Re: [Phys-L] .05 level of significance -

[John Denker <jsd@av8n.com>]

On 01/19/2015 03:00 PM, Chuck Britton wrote:

> In keeping with recent Statistical Analysis Discussion [...]
> Death is not certain to the .05 level of significance.  [1]
> Just curious as to how a Set Theoretic argument would respond - 

*IF* (big if) we are talking about statistics, then the 
response to all such queries is:    What's your ensemble?

Additional resources on this topic:

On 02/18/2014 09:07 AM, Paul Nord wrote:

> > http://www.nsftools.com/misc/DilbertRandom.gif

to which I might add:
  http://imgs.xkcd.com/comics/random_number.png

This touches quite directly on the question that triggered
the recent discussion.

On 01/12/2015 12:40 PM, Paul Lulai asked:

> How reasonable is it for a high school kid to say, "I measured 40.5cm
> ± 3cm" based solely on their own confidence in the measurement?  [1]

It's hard to say for sure what the student meant by
that, but here's a pretty good guess:
  "I measured the length once, and got 40.5cm.
   That is a number, a plain old number, with
   no error bars, with no uncertainty whatsoever.
   As an almost-separate matter, I estimate that if 
   we were to create an ensemble of similar measurements,
   the distribution would have a standard deviation of
   roughly 3cm.  That's because blah blah blah...."

If that's what he meant, then his statement [1] expressed it 
quite poorly.

A less-unreasonable (but alas less likely) possibility
is that the student meant to say:
  "I measured the length 150 times.  The distribution of
   readings appears to be Gaussian, with a mean of 40.5cm 
   and a sigma of 3 cm."

It must be emphasized that a number does not have any 
uncertainty whatsoever.  A raw data point from the experiment
does not have any error bars whatsoever.  Adams's "nine" and 
Munroe's "4" have no randomness whatsoever.  If you have a
/distribution/ of such things, the distribution may have
some width ... but that is a property of the distribution, 
not the individual data points.

I find the following pictures more-or-less unforgettable.
Compare the good:
  https://www.av8n.com/physics/probability-intro.htm#fig-frequentist-gaussian-400
to the bad:
  https://www.av8n.com/physics/probability-intro.htm#fig-frequentist-gaussian-bars-400

==============================

Perhaps more to the point, I reckon the "death" question [1]
goes off the rails before we even get around to considering 
the statistics.  Mostly it's a category error:  It provides 
evidence about one thing and then tries to draw a conclusion 
about something else.