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Re: [Phys-l] Significant figures -- again



At the risk of throwing myself into the fray... Let me stop you right there, John. The traditional method of writing a number to indicate the error or significant figures would be to include the trailing zeros. This indicates the precision in a manner consistent with professional publications. For scientists it communicates the precision clearly.

If your point is that this system gets abused, it is well taken. Writing 3.0 ± 0.1 really means that if I measure this same quantity a number of times I'm likely to get a value greater than 3.1 or less than 2.9 about 30 percent of the time. I'm presuming that the error here is all statistical. Usually these errors contain some systematic error as well.

The human tendency is to overstate the error because one is cautious about presenting the result. This is more true when publishing a value that disagrees with the currently accepted value. I think that you are trying to make a case that it is wise to keep this extra information throughout the calculation. Here's a contrived example: Suppose that it were difficult to measure pi and a world of scientists were doing it. Everybody reported 3.0 ± 0.1. The real value falls within 2 sigma of that result so it's a fairly reported answer. A minority of people measure 3.14 and round off their error to the same precision: 3.1 ± 0.1. The well-intentioned editorial staff at the CRC wants to publish a world-average value from all of the most prestigious journals. If you average all of those 3.0's together with the 3.1's you'll still be wrong. If the 3.0 group had been reporting 3.04 and the 3.1 group had reported 3.14, the world average would be closer to the correct number. Or... not quite as wrong. Given the reported limitations of the methods, it's within error.

It's not uncommon to see two digits of precision in the error. 2.37 ± 0.32 for example.

Paul


On Mar 13, 2012, at 12:21 PM, John Denker wrote:

Suppose, based on ten measurements, I determined x to be
drawn from a certain distribution, namely 3 ± 0.1 (and no,
I am *not* going to write that as 3.0 ± 0.1).