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Science Forum Index » Statistics - Math Forum » F-test & F-Stat...
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| Judge... |
 Posted: Sun Jul 13, 2008 11:09 am |
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F-test is used to check the hypothesis wether variances of two groups
are same or different. How value of F-Stat is used ?
Judge. |
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| Jack Tomsky... |
| Posted: Sun Jul 13, 2008 6:53 pm |
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Quote: F-test is used to check the hypothesis wether
variances of two groups
are same or different. How value of F-Stat is used ?
Judge.
Suppose that we have two samples with sample sizes N1 and N2, each coming from a normal distribution in which the means and variances are unknown. We want to test the null hypothesis H0: sig1^2 = sig2^2 against the alternative hypothesis H1: not H0 at the alpha significance level.
Let s1^2 and s2^2 be the respective sample variances. Then when H0 is true, s1^2/s2^2 is distributed as F with N1-1 and N2-1 degrees of freedom.
We therefore accept H0 if and only if
F(N1-1,N2-1,alpha/2) <= s1^2/s2^2 <= F(N1-1,N2-1,1-alpha/2).
Jack |
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| Luis A. Afonso... |
| Posted: Mon Jul 14, 2008 4:44 am |
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Judge
You fail to reject if the Test falls outside the critical region CR. IT is the correct way to express the occurrence.
On contrary is lies in the CR you reject H0, because it´s unlike that observed data be compatible with the Null Hypotheses.
The above conclusion is fully accepted by the Statistician People, since Ronald Fisher (circa 1910). TO ACCEPT THE NULL HYPOTHESES is equivalent to stay that a not charged defender is always INNOCENT. Think at the Orenthal James Simpson trial, for example.
NEVER SAY THAT A NULL HYPOTHESES IS ACCEPTED: Theory does´t allow.
Luis Amaral Afonso [The moderator destroyer] |
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| Old Mac User... |
| Posted: Mon Jul 14, 2008 6:15 am |
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On Jul 14, 10:44 am, "Luis A. Afonso" <lic... at (no spam) hotmail.com> wrote:
Quote: Judge
You fail to reject if the Test falls outside the critical region CR. IT is the correct way to express the occurrence.
On contrary is lies in the CR you reject H0, because it´s unlike that observed data be compatible with the Null Hypotheses.
The above conclusion is fully accepted by the Statistician People, since Ronald Fisher (circa 1910). TO ACCEPT THE NULL HYPOTHESES is equivalent to stay that a not charged defender is always INNOCENT. Think at the Orenthal James Simpson trial, for example.
NEVER SAY THAT A NULL HYPOTHESES IS ACCEPTED: Theory does´t allow.
Luis Amaral Afonso [The moderator destroyer]
There goes Adumbo again.
Ignore him is you value your sanity. OMU |
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| Jack Tomsky... |
| Posted: Mon Jul 14, 2008 8:50 am |
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Quote: On Jul 14, 10:44 am, "Luis A. Afonso"
lic... at (no spam) hotmail.com> wrote:
Judge
You fail to reject if the Test falls outside the
critical region CR. IT is the correct way to express
the occurrence.
On contrary is lies in the CR you reject H0,
because it´s unlike that observed data be compatible
with the Null Hypotheses.
The above conclusion is fully accepted by the
Statistician People, since Ronald Fisher (circa
1910). TO ACCEPT THE NULL HYPOTHESES is equivalent
to stay that a not charged defender is always
INNOCENT. Think at the Orenthal James Simpson trial,
for example.
NEVER SAY THAT A NULL HYPOTHESES IS ACCEPTED:
Theory does´t allow.
Luis Amaral Afonso [The moderator destroyer]
There goes Adumbo again.
Ignore him is you value your sanity. OMU
Afonso has given us a notorious example of a null hypothesis that his theory says should never be accepted. That null hypothesis is H: 5/13 <= 8/13.
Jack (moderator) |
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| Jack Tomsky... |
| Posted: Mon Jul 14, 2008 4:21 pm |
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Afonso does not believe that in hypothesis testing with the formulation of a null and an alternative hypothesis, that the null hypothesis can be accepted. Under the Afonso theory of statistical inference, the statistician is never allowed to make a decision.
He does not allow himself to accept his own null hypothesis H: 5/13 <= 8/13 against K: not H. I've been trying to teach him for years that 5/13 < 8/13, but nothing ever penetrates.
Jack (moderator)
Quote: DO NOT BELIEVE IN WHAT Jack Tomsky say
From the WEB
__1__"Accepting the null hypothesis" is like
acquitting a defendant. It does NOT prove that the
null hypothesis is true, or that the defendant is
innocent. It means there is a reasonable doubt about
the defendant's guilt. In statistical testing, the
significance level, Type I risk, or alpha risk is the
"reasonable doubt." It is the chance of wrongly
rejecting the null hypothesis when it is true. In
acceptance sampling, it is the producer's risk, or
risk of wrongly rejecting a lot that meets
requirements.
*****************************
And
__2__
HyperStat Online Contents
Why the Null Hypothesis is Not Accepted
A null hypothesis is not accepted just because it is
not rejected. Data not sufficient to show
convincingly that a difference between means is not
zero do not prove that the difference is zero. Such
data may even suggest that the null hypothesis is
false but not be strong enough to make a convincing
case that the null hypothesis is false. For example,
if the probability value were 0.15, then one would
not be ready to present one's case that the null
hypothesis is false to the (properly) skeptical
scientific community. More convincing data would be
needed to do that. However, there would be no basis
to conclude that the null hypothesis is true. It may
or may not be true, there just is not strong enough
evidence to reject it. Not even in cases where there
is no evidence that the null hypothesis is false is
it valid to conclude the null hypothesis is true. If
the null hypothesis is that µ1 - µ2 is zero then the
hypothesis is that the difference is exactly zero. No
experiment can distinguish between the case of no
difference between means and an extremely small
difference between means. If data are consistent with
the null hypothesis, they are also consistent with
other similar hypotheses.
********************************
Luis Amaral Afonso [The moderator ??? destroyer] |
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| licas_ at (no spam) hotmail.com... |
| Posted: Mon Jul 14, 2008 4:29 pm |
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On 14 Jul, 17:15, Old Mac User <chendrixst... at (no spam) yahoo.com> wrote:
Quote: On Jul 14, 10:44 am, "Luis A. Afonso" <lic... at (no spam) hotmail.com> wrote:
Judge
You fail to reject if the Test falls outside the critical region CR. IT is the correct way to express the occurrence.
On contrary is lies in the CR you reject H0, because it´s unlike that observed data be compatible with the Null Hypotheses.
The above conclusion is fully accepted by the Statistician People, since Ronald Fisher (circa 1910). TO ACCEPT THE NULL HYPOTHESES is equivalent to stay that a not charged defender is always INNOCENT. Think at the Orenthal James Simpson trial, for example.
NEVER SAY THAT A NULL HYPOTHESES IS ACCEPTED: Theory does´t allow.
Luis Amaral Afonso [The moderator destroyer]
There goes Adumbo again.
Ignore him is you value your sanity. OMU
Old Mac User
Being in the midle of the HERD of IMBECILES you try in despair to be
considered a Statistician , you a * teacher or agent *
in the WILD (Brasil, etc), with no category, no paper published or
authorising text-book
on Statistics, In short a zero on expertise, a no worth flatterer that
is unable to say
whatever, even scarcly interesting. But always apt to swindle *the
boss*.
Luis Amaral Afonso [ The moderator destroyer] |
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