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If I say: "there's a 25% chance that Pat is from North Dakota", I'm taking as a given that there is a person named Pat, and I'm talking about the chance that Pa

If I say: "there's a 25% chance that Pat is from North Dakota", I'm taking as a given that there is a person named Pat, and I'm talking about the chance that Pat, whom we know to exist, is from North Dakota. In this case, grammatically, they're talking about the chance that the measurement (data) is a statistical coincidence, as opposed to not being a statistical coincidence. They're not talking about the chance that the data exists, as opposed to not existing.

dataflow 6y ago
> If I say: "there's a 25% chance that Pat is from North Dakota", I'm taking as a given that there is a person named Pat, and I'm talking about the chance that Pat, whom we know to exist, is from North Dakota. Yes, and if I say "there's a 0.001% chance that these coin flip observations were coincidental", I'm taking it as a given that there were coin flips observed (indeed, there were!) I'm talking about the chance that the observations, which we (indeed) know to exist, were coincidental. That is... literally P(observations | null hypothesis) = P(10 heads | fair). It's clearly not P(null hypothesis | observations) = P(fair | 10 heads)... > In this case, grammatically, they're talking about the chance that the measurement (data) is a statistical coincidence, as opposed to not being a statistical coincidence. They're not talking about the chance that the data exists, as opposed to not existing. Which is... perfectly fine. The data clearly does exist (as would the coin flips in my example), so the chance of the data existing is 100%... there's nothing interesting to talk about there. But the chance of it having been coincidental is 0.001%. This all seems correct to me...
- DavidSJ 6y ago
  There's been a misunderstanding between us. To clarify, I'm not saying we know some data exists (that's of course true, since an experiment was done). I'm saying we know this data exists. Grammatically, they've worded it so that the question is whether this particular data that we have seen (as opposed to other data we could have seen) was in fact produced by chance or not. The difference between the data being a statistical coincidence and the data not being a statistical coincidence is precisely the difference between the null hypothesis being true and the null hypothesis not being true. So they're making a claim about the probability of a hypothesis.
  - dataflow 6y ago
    > There's been a misunderstanding between us. To clarify, I'm not saying we know some data exists (that's of course true, since an experiment was done). I'm saying we know this data exists. But that's exactly what I'm saying too? When I flip 10 coins and see 10 heads, that is the data, and it very much exists. Nobody is talking about any data except that one. Not me, not you, not BBC. > Grammatically, they've worded it so that the question is whether this particular data that we have seen (as opposed to other data we could have seen) was in fact produced by chance or not. Yes, and as I see it this is 100% correct. Like in my example where I saw 10 heads (that is the one and only dataset we know exists), and I'm wondering if they were produced by chance or not. That is precisely P(10 heads | fair coin) = P(observations | H0). > The difference between the data being a statistical coincidence and the data not being a statistical coincidence is precisely the difference between the null hypothesis being true and the null hypothesis not being true. Maybe your English analogy is the source of the confusion here? I don't know what rigorous definition you might have for "the difference" here(?), but whatever it is, "10 heads have a 0.001% chance with a fair coin" doesn't imply "10 heads have a 99.999% chance under an unfair coin"... right? Even though the former assumes H0 and the latter assumes !H0. Or to put it another way, just because H0 is true in one statement and false in another, that doesn't mean we're talking about the probability of H0 being true in one statement and the probability of H0 being false in another.
    - DavidSJ 6y ago
      The original wording is: "there is roughly a one in 1,000 chance that the measurement is a statistical coincidence". By definition, "the measurement is a statistical coincidence" means the same thing as "the null hypothesis is true". That's literally just how we define "statistical coincidence". So the sentence might as well be worded: "there is roughly a one in 1,000 chance that the null hypothesis is true".
      - davrosthedalek 6y ago
        The point is that, from the measurement alone, you cannot make a statement of whether the null hypothesis is true. You can only make a statement how likely the observed outcome was /if/ the null hypothesis is true. (edit: I realize that you mean this. I just wanted to make it clearer. The article should have said: It's a 1/1000 chance that a measured difference of this or larger magnitude occurs as a statistical fluctuation assuming the SM)

dataflow 6y ago

> If I say: "there's a 25% chance that Pat is from North Dakota", I'm taking as a given that there is a person named Pat, and I'm talking about the chance that Pat, whom we know to exist, is from North Dakota. Yes, and if I say "there's a 0.001% chance that these coin flip observations were coincidental", I'm taking it as a given that there were coin flips observed (indeed, there were!) I'm talking about the chance that the observations, which we (indeed) know to exist, were coincidental. That is... literally P(observations | null hypothesis) = P(10 heads | fair). It's clearly not P(null hypothesis | observations) = P(fair | 10 heads)... > In this case, grammatically, they're talking about the chance that the measurement (data) is a statistical coincidence, as opposed to not being a statistical coincidence. They're not talking about the chance that the data exists, as opposed to not existing. Which is... perfectly fine. The data clearly does exist (as would the coin flips in my example), so the chance of the data existing is 100%... there's nothing interesting to talk about there. But the chance of it having been coincidental is 0.001%. This all seems correct to me...

DavidSJ 6y ago
There's been a misunderstanding between us. To clarify, I'm not saying we know some data exists (that's of course true, since an experiment was done). I'm saying we know this data exists. Grammatically, they've worded it so that the question is whether this particular data that we have seen (as opposed to other data we could have seen) was in fact produced by chance or not. The difference between the data being a statistical coincidence and the data not being a statistical coincidence is precisely the difference between the null hypothesis being true and the null hypothesis not being true. So they're making a claim about the probability of a hypothesis.
- dataflow 6y ago
  > There's been a misunderstanding between us. To clarify, I'm not saying we know some data exists (that's of course true, since an experiment was done). I'm saying we know this data exists. But that's exactly what I'm saying too? When I flip 10 coins and see 10 heads, that is the data, and it very much exists. Nobody is talking about any data except that one. Not me, not you, not BBC. > Grammatically, they've worded it so that the question is whether this particular data that we have seen (as opposed to other data we could have seen) was in fact produced by chance or not. Yes, and as I see it this is 100% correct. Like in my example where I saw 10 heads (that is the one and only dataset we know exists), and I'm wondering if they were produced by chance or not. That is precisely P(10 heads | fair coin) = P(observations | H0). > The difference between the data being a statistical coincidence and the data not being a statistical coincidence is precisely the difference between the null hypothesis being true and the null hypothesis not being true. Maybe your English analogy is the source of the confusion here? I don't know what rigorous definition you might have for "the difference" here(?), but whatever it is, "10 heads have a 0.001% chance with a fair coin" doesn't imply "10 heads have a 99.999% chance under an unfair coin"... right? Even though the former assumes H0 and the latter assumes !H0. Or to put it another way, just because H0 is true in one statement and false in another, that doesn't mean we're talking about the probability of H0 being true in one statement and the probability of H0 being false in another.
  - DavidSJ 6y ago
    The original wording is: "there is roughly a one in 1,000 chance that the measurement is a statistical coincidence". By definition, "the measurement is a statistical coincidence" means the same thing as "the null hypothesis is true". That's literally just how we define "statistical coincidence". So the sentence might as well be worded: "there is roughly a one in 1,000 chance that the null hypothesis is true".
    - davrosthedalek 6y ago
      The point is that, from the measurement alone, you cannot make a statement of whether the null hypothesis is true. You can only make a statement how likely the observed outcome was /if/ the null hypothesis is true. (edit: I realize that you mean this. I just wanted to make it clearer. The article should have said: It's a 1/1000 chance that a measured difference of this or larger magnitude occurs as a statistical fluctuation assuming the SM)