Re: [Phys-l] calibration

[John Denker <jsd@av8n.com>]

On 08/07/2007 09:14 AM, Folkerts, Timothy J wrote:

> You took a page or two in give an brief
> explanation to practicing PhDs.  Perhaps a more basic approach is
> appropriate to a more basic audience.

Simplification is good.  There are various reasonable ways of
simplifying the topic for the benefit of naive students.  OTOH
teachers need to be /overqualified/ in the subject, so that they 
can appreciate the consequences of the simplifications they are 
introducing ... as opposed to just spouting something that is 
only approximately true, without even realizing that it is an 
approximation.

> While I agree you give a wonderfully sophisticated view of treating
> relationships as P(x,y), getting an upper-level science student (let
> alone a typical high-school student) to appreciate the subtleties
> would be a tall order. 

They don't need to appreciate the "subtleties".  They do 
need to make a scatter plot so that they have some hint of 
a glimmer of a clue as to the /meaning/ of what they are 
being asked to do.

>  This article seems to be aimed at an audience
> somewhere in between.  In such a case, I think "dependent" and
> "independent" are reasonable ways to think of the situation. 

If the objective is simplification, then let's simplify things, 
as follows:

Simplification #1 is to simply not mention "independent" or 
"dependent" at all.  The incoming students (and I dare say
most of the outgoing students) have no idea what those words
mean.  How much time are you going to spend attempting to
define those terms?  Why???????

>  Let's
> get the students to master the idea of p = f(rho) (and many will have
> a hard time makiing the jump from y =f(x) to p=f(rho) ) before
> takeing your next step.

That sounds fine.  Again:  There are various reasonable ways of 
simplifying things.

Simplification #2 is to consider the case where the uncertainty 
in y is vastly more significant than the uncertainty in x.  

My point remains that simplification #2 has, AFAICT, no connection 
to calling one variable "independent" and another "dependent".  
If there is any connection here, I'm not seeing it; please explain.
I would treat x and y on an equal footing.  I would say x has error 
bars and y has error bars, but the x error bars are smaller in the 
appropriate units.  (The slope of the trend line enters into the 
"appropriateness" of the units.)