

Fermilab Set to Reveal “Interesting” Higgs Boson Results - loboman
http://blogs.scientificamerican.com/observations/2012/02/17/fermilab-set-to-reveal-interesting-higgs-boson-results/

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DavidSJ
Yet another example of the confusion in popular science reporting between the
probability of A given B with the probability of B given A. How is this
acceptable?

 _the Tevatron would be able to identify the Higgs with 'three-sigma'
certainty. This is a statistical term that indicates the finding only has a
tenth of a percent chance of being due to a random statistical fluctuation._

No no no! It _actually_ means that random statistical fluctuation has a tenth
of a percent chance of producing the finding!

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extension
What's the difference?

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DavidSJ
It's the same as the difference between "0.1% of non-spam messages are marked
as spam" (false positive rate) vs. "0.1% of messages marked as spam are not
spam" (false negative rate).

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prodigal_erik
Those seem like the same false positive case to me. For a false negative, did
you mean "0.1% of spam messages are not marked as spam"?

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DavidSJ
Whoops, you're right, they're both false positives, but one is number of false
positives as a percentage of messages marked as spam, and the other is number
of false positives as a percentage of messages that aren't spam. The ratios
would be completely different.

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prodigal_erik
Oh yeah, there's only one absolute number of false positives, but when you
turn it into a rate you have to choose either "of all positive results, what
portion were false" or "of all test results, what portion were positive and
false", which are far apart for tests that give many negative results.

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yanowitz
Would this really be telling us anything? Presumably, they've chosen 5-sigma
for a good reason (they make so many observations?). So what would a 3-sigma
result signify?

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GavinB
At three or four sigmas we could be pretty sure it's true. At five sigmas
we're willing to bet the next generation of scientific research on it.

