Re: [Phys-L] Question on data analysis

["John Clement" <clement@hal-pc.org>]

There are already a number of answers to this question, so I will point out
a common student problem here.  Students want the line to go through zero.
When hand graphing they will take a line that clearly does not go through
zero and hook it to zero.  Insisting that the line go through zero is just
reinforcing that misconception.  I do not have my students do any analysis
using a spreadsheet or any graphing program until they all can reliably make
graphs correctly by hand.  So in most intro classes they never do an
analysis using a spreadsheet or other graphing programs because there are
still some who can't hand graph properly.

In Modeling they use a simple rule such as if the intercept is less than 5%
of the maximum data for deciding whether the intercept should be zero. Of
course using error analysis should reveal whether the intercept is within
the uncertainty for being zero.  That would be how it should be done in more
advanced classes, but for the intro class the students will generally not
understand nor have time for such a process.  Since most of the students do
not have good numeracy, keeping it simple and requiring hand graphing is the
most helpful method.  Since they do the analysis by the old fashioned method
of making test graphs, they can easily see how good their fit is to the
data.

The problem with a spread sheet analysis is that it is a black box which
easily cranks out ridiculous answers.  So because of the student
misconception about trend lines, it is inadvisable to have them always force
it to go through zero.  They should be required to interpet the intercept
and say whether it is reasonable.  Modeling always has them come up with an
meaning for the slope and the significance of the intercept.  That way it is
not a mindless follow the rules exercise.

Among the problem with hand graphing I frequently see the following from at
least one student in class:
1.  They skip a number  They will go 10,20,40,50,60 - I have seen this with
students who do not really know how to count.
2.  They make a non linear scale  1,2,4,6,8
3.  They put the points on the intersections of the graph paper lines and
then put on the scale  1.25,3.78,4.0...  This is partially because most
books show tren lines neatly going through the intersections!
4.  They hook the graph down or up to go through zero.  This is possible
because of the books almost always show perfect graphs going through 0.0.
5.  They make a broken scale and then try to hand fit the data.  There is a
big numeracy problem here and also they have no connection between algebra
and real data graphs.  This is a sign of mindless arithmetic and mindless
math.

In line with this I have seen a very curious test of numeracy.  In the Minds
on Physics book there is a strobe picture (motion map) of someone dropping a
ball from 2m high above the floor.  There are 2 meter sticks pictured end to
end calibrated in cm.  Some students have a huge difficulty with it.  Some
will graph the data for each meter stick so the data has a break between the
two meter sticks.  I go around and ask what the objects are in the picture.
This is an excellent exercise to get them out of the usual just follow rules
and into thinking about what they are doing.  

John M. Clement
Houston, TX 


> Hi,
>
> spreadsheet programs usually have a feature which allows to 
> force a trendline through the origin. Of course, the same 
> thing can be done manually as well. My question is: when it 
> is reasonable to force a trendline through the origin? I 
> mean, a non-zero y-xis intercept may have a physical 
> interpretation or it may indicate systematic error in 
> measurements or (more realistically) may be a combination of 
> both. Given these, what could be a benefit for the forcing of 
> the trendline through the origin?
>
> The question was motivated by an observation that a chemistry 
> colleague insists that her studenst must force a trendine 
> through the origin (in case there is no chemical 
> interpretation, I suppose) for the y-axis intercept.
>
> Regards,
>
> Antti
> Finland
> --
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