Understanding Experimental Error: Standard Deviation vs. Instrumental Precision

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Discussion Overview

The discussion revolves around the interpretation of uncertainty in experimental results, specifically whether the quantity represented by a plus or minus value (denoted as 'b') should be understood as standard deviation or as an arbitrary uncertainty related to instrumental precision. The context includes theoretical considerations and practical implications in experimental physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Andrew questions whether the quantity 'b' in a result like + or - b is always the standard deviation or if it can be an arbitrary uncertainty based on the experimenter's equipment.
  • Some participants note that the interpretation of + or - can vary widely across different contexts, such as mathematical equations or survey results, suggesting that more information is needed to clarify Andrew's question.
  • A specific example is provided where a scientist measures the acceleration due to gravity as 9.92 + or - 0.15 m/s², prompting a discussion on whether 0.15 represents standard deviation or another form of uncertainty.
  • One participant suggests that the uncertainty could arise from the limits of the instrument's precision, citing an example of a device with a finite number of digits of precision affecting the reported uncertainty.
  • There is a proposal that the nature of the quoted error may depend on the repeatability of the experiment, with the idea that non-repeatable measurements might reflect instrumental precision rather than standard deviation.
  • Another participant emphasizes that the only way to definitively determine the nature of the quoted error is to communicate directly with the experimenter.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of uncertainty in experimental results, with no consensus reached on whether 'b' should be classified as standard deviation or instrumental precision. The discussion remains unresolved regarding the criteria for distinguishing between these types of uncertainties.

Contextual Notes

The discussion highlights the ambiguity in interpreting uncertainty in experimental results and the dependence on specific contexts and definitions. There are unresolved questions about the assumptions underlying the interpretations of uncertainty.

amm17
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When coming into contact with a result such as a + or - b, what should one take the quantity 'b' as? Is it always the standard deviation? Or is it an arbitrary uncertainty decided by the scientist running the experiment, based on the equipment? Please help.
Thanks,
Andrew
 
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Um it really depends on the context. It is hard for us to know what you are talking about because we use + or - all the time.

For example

|x| = 5 implies that x = + or - 5.

or in the quadratic equation

x = + or - the square root of b squared minus 4 ac...

These have nothing to do with standard deviation.

Or for example survey results.

60% or a population + or - 3%, this is error not standard deviation.

These are just a few examples, but we use + or - in a huge number of ways and contexts. So can you tell us a little more what you are talking about? Is there a specific scientific result you are looking at that prompted this question?

We need more info.
 
Say that a scientist has found, using some experiment, that the acceleration due to gravity is 9.92 +or- .15 m/s^2. Is the .15 the standard deviation, or not necessarily? What else could it be?
Thanks
 
amm17 said:
What else could it be?

It could be the uncertainty due to having only a finite number of digits of precision. For example, someone may calibrate a device that has a 16 digit binary output so that its min reading (sxteen zeroes) is 2.80 V and its max reading (sixteen ones) is 900.60 V. If the device gives a reading in between these values, it will only be precise to 16 binary digits. The uncertainty in what a missing 17th digit would represent gives you an error that doesn't necessarily correspond to the uncertainty in not knowing a base 10 digit.
 
Great, thank you. Now how do you know when the quoted error is standard deviation or instrumental precision? I would guess that an experiment that has no use being repeated (like measuring the length of a dollar bill) would feature an error due to instrumental precision, whereas an experiment worth repeating might have a standard deviation as an error. Thoughts?
 
amm17 said:
Great, thank you. Now how do you know when the quoted error is standard deviation or instrumental precision?

The only way to know for sure is to communicate directly with the person who did the experiment.

I would guess that an experiment that has no use being repeated (like measuring the length of a dollar bill) would feature an error due to instrumental precision

One of my brothers once showed me that he could shrink a dollar bill by repeatedly folding it up and unfolding it. - I couldn't resist mentioning that.
 

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