Test ur logic, Probability question

[xniNja]

Yes, I repeated it for emphasis. I don't see why it is useless or a tautology. Anyone can plug in 2 numbers into Baye's Theoreom... You claim I'm ignoring the relevant information of 1% of the pop. being sick, but at the same time I think it's an equally valid claim, and if not correct, interesting and logical approach to claim the reverse. It's a conceivable logical argument that if the results of a test are 90% accurate, then any result is 90% accurate- I don't see this as tautology.

[BruceZ]

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Yes, I repeated it for emphasis. I don't see why it is useless or a tautology.

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Oh come on. You don't see why it's useless to state that If the probability of a test being correct is 90%, then the probability of a test being correct is 90%? You've just asserted the reflexive property that A = A. Congratulations.

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Anyone can plug in 2 numbers into Baye's Theoreom

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Not so. A very small percentage of people can plug in 2 numbers (actually 4 numbers in this case) into Bayes' theorem correctly. Most people can't even spell "Baye's Theoreom".


[ QUOTE ]
You claim I'm ignoring the relevant information of 1% of the pop. being sick, but at the same time I think it's an equally valid claim, and if not correct, interesting and logical approach to claim the reverse. It's a conceivable logical argument that if the results of a test are 90% accurate, then any result is 90% accurate- I don't see this as tautology.

[/ QUOTE ]

No *that's* not a tautology. That's a false statement. Any result is not 90% accurate. The only results that are 90% accurate are the results which are unknown. There were no unknown results in this problem. There was but one result in this problem, and it was clearly stated that the result was positive. Yet you stated in your original post that this *positive* result was 90% accurate. WRONG.

If you want to ignore the conditions of a problem, make false statements, and amuse yourself by stating the reflexive property, fine, go ahead. But don't do it in response to a clearly defined problem, and then try to state that what you have done is in some way relevant. I have no more time for this.

[xniNja]

I immediately retracted my first post... but fine, you're right... It's true I was much more concerned with my amusement of an antithetical construct than actually solving the problem, but that post was definitely not clearly defined, and I wasn't merely quoting the reflexive property.

[lastchance]

I think it is 90%.

If this question was a Bayes Theorem Question, it was very poorly worded.

What does, "the test results are true only 90% of the time" mean?

Is that the rate of false positives to false negatives? What does it mean?

Does it mean if you select a random test result, it's true 90% of hte time?

[BruceZ]

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I think it is 90%.

If this question was a Bayes Theorem Question, it was very poorly worded.

What does, "the test results are true only 90% of the time" mean?

Is that the rate of false positives to false negatives? What does it mean?

Does it mean if you select a random test result, it's true 90% of hte time?

[/ QUOTE ]

I took it to mean that it will call a well person well 90% of the time, and it will call a sick person sick 90% of the time. These two probabilities should have been specified separately, but since they weren't, the obvious assumption is that they are both 90%. If it right in 90% of well people, then it must be right in 90% of sick people too if it is to be right in 90% of all people. Then this is clearly a Bayes' theorem problem with an answer of 11:1 against being sick.

A real world problem might have 10% false positives, and no false negatives, and it is possible that the OP miscopied this problem. In this case, the chance that the man is really sick would be 1%*100% = 1%, and the chance that he is well would be 99% * 10% = 9.9%. Then the odds against him being sick would be 9.9:1.

[xniNja]

See, I wasn't the only one. The poor English and "u r is tru" and such is deceptive! Does this also prove the 90% 1st-priority logic is reasonable? Maybe not sound, but it's logical.

If it is a standard Bayes' Theorem problem, that's fine- you're correct. Learn to be able to see other viewpoints on the same problem.

[PairTheBoard]

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pif --
But the test results r true only in 90% from the tests

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My opinion now is that this problem is technically not well defined because this phrase can technically be translated in two ways. The phrase "from the tests" seems redundant and unnecessary or else impossible to glean precise meaning from. Dropping that phrase the statement becomes,

'But the test results r true only in 90% '

The words "but" and "only" just serve to emphasize that the test is not 100% accurate, so they can be dropped. We already know that.

'the test results r true in 90%'

Now, what does this mean? Does it mean that whatever the test result Is there is a 90% chance that it is True? In other words, If the test result says you are sick there is a 90% chance you are sick, and if the test result says you are ok there is a 90% chance that you are ok? Technically I don't think you can rule that out. But if that's what pif means then why does he ask the chances of being sick when the test result says you are sick? There's no point to it. He's just wasting our time if that's what he means. Although you might get a real problem out of it by asking what the False Positive and False Negative probabilties would have to be for the test to yield such a 90% overall accuracy in this population.

So, assuming pif does not intend to waste our time, what can we Infer the vauge statement means. As Bruce and I have done, the natural inference given the context is that when pif says essentially,

'the test results r true in 90%'

he means the Test gives 10% False positives and 10% False Negatives.

A good example for how difficult it is to get a computer to understand people language.

PairTheBoard