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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 sayin

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
    > By definition, "the measurement is a statistical coincidence" means the same thing as "the null hypothesis is true". OK, now I see what you're saying. I'm not sure that's how people interpret it in plain English though. I feel like people would interpret "is a coincidence" to mean "occurred coincidentally", aka "occurred naturally [by chance]". It might be kind of like arguing that "ladies and gentlemen" refers to their intersection rather than union. Mathematically it does, but English is another matter... Maybe the only way to settle this is to actually go do an experiment on people. I could be wrong, but I feel like if you go up to people and say "I think these 2 dice are fair, and I got two 6's when I tossed them; what are the chances this is a coincidence?" you'd get back "1/36" from most people. (Assuming they remember basic probability at all. You can filter against that by first asking them something more obvious, like maybe "what are the chances of getting 2 heads in a row with a fair coin" and making sure they tell you 1/4 before you proceed.)
    - DavidSJ 6y ago
      I consider “occurred coincidentally”, “is a coincidence”, and “occurred by chance” interchangeable. They are all equivalent to the null hypothesis. If my dice are loaded then the two 6’s weren’t a coincidence. They were guaranteed. So to say they happened by coincidence is to say the dice are fair (the null hypothesis is true). Consider a typical English sentence: “was it just a coincidence that I saw Frank in town, or was he following me?” They are two alternative hypotheses to explain the same observation: In the first scenario, we assume that Frank was going about his business and just happened by chance to be in the same place as I. In the second, we assume Frank was following me and that’s why he was in the same place. The question is about the hypothesis invoked to explain the observation. “Coincidence” is a (null) 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
  > By definition, "the measurement is a statistical coincidence" means the same thing as "the null hypothesis is true". OK, now I see what you're saying. I'm not sure that's how people interpret it in plain English though. I feel like people would interpret "is a coincidence" to mean "occurred coincidentally", aka "occurred naturally [by chance]". It might be kind of like arguing that "ladies and gentlemen" refers to their intersection rather than union. Mathematically it does, but English is another matter... Maybe the only way to settle this is to actually go do an experiment on people. I could be wrong, but I feel like if you go up to people and say "I think these 2 dice are fair, and I got two 6's when I tossed them; what are the chances this is a coincidence?" you'd get back "1/36" from most people. (Assuming they remember basic probability at all. You can filter against that by first asking them something more obvious, like maybe "what are the chances of getting 2 heads in a row with a fair coin" and making sure they tell you 1/4 before you proceed.)
  - DavidSJ 6y ago
    I consider “occurred coincidentally”, “is a coincidence”, and “occurred by chance” interchangeable. They are all equivalent to the null hypothesis. If my dice are loaded then the two 6’s weren’t a coincidence. They were guaranteed. So to say they happened by coincidence is to say the dice are fair (the null hypothesis is true). Consider a typical English sentence: “was it just a coincidence that I saw Frank in town, or was he following me?” They are two alternative hypotheses to explain the same observation: In the first scenario, we assume that Frank was going about his business and just happened by chance to be in the same place as I. In the second, we assume Frank was following me and that’s why he was in the same place. The question is about the hypothesis invoked to explain the observation. “Coincidence” is a (null) hypothesis.