Robert Matthew
speaker
52 appearances
1 recordings
1 series
first heard Dec 2011
last heard Dec 2011
Robert Matthew’s voice in public audio — every appearance, attributed to the second.
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Appearances
When the result was announced at CERN on Tuesday...
there was talk about two experiments there, finding what they described as two sigma evidence for the existence of the Higgs.
And this was often explained in terms of it representing a
just 5% chance that the result was just a fluke.
Yes, that's right.
And it's often bandied around as being a measure of the probability that your result is just a fluke.
Now, unfortunately, it doesn't mean that.
What it actually means, and here the definition is something that you need to slightly concentrate for, it's the probability of getting at least as impressive evidence as you actually got on the assumption that fluke was the true explanation.
Now, instantly you can see that there's probably an issue with simply flipping that figure around and saying, oh, so it's also the probability that fluke really is the explanation for the results, because you can't simultaneously assume something and then use exactly the same result to claim it as evidence for what you're looking for.
A sort of an everyday analogy of the problem here of doing that flipping around is,
is a doctor has a patient come into the surgery and the patient's covered with spots.
Now, everyone knows that the probability that a patient has got spots given they've got measles is about 100%.
But clearly, the probability that someone has got measles given they've got spots is a completely different question and could be a completely different probability.
And that's the core of this misconception about these sigma levels.
When the scientists say they've got a two sigma level of evidence, they say it means there's a 5% chance their result is a fluke.
It actually doesn't mean that.
And this is why the physicists have reached for a much higher level of significance called a five sigma, which again, they're erroneously often explaining as a one in a million chance that their result is a fluke.
Now,
It turns out that the definition of sigma is such that as more and more evidence comes in, the exact interpretation of it becomes less and less important.
After a while, the data sort of dominates the interpretation.
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