Hypothesis Testing vs Criminal Court of Law: in http://tinyurl.com/mlzg6
Reef Fish
of the verdict of a Hypothesis Test of Ho vs Ha.
I found I had posted a FULL explanation in April 2006. That should
serve as the basis of understanding EVERYONE should have. OMU
wasn't aware of my lecture because it was before his time, and he
was actually believed that Afonso had something to say about
hypothesis testing that I might have "miscommunicated". So, the
post
http://tinyurl.com/mlzg6
serves much more than just correcting OMU on his misperception,
but serves as a SOLID FOUNDATION to the subject matter of
Hypothesis Testing, that it has a 100% parallel, in terms of setup
and decision making, as the Court of Criminal Justice in the USA.
Because of the importance of the subject matter and the frequency
at which the subject is mangled by its users, including ALL of the
Afonsos, I am pulling this out as a separate thread for that purpose,
even thought most of what's here is already in my direct reply to OMU.
OMU> It seems that
OMU> every time I go away there is another uproar. That conclusion is
drawn
OMU> from limited data, and I'll not get more data until late October.
But
OMU> in the meantime let's see if we can slow down to a gentle simmer
and
OMU> review what's happening here.
Be glad to do it. But let me hasten to say that you have a good
excuse for misreading what the Afonsos did, because you haven't
had time to examine the DATA and how they were (MIS)analyzed by
the Afonsos. Secondly, you're singing in the wrong choir at the
wrong
church -- as I shall calmly prove it to you how wrong you are about
all of the Afonsos.
OMU> It seems to me that the current uproar stems from another
OMU> case of malcommunication.
There was no malcommunication on MY part. What you SHOULD
have witnessed (which I'll show you that you didn't) was how WRONG
the Afonsos are in BOTH their statement AND the execution of a
hypothesis test. The errors are clear-cut and no ifs or buts about
it.
I spoke about only a SMALL part of the Hypothesis Testing in that
thread -- only about the role of the TEST STATISTIC in relation to
Ho.
OMU> As you said in your mini-tutorial, it all begins with a null
OMU> hypothesis of the form H0:m1 = m2 (I'm using means here
OMU> for convenience, recognizing there are other such comparisons).
Now go read my MAXI lecture, and see if you learn something
there or finding something you could DISAGREE. As a corollary
exercise, if you CAN'T find PRECISE errors in Afonso's usage of
both language AND execution of a hypothesis test, then you are
SERIOUSLY DEFICIENT in your understanding of the subject
matter.
Your next paragraph has been read by me. That was prima facie
evidence that you are signing to the wrong church. What is being
tested is called a "sharp" hypothesis, which is often stated that way
in the Neyman Pearson jargon. As such, any statistician worth his
salt, or even my students who are not as much salt, KNOWS what
it means when it is "accepted" or "rejected", in that "acceptance"
means in sufficient to reject, etc. In fact, I had written lecture
notes
relating the acceptance and rejection to the "not guilty" and
"guilty" verdict in a court of criminal law. The STATUS QUO in
each is that the DEFENDANT (Ho in a hypothesis test) is NOT
QUILTY until proven guilt. Whether the hypothesis is sharp or
not is subject to the SAME interpretation. That is why OJ was
acquitted in his criminal court trial, but left much about his true
innocence, which the court can NEVER prove, nor does the court
intend to prove.
THe SAME (identical and parallel) idea is imbedded in a Test of
Hypothesis. Ho is the DEFENDANT. Ha is the GUILTY verdict.
Whether one says "there is not sufficient evidence to reject Ho"
or "one accepts Ho at the alpha significance level" means EXACTLY
the same thing to the EDUCATED. It means NOT GUILTY. It
does not prove the innocence of Ho.
That is what you're trying to convey. But it is much clearere
presented and understood as a completely parallel to the
CRIMINAL court of law where the weight of evidence is approx.
the same as the usual alpha level of .05 (which is equated in
the legal jargon as "conviction on the evidence beyond a
reasonable doubt")
I presented this idea on May 2, 2006 in a brief comment in
http://groups.google.com/group/sci.stat.edu/msg/9cf8d77ca7dc3b21?hl=en&
In fact, I found my FULL document on the equivalence of the Criminal
Court and a Hypothesis Testing setting, in
http://groups.google.com/group/sci.stat.edu/msg/8b0355db998016b2?hl=en&
or
http://tinyurl.com/mlzg6 if the above URL gets truncated.
That IS a text book piece I used in MY teaching, stolen by an author
who
had it published in his book but made the SAME mistake he did (which
was how I knew he stole it because I had given my material to the
publisher to help him sort out that part of Hypothesis Testing, in the
textbook which was flawless otherwise.) The ESSENTIAL elements
are these:
So, the 2 x 2 table would look like this:
LAW Not Guilty Guilty
(Defendant) verdict verdict
true state Correct Incorrect
Not Guilty verdict verdict
true state Incorrect Correct
Guilty verdict verdict
In statistical Hypothesis Testing, the corresponding 2 x 2 table is
Ho Accept Ho Reject Ho
(Null Hyp)
Ho TRUE Correct Type I Error
Ho NOT true Type II Error Correct
These are the KEY elements of the analogy:
1. In a court of law, a defendant is INNOCENT until PROVEN guilty.
In Hyp testing, Ho is assumed to be TRUE until proven otherwise
Defendant = Ho
Guilty = Reject Ho
2. When a "Not Guilty" verdict is rendered, it does NOT prove the
innocence of the defendant; it simply means the evidence is
not sufficiently strong to warrant a "Guilty" verdict.
In the ensuing discussion of that thread, some noises were heard
about my use of "Accept Ho" over "Ho is not rejected". But
Accept Ho is a perfectly acceptable and CORRECT statement to
make in a Hypothesis testing, especially when it is equated to the
criminal court trial evidence to "convict" or "acquit".
To put it in PARALLEL with the statement 2 above about Law, in
Hypothesis Testing, we would have:
2. When a "Ho is Accepted" verdict is rendered, it does NOT prove
the truth or falsehood of Ho; it simply means the evidence is
not sufficiently strong to warrant a "Reject Ho" verdict.
Anyone who reads more into "Accept Ho" or thinks "does not have
sufficient evidence to reject Ho" is better, is either UNEDUCATED
or ILL-EDUCATED in this matter.
The Afonsos are UNEDUCATED about Hypothesis Testing in
every respect ot that process!
Read MY lecture and you'll see that there is NO ROOM for anyone
to think as you do, that I could POSSIBLY be wrong and any of the
Afonsos, or ANYONE in the entire readership can say what I taught
about Hypothesis Testing (together with its fine points) is WRONG
in the slightest way.
Snip the rest of OMU's misread and misunderstanding of MY position
on the subject.
http://tinyurl.com/mlzg6 contains MUCH more than what you tried
to express, in precise terms, and precise analogy to the decision
making in a Criminal Law of Justice. The analogy is PERFECT.
OMU> It's not unusual to find that someone has been careless with words
and
OMU> has left such a "no detectable difference" outcome framed as if
they
OMU> they proved there is no difference between m1 and m2.
The language cause problem ONLY with the ILL-EDUCATED. If
Neyman (or any of the statisticians I know) says Ho is accepted,
everyone SHOULD KNOW precisely what's meant.
OMU>That's no only
OMU> misleading, it is simply wrong. More than once I've served as an
expert
OMU> witness and have relished the opportunity to explain this delicate
OMU> matter in the presence of a judge and jury. "Words, like parts,
should
OMU> fit with precision."
Then you should study my analogy carefully and precisely, and see
that EVERYTHING you know about hypothesis OR law (for that matter)
is contained in that SINGLE post, in terms of how VERDICT is
"technically" expressed, and what the verdicts mean. It's 100%
impervious to distortion by the uneducated.
.
PMU> So I write this one off as another case of malcommunciation. Your
OMU> minitutorial is accurate and even fun to read. It communicates
that
OMU> part of the story accurately.
No, OMU, it communicates ONLY the part about the role of the
TEST STATISTIC and its relation to Ho tested. It's a tiny part of the
story.
My MAXI lecture http://tinyurl.com/mlzg6 was delivered
on Fri, Apr 28 2006 11:11 am , long before you found sci.stat.math.
If you had read THAT lecture, you wouldn't have been doing your
song and dance about how I miscommunicated to Afonso, or how
he had anything correct to say about the subject.
This post serves only to bring any interested readers on the subject
of Hypothesis Testing up-to-date on what I have to say about it, in
OMU> LA has tried to make the point "but a
OMU> failure to establish a difference between m1 and m2 does not imply
OMU> there is no difference whatsoever"... and he is correct.
That was his MISREPRESENTATION of MY position. You should be
wise enough NOT to be so damned gullible about what Afonso, ANY
of the Afonsos say. They also called me a MISERABLE and
HORRIBLE FORGER over a typo by one of the Afonsos.
I'll return and teach YOU (and anyone who still needs to learn about
Hypothesis Testing) on the ERRORS (in the statement of hypotheses,
execution of the test, AND the erroneous ways of expressing the
conclusion) in the analysis of Example 1.
Example 1 was the initial example analyzed by Afonso #1 -- in
the 2nd post of the 60+ posts thread, and the one which I pointed
out many of his errors in the 3rd post of that thread.
I realized, only NOW, that the RE-analysis of that same example,
and the introduction of the 65/161 = .4962 was NOT by Afonso #1,
but by one of the OTHER Afonsos, probably #2, after he had been
exposed of his blunders in his initial analysis, not realizing Afonso
#1
had done it. I'll show HIS errors in his presentation of the
example.
Finally, I want to pull this post out, separate from the "Mad, Mad,
Mad, Mad, World" heading, to point to the important MAXI lecture
on this subject.
-- Reef Fish Bob.