Re: [Phys-l] Treatment of Experimental Error

["Michael Edmiston" <edmiston@bluffton.edu>]

Your mistake #1... You assumed the pairs should be identical.  I originally 
thought that also, but they are not.  This is not an experimental error. 
Tires are not perfectly round.  Repeat... the mismatched pairs are not 
experimental error.  That's the way tires are.

Your mistake #2... You apparently think the non-identical measurements on, 
for example, the right-top and left-top invalidate the end result.  This was 
not a test to see if the tire is round (which it isn't).  This was a test to 
see how the sidewall radial length changes from an unloaded tire to a loaded 
tire.   That is, you are comparing the wrong pairings in an attempt to 
invalidate data that doesn't support your theory.   One valid pairing is 
top-left before loading to top-left after loading.  The fact that the top 
left length is not the same as the top-right length is not a valid pairing.

If you want to compare top-right to top-left on this particular pair of 
photos, compare the change (0.379 stretch compared to 0.315 stretch).  The 
average stretch at these locations was 0.347 cm and the two measurements are 
well within 0.05 cm of this average.  This seems pretty good to me, and I 
don't necessarily expect this to be perfect because tires are not built 
perfectly symmetrically.  They have to be balanced when they're installed, 
you know.

The comparison of the change is not quite this close for right (0.167) 
versus left (0.059) with an average of 0.113 but that is to be expected 
because at right/left the average stretch is only one third of the stretch 
at top-left/top-right, and the tire indeed has internal stresses or 
thickness differences (acting to make it slightly out-of-round) either from 
the original manufacture or from wear.  So these inequalities show up more 
in regions where the stretch is not as much.  By the way, these tires have 
40,000 miles on them.

In the end, the pattern in the radar graphs is perhaps remarkably symmetric, 
and this is evident in the analysis of all photos.

Your mistake #3... You didn't know that I raised and lowered the tire 5 
times and I have 10 photographs.  The wheel was rotated so that it was not 
in the same orientation for all pairs of photos.  The car was driven for 
several miles between the first two sets and the last three sets.  I did, 
however, present only one set of data, so this is an understandable mistake. 
I spent so much time on this... actually about 9 hours when I had (still 
have) a pile lab reports to grade... that I had to quit and post some 
results that are not yet in the form that I would publish in TPT or AJP.  I 
think that is what Phys-L is about.. the ability to discuss ideas and 
results that are not 100% polished.  But that does not mean I was oblivious 
to error... see the next point.

Your mistake #4... You ignored that I did determine a probable error and I 
reported that result.  I believe the error is less than  +- 0.05 cm.  There 
were many repeat measurements taken from multiple photos.  Since the photos 
are about 1.5 Mbytes each, I did not post all the photos and I did not 
present all the analysis.  I may do that in TPT, but I have to move on to 
other things for a while.  If I make a wild guess, I will say so.  My 
estimated error of 0.05 cm was not a wild guess.

Your mistake #5... Related to the previous point, is seems you are not aware 
of the accuracy of making measurements from high-resolution digital 
photographs.  This has become quite common and works amazingly well.  One of 
the ways I estimated my measurement error was to measure the rim diameter 
itself.  My rims/wheels are fairly expensive machined alloy wheels that 
added significantly to the purchase price of the car.  I didn't special 
order them; I bought the car off the lot.  These wheels ought to be very 
round, even if the tire is not.  I measured the rim once with calipers and 
got 44.185 cm.  I did not repeat this measurement because it does not have 
to be real accurate in order to set the photograph scale accurately enough 
for the measurements I was trying to make.

Anyway, go to the AccordTireOffGround photo and measure the rim diameter at 
several spots.  If we assume it is perfectly round (which it may not be, but 
it should be close) that gives us a pretty good idea of how well our 
photographic analysis works.  Here's is what I did, and you can do the same. 
I used the Photoshop ruler tool and eyeball-judged where to click the cursor 
on the outside of the rim.  Then I dragged the mouse so the ruler line went 
through the center of the wheel (by eyeball), and released the mouse button 
when the cursor got to the rim on the opposite side.  The photo was on my 
screen at slightly more magnification than "actual pixels."  I needed to 
have one side of the rim and the wheel center in view at the same time, so 
my magnification was just less than the amount that prohibited this.  There 
are other ways to do the measurement, (such as writing down pixel 
coordinates) but the method I used is the quickest.

I measured the rim diameter every 30 degrees all the way around.  There are 
three eyeball judgments in each of these measurements... (1) eyeballing the 
initial click on one edge of the rim... (2) eyeballing when the ruler line 
passes through the center of the wheel... (3) while simultaneously releasing 
the mouse button by eyeball-judgment of the other side of the rim.

Here are those 12 measurements from that photo.

44.169
44.173
44.176
44.168
44.179
44.214
44.220
44.244
44.194
44.176
44.199
44.176

Average 44.191
standard deviation 0.02413

Therefore, please note that when I stated my measurement error at 0.05 cm I 
was actually doubling what I really think it is.  It appears the error is 
about 0.024 cm if the rim is truly round.  One reason for doubling it from 
0.024 to 0.05 cm when I reported it was because the contrast of the rim 
makes it a bit easier to judge the rim edge than when I judge the tread 
edge.  Since one pixel is 0.037 cm, I would prefer not to be even one pixel 
off with my click.  The rim data above show that I achieved this fairly well 
even though these represent just one diameter measurement at each angle (one 
mouse click and one mouse release for each diameter measurement).  The data 
I presented for the sidewall-stretch consisted of several measurements at 
each location to help even out "mis-clicks"

In the end, you need to face the facts.  When the tire is loaded, the 
sidewall indeed stretches in roughly the upper 2/3 of the tire, and this 
stretch gradually increases from zero to a maximum at the top.  If you think 
my experimental data are incorrect or are interpreted incorrectly, go out 
and take your own data, analyze it, and present your results here.

Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
1 University Drive
Bluffton, OH 45817
419.358.3270
edmiston@bluffton.edu


----- Original Message -----
From: "Brian Whatcott" <betwys1@sbcglobal.net>
To: <Phys-l@carnot.physics.buffalo.edu>
Sent: Sunday, November 11, 2007 11:19 AM
Subject: [Phys-l] Treatment of Experimental Error

> Lets suppose we have just taken a series of eight measurements
> for each of two experimental conditions.
>
> We carefully arranged an internal control scheme so that the
>  eight measurements could be taken in pairs, for which we expect
>  each pair to be identical.
> If we note the difference between each [identical] pair is in fact
> 0.4 cm, -0.237 cm, -0.374 cm, and -0.198 cm in Case #1
> AND
> 0.301 cm, 0.341 cm, and 0.482 cm in the other case ( the fourth pair
> is expected to be unbalanced)  can anyone tell me what value
> we should assign to the experimental error of a particular reading?
>
>
>
> Brian Whatcott    Altus OK    Eureka!
>
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