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Numbers to think about



 
 
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  #101  
Old August 2nd 06, 01:29 AM posted to rec.bicycles.racing
Jack Hollis
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Default Numbers to think about

On 1 Aug 2006 14:45:15 -0700, "
wrote:

What is the probability that FL's positive result is false?


I don't know.
In order to compute this, you need to have at least a decent guess at
A) the fraction of the tested population that's clean
B) the fraction that's dirty (okay, just B=1-A)



Well, you've just pointed out why these Bayesian formulas don't work
in a situation where you don't know the incidence of whatever it is
that your measuring in the population, which is the case in this
situation.

Intuitively, the incidence of X in the population shouldn't matter
regarding the probability of a false positive being indeed false
because this seems to be a function of the test and the sample, but
who am I to disagree with the late Reverend Bayes. Like you, Bayes
often leaves me scratching my head. It took me quite a while to get
the Monty Hall Problem.

There must be a way to calculate the probability of a positive being
false given the information we have. Perhaps the answer will not be
as accurate as it could be if we had information on the actual number
of dopers in the entire group, but there has to be a way. My guess is
that the best estimate given the information we have is 1%.

In any case, the probability of a positive result being false is not
the ratio of false verses real positives in the total population. I
assume even a Bayesian would agree with that.
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  #102  
Old August 2nd 06, 01:33 AM posted to rec.bicycles.racing
Jack Hollis
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Default Numbers to think about

On Tue, 01 Aug 2006 23:23:42 GMT, Keith wrote:

On Mon, 31 Jul 2006 20:52:10 +0200, Montesquiou wrote:

Personally, I hope that FL is exonerated, but my hopes do not change
probability theory.

Of course, as you know, I have the same.. but opposit hope


Of course, as an American, I can understand how a Frenchman might be
happy to see an American stripped of his TdF title. BTW, how did you
like the World Cup Final?


A fabulous event obviously, hope you can enjoy it someday too...doubt
it. ****wit.


First of all Keith, this remark was for Monty and, judging from his
response, he took it in the spirit that it was intended.

Second, there's no need to be rude.
  #103  
Old August 2nd 06, 01:37 AM posted to rec.bicycles.racing
[email protected]
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Default Numbers to think about


Jack Hollis wrote:
On Mon, 31 Jul 2006 04:24:15 GMT, Ed wrote:

IN each of these cases, the accuracy of the test is 99% but the chance
that a positive test is valid is very different - due to the actual
number of true positives, low in the first case and high in the second.


Absolutely not. What your proposing would be true if the results of a
specific test were dependent on the number of samples tested and the
number of dirty verses clean urines in the sample. However, this is
not the case. All of the tests are independent events and, as such,
the chance of a clean sample testing positive is always 1%.


Independent events?
same source sample? (split)
same lab?
same procedure?

these are not independent events.

separate days, separate custody of sample, different lab - would sound
much more "independent" to me.

-bdbafh

  #104  
Old August 2nd 06, 01:43 AM posted to rec.bicycles.racing
Jack Hollis
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Default Numbers to think about

On 1 Aug 2006 14:45:15 -0700, "
wrote:

I don't have a reliable source for any of these numbers.
If you go back to the _original_ post in this thread, it posits
that the UCI does 12000 tests, found 380 positives, and pulls
out of thin air the supposition that the test is 99% accurate.


I agree that most of this thread is based on dodgy suppositions, but
the theoretical discussion has been interesting nonetheless.
  #105  
Old August 2nd 06, 01:52 AM posted to rec.bicycles.racing
KV
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Default Numbers to think about

It seems to me that if they used two independent labs, splitting the samples
at time of collection, this could eliminate a lot of doubt.

Montesquiou wrote in message
...

a icrit dans le message de news:
...

Montesquiou wrote:
"CowPunk" a icrit dans le message de news:
...
1% of 12000 = 120

120:380 ~ 1:3


Oh my friend !!!

With all due respect if it is way they teach statistic in your country
...
You are lost.

However as I have many friends in the USA and I know they are not so
ignorants in Math, I believe the problem is your.

Since your original post you DECIDED that 1% of the test were wrong.

So 1% of the 380 positive (that you DECIDED BY YOUR OWN) are wrong.

1% of 380 is 3.8.

Turn your problem the way you want 1% is allway 1% and NEVER 1:3 (33.33
%)
!!

Oh my God, pls help me !


I am here and I will help you.

First, in each test there is an A and B sample and the test is done on
each. So if the there is a 1% chance of error on any give sample,
then the probablitity or an error both is found be multiplying .01
times .01 or .0001 or 0.01%.

Second, do not assume any error percentage until one appears in the
scientific literature, that is one that has been established with a
proven protocol and by actual perfroming many blind tests with samples
of known quality. One of the difficulties in this area is that test
error rates have not been established and made publicly available.

***

Correct.

It was so difficult for me to explain to him his wrong mathematical
reasoning that I did not even argued on the wrong initial suppositions he
did.





  #106  
Old August 2nd 06, 02:04 AM posted to rec.bicycles.racing
CowPunk
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Default Numbers to think about


KV wrote:
It seems to me that if they used two independent labs, splitting the samples
at time of collection, this could eliminate a lot of doubt.


ditto. When I did research we used 3 labs. And we always got
differrent
results for the same sample. I don't understand why the UCI, and
especially
the riders union, don't demand that the samples be tested by several
labs.

  #108  
Old August 2nd 06, 10:48 AM posted to rec.bicycles.racing
Donald Munro
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Default Numbers to think about

Tom Kunich wrote:
If some OTHER lab doesn't do the testing I simply won't accept the
results.


You could consider having your world reprogrammed to include this
directive.


 




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