Numbers to think about

Ed wrote:

I believe what the original poster meant was that the occurance of a false
positive is 1%. That would mean that after taking 12000 tests, 1% or 120
false positive results would be expected. If there were a total of 380
positives out of that same 12000, 120 would be false ones and the other 260
would be real.

HTH

Ed

Yes.

On Sun, 30 Jul 2006 01:12:43 +0200, Montesquiou wrote:

In the 120 we have some Good Guys wrongly called cheaters, and some cheaters
called Good Guys

OK ?

If the errors are random, then half of them are false negatives which
would never be reported. So the probability of a false positive in a
sample of 12000 is 60 or .005.

CowPunk wrote:
Ed wrote:

I believe what the original poster meant was that the occurance of a false
positive is 1%. That would mean that after taking 12000 tests, 1% or 120
false positive results would be expected. If there were a total of 380
positives out of that same 12000, 120 would be false ones and the other 260
would be real.

HTH

Ed

Yes.

But you know see that the percentage of the false positives has to be
independent of the number of the number of total positives, right?

I mean, imagine you test 10000 subjects, where 10000 have done Tes. I.e.
you get 10000 positives, and none of them is wrong.

The percentage describes the probability of a positive being false, not
the probability of any test producing a false positive.

On Sun, 30 Jul 2006 14:35:23 +0200, Montesquiou wrote:

"CowPunk" a écrit dans le message de news:
. com...
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 !

You do need help.

If the probability of error is 1%, then there will be 120 errors in a
sample of 12000. If the number of positives actually found is 380,
then by chance slightly less than 1 in 3 are errors.

There is also the probability of a false negative when the sample
actually was dirty but the test failed to pick it up. Contrary to my
previous post this does make the chance of a false positive .005
because you can only have a false negative if the sample was actually
dirty and I hope that half the 12000 samples were not dirty.

Ernst Noch wrote in :

CowPunk wrote:
Ed wrote:

I believe what the original poster meant was that the occurance of a
false positive is 1%. That would mean that after taking 12000
tests, 1% or 120 false positive results would be expected. If there
were a total of 380 positives out of that same 12000, 120 would be
false ones and the other 260 would be real.

HTH

Ed

Yes.

But you know see that the percentage of the false positives has to be
independent of the number of the number of total positives, right?

I mean, imagine you test 10000 subjects, where 10000 have done Tes.
I.e. you get 10000 positives, and none of them is wrong.

The percentage describes the probability of a positive being false,
not the probability of any test producing a false positive.



The number of false positives is based on the number of tests performed.
The percentage gives the number of false positives expected for every 100
tests performed. The percentage is not the probility of a positive being
false. If 100 tests were done, then one would expect 1 negative sample to
show up positive. Thus if you did 100 tests, and there was one positive,
it is likely that this result is in error. If 65 of the 100 were positive,
then (statistically) 64 were correct and 1 was a false positive.

Ed

"Jack Hollis" a écrit dans le message de news:
...
On Sun, 30 Jul 2006 14:35:23 +0200, Montesquiou wrote:

"CowPunk" a écrit dans le message de news:
.com...
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 !

You do need help.

If the probability of error is 1%, then there will be 120 errors in a
sample of 12000.

Yes 120 errors, but in both side :
False Negative - true positive = (12000 - 380)*1% = 116.2
False Positive - true Negative = 380*1%= 3.8
3.8+116.2 = 120 errors.

As you an see the error is alway 3.8 out of 380 = 1%
116.2 out of 11600 = 1 %

By chance ; )



If the number of positives actually found is 380,
then by chance slightly less than 1 in 3 are errors.

There is also the probability of a false negative when the sample
actually was dirty but the test failed to pick it up. Contrary to my
previous post this does make the chance of a false positive .005
because you can only have a false negative if the sample was actually
dirty and I hope that half the 12000 samples were not dirty.

On 30 Jul 2006 08:47:16 -0700, wrote:

Dear Bovine:

Your reasoning is wrong. the french philosopher's explanation was on
target. 1% error does no mean that 1 out of 3 tests will be wrong. No
matter how you articulate the problem.

Andres


First you have to define error. If the 1% error rate is only false
positives, then 12000 tests of clean samples will result in 120 false
positives. Obviously, you can't have a false positive on a sample
that is a real positive. In that case, the only chance of error is a
false negative.

It would be nice to know exactly what this reported 1% error rate
actually represents. If it means that 1 out of 100 positive samples
return a false negative and 1 out of 100 negative samples return a
false positive, then the only way to accurately calculate the number
of errors in a sample of 12000 tests is to know how many of them are
actually positive and negative.

"Jack Hollis" a écrit dans le message de news:
...
On 30 Jul 2006 08:47:16 -0700, wrote:

Dear Bovine:

Your reasoning is wrong. the french philosopher's explanation was on
target. 1% error does no mean that 1 out of 3 tests will be wrong. No
matter how you articulate the problem.

Andres


First you have to define error. If the 1% error rate is only false
positives, then 12000 tests of clean samples will result in 120 false
positives. Obviously, you can't have a false positive on a sample
that is a real positive. In that case, the only chance of error is a
false negative.


As the poster said "Let's assume that the labs and their tests are 99%
accurate." it is clear that
the 1 % came on his own. He said 1% as he could have said 0.1% or 10 %

It would be nice to know exactly what this reported 1% error rate
actually represents. If it means that 1 out of 100 positive samples
return a false negative and 1 out of 100 negative samples return a
false positive, then the only way to accurately calculate the number
of errors in a sample of 12000 tests is to know how many of them are
actually positive and negative.

Jack Hollis wrote:
On 30 Jul 2006 08:47:16 -0700, wrote:

Dear Bovine:

First you have to define error.
I'm just saying for the sake of argument that the 1% error represents:
0.1% false positive errors i.e. those for which no one can account, a
function of the test itself.
+ 0.5% contamination errors
+ 0.4% lab technician erros
0.1 + 0.4 + 0.5 = 1% overall error


actually positive and negative.

real numbers a
@12100 test performed
3.8% positive

Ed wrote:
Ernst Noch wrote in :

CowPunk wrote:
Ed wrote:

I believe what the original poster meant was that the occurance of a
false positive is 1%. That would mean that after taking 12000
tests, 1% or 120 false positive results would be expected. If there
were a total of 380 positives out of that same 12000, 120 would be
false ones and the other 260 would be real.

HTH

Ed
Yes.

But you know see that the percentage of the false positives has to be
independent of the number of the number of total positives, right?

I mean, imagine you test 10000 subjects, where 10000 have done Tes.
I.e. you get 10000 positives, and none of them is wrong.

The percentage describes the probability of a positive being false,
not the probability of any test producing a false positive.



The number of false positives is based on the number of tests performed.
The percentage gives the number of false positives expected for every 100
tests performed. The percentage is not the probility of a positive being
false. If 100 tests were done, then one would expect 1 negative sample to
show up positive. Thus if you did 100 tests, and there was one positive,
it is likely that this result is in error. If 65 of the 100 were positive,
then (statistically) 64 were correct and 1 was a false positive.

Ed

I was wrong above.
I just forgot that stuff, so I looked it up, here's a good explanation:
http://en.wikipedia.org/wiki/Binary_classification
What I was thinking of is sensitivity and specificity.