3 ms·

There is no principled reason you can't compute a p-value from a sample size of 1.

deleted 10y ago
[deleted]
Retric 10y ago
What's the standard deviation of a sample size of one? Now, the standard counter example is a composite statistic. Like roll 100 6 sided dice get 600 and assume they are not fair. But, importantly there is a standard deviation assumed in the experiment and there was more than one dice roll. However, if you combine that with something else then your sample size drops back to one.
- yummyfajitas 10y ago
  The p-value is defined as p=P(evidence seen | null hypothesis). The standard deviation is only relevant if it is required to compute that number. You can run NHST on distributions without a p-value, e.g. a Cauchy distribution. You might need a standard deviation if you want to do some naive Z-test based on the CLT approximation (since the normal distribution requires a standard deviation), but that's not what XKCD was describing. XKCD was describing an exact test using the true distribution.
  - Retric 10y ago
    True distribution is not what they where using. They assumed the dice had zero bias which is never true for any physical system. I can say this is a dice and therefore it should have distribution X in theory. But, that does not mean it's actual distribution is X without testing. Further, even after testing nothing says the distribution will be unchanged. Note: The above seem pedantic, but it has significant real world implications.
    - yummyfajitas 10y ago
      All you're saying is models are imperfect. That's true. That doesn't mean you need a standard deviation or more than 1 sample. In this case, the model of 1/36 odds of rolling 2x6 would have to actually be 1/20 (or smaller) to invalidate this test. Do you find it plausible that the bias in 2 die is that high?
      - Retric 10y ago
        In that specific case yes, because there was no dice roll it was just a comic. In a wider context that single data point is evidence that the detector was tripped or was not tripped. But, unlike a Bayesian the frequentest does not say they then know the actual probability involved and they don't update their priors. Because, to do it correctly you need to pick a P value and a model before doing the test. Significant: https://xkcd.com/882/ https://xkcd.com/882/ makes a similar mistake by assuming a frequentist would accept that study design before running the tests. Multiple tests require more evidence, though when multiple groups are involved and not all publish you do get this problem.

deleted 10y ago

[deleted]

What's the standard deviation of a sample size of one? Now, the standard counter example is a composite statistic. Like roll 100 6 sided dice get 600 and assume they are not fair. But, importantly there is a standard deviation assumed in the experiment and there was more than one dice roll. However, if you combine that with something else then your sample size drops back to one.

yummyfajitas 10y ago
The p-value is defined as p=P(evidence seen | null hypothesis). The standard deviation is only relevant if it is required to compute that number. You can run NHST on distributions without a p-value, e.g. a Cauchy distribution. You might need a standard deviation if you want to do some naive Z-test based on the CLT approximation (since the normal distribution requires a standard deviation), but that's not what XKCD was describing. XKCD was describing an exact test using the true distribution.
- Retric 10y ago
  True distribution is not what they where using. They assumed the dice had zero bias which is never true for any physical system. I can say this is a dice and therefore it should have distribution X in theory. But, that does not mean it's actual distribution is X without testing. Further, even after testing nothing says the distribution will be unchanged. Note: The above seem pedantic, but it has significant real world implications.
  - yummyfajitas 10y ago
    All you're saying is models are imperfect. That's true. That doesn't mean you need a standard deviation or more than 1 sample. In this case, the model of 1/36 odds of rolling 2x6 would have to actually be 1/20 (or smaller) to invalidate this test. Do you find it plausible that the bias in 2 die is that high?
    - Retric 10y ago
      In that specific case yes, because there was no dice roll it was just a comic. In a wider context that single data point is evidence that the detector was tripped or was not tripped. But, unlike a Bayesian the frequentest does not say they then know the actual probability involved and they don't update their priors. Because, to do it correctly you need to pick a P value and a model before doing the test. Significant: https://xkcd.com/882/ https://xkcd.com/882/ makes a similar mistake by assuming a frequentist would accept that study design before running the tests. Multiple tests require more evidence, though when multiple groups are involved and not all publish you do get this problem.