5 ms·

Actually, you can. It's just a custom to do differently. But if you estimate your first moment is 2.1374 and your second moment is 1, I want to know just that,

Actually, you can. It's just a custom to do differently. But if you estimate your first moment is 2.1374 and your second moment is 1, I want to know just that, because it is the numbers I'll plug in my equations. I will decide to round if and when necessary

dTal 8y ago
You're implying that by rounding before handing off the numbers, valuable information is lost. Actually, the reverse is true - the rounding itself contains valuable information (how many digits are actually relevant) which is a hidden property of the process that obtained them. Unless you provide it through a side channel, failing to round hides this information, for no benefit at all (because the digits you provide are known to be meaningless). The only time this wouldn't be true is if you mistrust the significant figure calculation of the source, and believe you have sufficient insight to do better.
- devereaux 8y ago
  Yes, I do. In general, I stick to simple things. Enough samples and everything is normal, god bless the law of large numbers. If the precision of your estimation is not a direct function of the standard deviation, but is a "hidden property of the process that obtained" it, we have much bigger problems that losing "valuable information"
  - jeena 8y ago
    Back in high school in physics we would get minus points if we indicated a too high precision in the numbers we used for calculations, it was considered plain wrong to say 2.232cm if you actually only were able to measure that it's roughly 2cm.
    - godelski 8y ago
      And that's good, because you'll get the wrong answer if you used the number with too many points (nit picking: more decimal points does not mean higher precision). In fact, this is part of why you'll see physicists do all their reductions with variables and plug in numbers at the very end. This ensures that you doing get (what we could call) floating point errors. You don't have extra numbers hanging around (from real numbers like 1/9 or pi). There are also other benefits to doing this.
  - godelski 8y ago
    > If the precision of your estimation is not a direct function of the standard deviation, but is a "hidden property of the process that obtained" it I think you're confusing different types of error. There is error between measurements and an inherent error to the device you use to measure. There's also a difference between precision and accuracy. Standard deviation is the difference in multiple measurements. For example if you measure something 10 times to be 51mm, then your standard deviation is 0. But that doesn't mean you have no error. The "property of the process that obtained it" is not hidden. A simple case is a ruler. You have lines on the ruler that tell you certain intervals. If the smallest interval on your ruler is 1mm, then all your calculations can be made to +/- 1mm (that is, up to 30.5cm on a standard 12in ruler). There is nothing hidden about this. All that is being said here is that your measuring device is not perfect. So using the two errors, we have a measurement of 51mm +/- 1mm (or frequently in a short hand you'd just say 51mm). It would in fact be deceptive to say that your measurement was 51.0mm, because that implies that you have more precision than you actually have (implying that you have on the order of +/- 0.1mm precision).
    - devereaux 8y ago
      Assuming we are talking about software, error between measurements is a direct function of the device you use to measure, which is itself close to perfect Even if we go to the example you give, the measurement should be done n times, each reporting the exact result found like 51.0 51.9 51.95 etc. Even if the decimals are outside the smallest interval of your ruler: take enough of them and you can get closer to the actual length which may be 51.55345 and that you would never have been able to measure anyway without a caliper The best thing is you can even do that by resampling old measurements (a process called bootstrapping) So yes, if you remove the tenth of millimeters, you lose information. What's wrong is not the number, but that custom makes people think 51.0 means 51.0 +- 0.01 or anything else while it was never said like this.
      - dTal 8y ago
        How are you getting a measurement of 51.95mm from a ruler with 1mm ticks? If your ruler is capable of outputting that, and if those digits are actually meaningful (even if they do have error bars) then obviously yes they are definitionally significant digits and you shouldn't round them away.

dTal 8y ago

You're implying that by rounding before handing off the numbers, valuable information is lost. Actually, the reverse is true - the rounding itself contains valuable information (how many digits are actually relevant) which is a hidden property of the process that obtained them. Unless you provide it through a side channel, failing to round hides this information, for no benefit at all (because the digits you provide are known to be meaningless). The only time this wouldn't be true is if you mistrust the significant figure calculation of the source, and believe you have sufficient insight to do better.

devereaux 8y ago
Yes, I do. In general, I stick to simple things. Enough samples and everything is normal, god bless the law of large numbers. If the precision of your estimation is not a direct function of the standard deviation, but is a "hidden property of the process that obtained" it, we have much bigger problems that losing "valuable information"
- jeena 8y ago
  Back in high school in physics we would get minus points if we indicated a too high precision in the numbers we used for calculations, it was considered plain wrong to say 2.232cm if you actually only were able to measure that it's roughly 2cm.
  - godelski 8y ago
    And that's good, because you'll get the wrong answer if you used the number with too many points (nit picking: more decimal points does not mean higher precision). In fact, this is part of why you'll see physicists do all their reductions with variables and plug in numbers at the very end. This ensures that you doing get (what we could call) floating point errors. You don't have extra numbers hanging around (from real numbers like 1/9 or pi). There are also other benefits to doing this.
- godelski 8y ago
  > If the precision of your estimation is not a direct function of the standard deviation, but is a "hidden property of the process that obtained" it I think you're confusing different types of error. There is error between measurements and an inherent error to the device you use to measure. There's also a difference between precision and accuracy. Standard deviation is the difference in multiple measurements. For example if you measure something 10 times to be 51mm, then your standard deviation is 0. But that doesn't mean you have no error. The "property of the process that obtained it" is not hidden. A simple case is a ruler. You have lines on the ruler that tell you certain intervals. If the smallest interval on your ruler is 1mm, then all your calculations can be made to +/- 1mm (that is, up to 30.5cm on a standard 12in ruler). There is nothing hidden about this. All that is being said here is that your measuring device is not perfect. So using the two errors, we have a measurement of 51mm +/- 1mm (or frequently in a short hand you'd just say 51mm). It would in fact be deceptive to say that your measurement was 51.0mm, because that implies that you have more precision than you actually have (implying that you have on the order of +/- 0.1mm precision).
  - devereaux 8y ago
    Assuming we are talking about software, error between measurements is a direct function of the device you use to measure, which is itself close to perfect Even if we go to the example you give, the measurement should be done n times, each reporting the exact result found like 51.0 51.9 51.95 etc. Even if the decimals are outside the smallest interval of your ruler: take enough of them and you can get closer to the actual length which may be 51.55345 and that you would never have been able to measure anyway without a caliper The best thing is you can even do that by resampling old measurements (a process called bootstrapping) So yes, if you remove the tenth of millimeters, you lose information. What's wrong is not the number, but that custom makes people think 51.0 means 51.0 +- 0.01 or anything else while it was never said like this.
    - dTal 8y ago
      How are you getting a measurement of 51.95mm from a ruler with 1mm ticks? If your ruler is capable of outputting that, and if those digits are actually meaningful (even if they do have error bars) then obviously yes they are definitionally significant digits and you shouldn't round them away.