Re: [Phys-l] Data Analysis Questions

["Thomas O'Neill" <oneillth@jmu.edu>]

Hugh,
  I am speaking from memory but the results usually go something like this:

one resistor measured ten times:
Rare for a student to get the same resistance all ten times
nominal 100 ohms measured to 0.1 ohms

Same resistor measured alone without test leads:
Usually about 0.2 to 0.1 ohms less although sometimes there is no change.  

A sample of twenty 100 ohm resistors: 100 ohms with a standard deviation of about 0.3 ohms.

The same sample re-measured will yield about the same average but very rarely 20 identical values.  Typical p-stat for a t-test with the first sample: 0.80 (cut-off at 0.05).

A different 20 resistor sample will yield about the same average but most definitely will have different values.  Typical p-stat for a t-test with the first sample: 0.40 (cut-off at 0.05).

Old 100 ohm resistors sample of 20 yields an average of about 105 ohms with a standard deviation of about 2 ohms (these things look like they are Sputnik vintage).  Typical p-stat for a t-test with the first sample : 0.000 000 001 or even less (cut-off at 0.05).

Answer to the lab question about the Null Hypothesis: Are the last resistors the same as the first resistors? No, although I admit to having set up the lab to get that answer.

The topic of measurement uncertainty flows naturally out of this lab.  In any event, the logic of rejecting the Null Hypothesis is difficult for beginning students to master and I don't pretend that this lab magically provides that mastery.

I hope this helps.


---- Original message ----
> Date: Fri, 28 Nov 2008 14:37:17 -0500
> From: Hugh Haskell <hhaskell@mindspring.com>  
> Subject: Re: [Phys-l] Data Analysis Questions  
> To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
>
> At 11:17  -0500 11/28/08, Thomas O'Neill wrote:
> > Actually, we do this as an introduction to uncertainty analysis and 
> > Student's t test.  We have our students pick a sample of twenty 
> > nominal 100 ohm resistors from a larger set of 100.  Measure the 
> > resistance of each.  They mix-up the first sample then re-measure 
> > the resistance of each resistor.  Then they measure the resistance 
> > of a second random sample of 20 from the set of 100 after throwing 
> > the first sample back in.  Finally they measure the resistance of a 
> > sample of 20 different resistors with the same nominal value. We 
> > have reels of old (>30 years) resistors that on average are about 5% 
> > higher than the new ones. 
> I'd be interested in what sorts of results this exercise leads to. My 
> understanding is that resistors are sold in three (?) different 
> tolerance groups-1%, 5% 15% (?), but they are all manufactured by the 
> same process. The finished resistors are then measured and those that 
> meet the tolerance of the 1% group are put in one pile, those that 
> meet the tolerance of the 5% group are put in another pile and all 
> those that meet the 15% tolerance are put in a third pile. The rest 
> are rejected. If this is true then one would seldom find a resistor 
> in, say, the 15% category that is closer to the nominal value than 
> 5%--hardly the expected Gaussian distribution. And in any event, 
> there should be few if any whose tolerance is greater than 15%.
>
> If this scenario is true then it would be very difficult to get any 
> realistic statistics out of the results unless there was a mix of the 
> three tolerance categories sufficient to simulate the original 
> manufacturing distribution. I'd appreciate any input on this since my 
> evidence is entirely by hearsay.
>
> Hugh
> -- 
>
> ************************************************************
> Hugh Haskell
> <mailto:haskell@ncssm.edu>
> <mailto:hhaskell@mindspring.com>
>
> (919) 467-7610
>
> So called "global warming" is just a secret ploy by wacko tree 
> huggers to make America energy independent, clean our air and water, 
> improve the fuel efficiency of our vehicles, kick-start 21st-century 
> industries, and make our cities safer and more livable. Don't let 
> them get away with it!!
> 						Chip Giller, founder 
> of Grist.org
> _______________________________________________
> Forum for Physics Educators
> Phys-l@carnot.physics.buffalo.edu
> https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
THO

Thomas O'Neill
Physics Teacher in Residence
James Madison University
Shenandoah Valley Governor's School