > The P is the probability of getting a value of a test statistic equal to =
> > or
> > > greater than the one observed in your data, if it is a random pick from t=
> > he
> > > distribution of the test statistic that would be created if a specified n=
> > ull
> > > hypothesis were true. So, in the situation where the means of two
> > > distributions are being compared, a t statistic might be calculated. If t=
> > he
> > > null hypothesis is that the distributions have an identical mean, the t
> > > statistic comes from a distribution of t with mean of zero. In such a
> > > distribution, there is a particular probability (P) that any given value =
> > of
> > > t will be equaled or exceeded if you pick t values at random. It is not t=
> > o
> > > be confused with the probability you choose to decide to reject the null
> > > hypothesis (i.e. alpha, which is then the probability of rejecting the nu=
> > ll
> > > hypothesis incorrectly - you think it is wrong when it is true, i.e. the
> > > probability of Type I error).
> > >
> > > But....... I think this is very dificult to teach for young students (usi=
> > ng
> > > these words!). So, does anyone can send me a suggestion? I would like to =
> > use
> > > a more simple explanation!
> > >
> > > For instance, in the book "The truth about Science" (p.101) I read:
> > >
> > > "A p-value of 0.80 means that
> > > there is an 80% chance of finding the data
> > > when the population are exactly the same".
> > >
> > > So, for many students this statement means like "the P value is the
> > > probability of Ho is correct" !
> > >
> > > I would like to avoid a simple explanation to my kidos like "just look if
> > > the P value is above or below 0.05 to reject or accept the Ho" :(
> > >
> > >
> > > Thanks for any help !!!
> > >
> > >
> > >
> > >
> > > Voltolini
> > >
> > >
> > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> > > Prof. J. C. VOLTOLINI
> > > Grupo de Estudos em Ecologia de Mamiferos (ECOMAM)
> > > Universidade de Taubate, Departamento de Biologia
> > > Praca Marcelino Monteiro 63, Bom Conselho.
> > > Taubate, SP. CEP 12030-010. BRASIL.
> > > Tel: 0XX12 - 2254165 (Lab. Zool.) ou 2254277 (Depto. Biol.)
> > > E-Mail: [EMAIL PROTECTED]
> > > http://jcvoltol.sites.uol.com.br/personalidades/
> > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> > >
> > >
> > > "Tutto di noi =E8 un angelo con un'ala e
> > > possiamo volare soltanto se ci abbracciamo"
> > >
> > > .
> > > .
> > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
> > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
> > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
> > > Instructions for joining and leaving this list, remarks about the
> > > problem of INAPPROPRIATE MESSAGES, and archives are available at:
> > > . http://jse.stat.ncsu.edu/ .
> > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
> > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
> > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
> > >
> > .
> > .
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>
> --
> Jay Warner
> Principal Scientist
> Warner Consulting, Inc.
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