I have a device that displays three numbers when a button is pressed. If any two numbers are different then one of the numbers is the exact room temperature but no telling which one it is.
If all the numbers are the same number I don’t have any reason to think the displayed number would be the room temperature. In a way I have two info channels “did the button pressing result in a temperature reading?” and “if there was a temperature reading what it tells me about the true temperature?”. The first of these channels doesn’t tell me anything about the temperature but it tells me about something.
Or I could have three temperature meters one of which is accurate in cold, on in moderate temperatures and one in hot temperatures. Suppose that cold and hot don’t overlap. If all the temperature cauges show the same number it would mean both the cold and hot meters would in fact be accurate in the same temperatures. I can not be more certain about the temperature than the operating principles of the measuring device as the temperature is based on those principles. The temperature gauges showing differnt temperatures supports me being rigth about the operating principles. Them being the same is evidence that I am ignorant on how those numbers are formed.
That is the case that +ing amongs many should be gaussian. If the distribution is too narrow to be caussian it tells against the “+ing” theory. Someone who is amadant that it is just a very narrow caussian could never be proven conclusively wrong. However it places restraints on how ranodm the factors can be. At some point the claim of regularity will become implausible. If you have something that claims that throwing a fair dice will always come up with the same number there is an error lurking about.
The variance of the Gaussian you get isn’t arbitrary and related to the variance of variables being combined. So unless you expect people picking folks out of a lineup to be mostly noise-free, a very narrow Gaussian would imply a violation of assumptions of CLT.
This Jewish law thing is sort of an informal law version of how frequentist hypothesis testing works: assume everything is fine (null) and see how surprised we are. If very surprised, reject assumption that everything is fine.
having unanimous tesitimony means that the gaussian is too narrow to be the results of noisy testimonies. So either they gave absolutely accurate testimonies or they did something else than testify. Having them all agree raises more doubt on that everyone was trying to deliver justice than their ability to deliver it. If a jury answers a “guilty or not guilty” verdict with “banana” it sure ain’t a result of a valid justice process. Too certasin results are effectively as good as “banana” verdicts. If our assumtions about the process hold they should not happen.
Can you clarify what youre talking about without using the terms method, operating and spread.
I have a device that displays three numbers when a button is pressed. If any two numbers are different then one of the numbers is the exact room temperature but no telling which one it is.
If all the numbers are the same number I don’t have any reason to think the displayed number would be the room temperature. In a way I have two info channels “did the button pressing result in a temperature reading?” and “if there was a temperature reading what it tells me about the true temperature?”. The first of these channels doesn’t tell me anything about the temperature but it tells me about something.
Or I could have three temperature meters one of which is accurate in cold, on in moderate temperatures and one in hot temperatures. Suppose that cold and hot don’t overlap. If all the temperature cauges show the same number it would mean both the cold and hot meters would in fact be accurate in the same temperatures. I can not be more certain about the temperature than the operating principles of the measuring device as the temperature is based on those principles. The temperature gauges showing differnt temperatures supports me being rigth about the operating principles. Them being the same is evidence that I am ignorant on how those numbers are formed.
Very well explained :)
https://en.wikipedia.org/wiki/Central_limit_theorem
That is the case that +ing amongs many should be gaussian. If the distribution is too narrow to be caussian it tells against the “+ing” theory. Someone who is amadant that it is just a very narrow caussian could never be proven conclusively wrong. However it places restraints on how ranodm the factors can be. At some point the claim of regularity will become implausible. If you have something that claims that throwing a fair dice will always come up with the same number there is an error lurking about.
The variance of the Gaussian you get isn’t arbitrary and related to the variance of variables being combined. So unless you expect people picking folks out of a lineup to be mostly noise-free, a very narrow Gaussian would imply a violation of assumptions of CLT.
This Jewish law thing is sort of an informal law version of how frequentist hypothesis testing works: assume everything is fine (null) and see how surprised we are. If very surprised, reject assumption that everything is fine.
Thus our knowledge on people being noisy means the mean is illdefined instead of inaccurate.
Sorry, what?
having unanimous tesitimony means that the gaussian is too narrow to be the results of noisy testimonies. So either they gave absolutely accurate testimonies or they did something else than testify. Having them all agree raises more doubt on that everyone was trying to deliver justice than their ability to deliver it. If a jury answers a “guilty or not guilty” verdict with “banana” it sure ain’t a result of a valid justice process. Too certasin results are effectively as good as “banana” verdicts. If our assumtions about the process hold they should not happen.