Re: [Phys-L] uncertainty on the uncertainty

[John Denker <jsd@av8n.com>]

On 07/06/2017 04:02 AM, Peter Schoch wrote:

> 3.  I do expect them to then compare their average ± the standard error
> to an accepted value (if possible) or to analyze the results; i.e., what if
> the error is artificially low?  What could have caused that?  Is the sample
> size unreasonably small?
       ^^^^^^^^^^^^^^^^^^^

Yes, all too often, especially at the introductory level, the
assignment demands a sample size that is indeed unreasonably
small.

There are never enough hours in the day, or minutes in the hour,
so people try to get by with only two or three data points.

Usually they are required to do a big fancy propagation-of-error
analysis, but they don't check it against the experimentally
observed standard deviation.  If they did, any student who was
not exceptionally lucky would see a big disagreement.

> What could have caused that? 

You will never know, and the students will never know.  It could
be that they screwed up the experiment ... or they just weren't
lucky enough, and got clobbered by statistical noise.

For small N, this problem is simply not fixable.

Just now I put up an article with some diaspograms that make
it easier to see how bad the problem is:
  https://www.av8n.com/physics/stdev-estimate.htm