Re: Who "invented" the null hypthesis?
- From: "Matt Dz." <matt-NO-SPAM.please@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Sun, 30 Apr 2006 02:38:06 +0200
"Luis A. Afonso" wrote:
Matt Dz.
My response
If BY CHANCE you read WIKIPEDIA you would find the following: (quoting)
***If the test statistic is outside the critical region, the only conclusion is that
There is not enough evidence to reject the hypothesis. This is *not* the same as evidence in favor of the hypothesis. That we cannot obtain using these arguments, since lack of evidence against a hypothesis is not evidence for it. On this basis, statistical research progresses by eliminating error, not by *finding the truth*
Contrary to you, I DO know the subject of hypothesis testing, thank you. Please also note, that "Wikipedia" is not an acronym, and therefore its correct spelling is... "Wikipedia".
Enough
Therefore
a) the term *acceptance region* should not be used because he induces in IGNORANT PEOPLE like you that HT leads to directly accept H0 which is a enormous error. This you should be learned at the COLLEGE because is the most ELEMENTARY THING of the Theory.
Wonderful. Because you think it should not be used, as YOU CANNOT understand it, you will invent your own terminology and perhaps redefine the whole statistics, just because you do not like the particular term?
Whether you like it or not, it is used, quite often, as one may note: http://www.google.com/search?q=%22acceptance+region%22
Maybe you will go as far as to say that the authors of the ca. 2,600 articles are wrong to use it as well?
http://scholar.google.com/scholar?q=%22acceptance+region%22
It seems you might need some help with understanding the term: http://www.statistics.com/content/glossary/a/acceptreg.php
I would also recommend you reading Bob's (Reef Fish) posts in this thread - his explanations should be very enlightening, even to you.
Therefore
In the case that we are concerned WE FAIL TO REJECT (we do not reject) the null Hypotheses.
IF you read (NET) the definition:
***Definition: The significance level of a test is the probability that the test statistic will reject the null hypothesis when the [hypothesis] is true. Significance is a property of the distribution of a test statistic, not of any particular draw of the statistic.***
In numbers (to make easier to your confused mind (?)
5% Significance Level = = 95% Confidence Level
(or the probability of NOT TO REJECT the null Hypotheses).
Now you are confusing several other things - and by using the "=" sign you are making a statement, which is not always true.
Let Q(\theta) be the power function of a test; i.e. the probability of rejecting the null hypothesis H0 when \theta \in \Theta is the true parameter value.
\theta denotes parameter value
\Theta denotes parameter space
\Theta0 denotes parameter space when the null hypothesis H0 is true
// in case you are not be familiar with the above way of writing mathematical symbols, take a look at: http://en.wikipedia.org/wiki/TeX
Now, a test is called SIZE \alpha, when the supremum of Q(\theta) = \alpha (for \theta \in \Theta0).
A test is called LEVEL \alpha, when the supremum of Q(\theta) <= \alpha (for \theta \in \Theta0).
Note, that there are cases when this supremum is not even attainable.
Now, I hope that you see the difference between SIZE and LEVEL and understand why the statement "The significance level of a test *IS* the probability that the test statistic will reject the null hypothesis" may not be always correct. // *IS* - emphasis mine
The above terms are related to the hypothesis testing.
Now, the term "confidence level" comes from the world of the confidence interval estimation. If one comes up with a confidence interval by a means of inversion of a test procedure, then there is relation between (1-\alpha) coverage probability of the CI (or the confidence coefficient, being the infimum of the coverage probability for all \theta \in \Theta) and (1-\alpha) significance level of the APPROPRIATE test.
And this "APPROPRIATE" requirement is crucial - by failing to mention it, you have shown that you may not understand the whole concept of the relation between CIs and hypothesis testing. Without EXACTLY specifying the CI you have in mind you CANNOT say that "5% Significance Level = 95% Confidence Level".
For example, the UPPER-SIDED \alpha level test corresponds to the (1-\alpha) LOWER CI estimator for \theta, while the LOWER-SIDED \alpha level test corresponds to the (1-\alpha) UPPER CI estimator for \theta.
Nevertheless, if you have said: "The construction of a confidence interval and its confidence coefficient
are both closely tied in with the nature of the acceptance region and
the level of the test", then it would be a correct statement.
However, "closely tied" does not mean "the same".
Sincere advise of mine:
Take an ELEMENTARY course on Statistics before you post further nonsense.
I think that the only person posting "nonsense" in so far was you.
And, as incompetent as you are, you are definitely the last person entitled to give me this kind of advices (also note, that "advise" is a verb, it seems you should learn basic English grammar as well).
A last note:
***Excusez-moi Monsieur j´ai fait une erreur impardonnable .En fait *e-mail* et *post* ce sont des choses tellement différents que très difficilement je pouvais faire confusion. J´espère bien votre bienveillance.***
I remind you, that the language used in this newsgroup is English. However, I accept your apology.
Regards,
Matt
______licas (Luis A. Afonso).
- References:
- Re: Who "invented" the null hypthesis?
- From: \"Luis A. Afonso\"
- Re: Who "invented" the null hypthesis?
- Prev by Date: Time Trials in pairs
- Next by Date: Re: Who "invented" the null hypthesis?
- Previous by thread: Re: Who "invented" the null hypthesis?
- Next by thread: Re: Who "invented" the null hypthesis?
- Index(es):
Relevant Pages
|
|
