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!

What's the difference?

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).

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"?

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.

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.

Hmm are not those two sentences equivalent? That is, P(finding | random fluctuation) = 0.10

Nope, statistical significance is based on two things.

1) Assume the model is true.

2) Conditional on the model, what is the probability that the observed differences are due to chance? The p value is then the probability that a test statistic at least this extreme could have been produced by chance.

Its actually p=0.001, not p=.10 also.

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?

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.

The LHC has two independent detector/teams: Atlas y CMS. Each one announced last December "evidence" of the existence of the Higgs Boson with a mass near ~125GeV, with a ~3 sigma significance. This is another ~3 sigma result in the same range from a different laboratory.

Combining naively the three results we get a ~sqr(3)3=~5 sigma significance. The real combination methods are more difficult, and probably involve a few Ph.D. thesis. But if someone that really knows about the subject does the calculations and get a 5 sigma result, I wouldn’t be very surprised. So another 3 sigma result in the same region is very interesting.

For the official result, I think that it is difficult to combine the results of different laboratories. Each laboratory will continue to get more data and try to get it own 5 sigma result, probably next year.