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> 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 no

> 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.
davrosthedalek 6y ago
Again, the chance that the ten heads occurred "by chance", "occurred coincidentally" or "is a coincidence" is not 1/1000. IF they occurred by chance, the probability for such a thing to occur (again) is 1/1000. 1/36 is the wrong answer for the question "what are chances this is a coincidence?". That probability is unknown, because it depends on whether the dice are actually fair, and what other dice are there. For example, if you have to discriminate between fair dice and unfair dice with only 2s on them, a 12 would indicate that with 100%, it was a coincidence. You might ask differently though: "What WAS the probability to throw a 12 with two fair dice?". But that probability collapsed to 100% when you actually throw them and got the result.
- dataflow 6y ago
  Again, I'm saying I think people would interpret "what are the chances this is a coincidence" as "what are the chances of this occurring coincidentally (i.e. by chance, naturally, not influenced by an outside force)", to which they would answer 1/36.

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.

davrosthedalek 6y ago

Again, the chance that the ten heads occurred "by chance", "occurred coincidentally" or "is a coincidence" is not 1/1000. IF they occurred by chance, the probability for such a thing to occur (again) is 1/1000. 1/36 is the wrong answer for the question "what are chances this is a coincidence?". That probability is unknown, because it depends on whether the dice are actually fair, and what other dice are there. For example, if you have to discriminate between fair dice and unfair dice with only 2s on them, a 12 would indicate that with 100%, it was a coincidence. You might ask differently though: "What WAS the probability to throw a 12 with two fair dice?". But that probability collapsed to 100% when you actually throw them and got the result.

dataflow 6y ago
Again, I'm saying I think people would interpret "what are the chances this is a coincidence" as "what are the chances of this occurring coincidentally (i.e. by chance, naturally, not influenced by an outside force)", to which they would answer 1/36.