OK here is the lowdown.  These were 200 tests of how accurately I could
juggle two sharp knives and a bottle of nitroglycerine.  Each miss
represents one trip to the hospital.   ;-)

Actually (seriously) the tests are of two barcode scanners.  Each group of
ten was ten consecutive scans of the same product.  In a successful test
the scanner read the UPC code in one pass.  Some packages have different
color ink, wrinkly bags, shiny surfaces, others are flat black ink on
cardboard boxes.   So yes, the sets of ten are *different* but the idea is
to get an overall mix of products that might represent a shopping basket
full.

Of course, the consequences of a miss are not catastrophic, just annoying.
 And there is another annoying thing, some products will not scan at all
with either scanner.

I guess my statistics question is this:  Given that the standard deviation
of the data is over 30%, is a difference of  9% between one scanner and
the other *signifigant*?   Or is this fact even relevant?

-- Lawrence Lile






Wagner Lipnharski <wagner@USTR.NET>
Sent by: pic microcontroller discussion list <PICLIST@MITVMA.MIT.EDU>
04/17/2003 01:07 PM
Please respond to pic microcontroller discussion list


        To:     PICLIST@MITVMA.MIT.EDU
        cc:
        Subject:        Re: Fun with Statistics - Which is better?


Lawrence Lile wrote:
> Which unit is better?
>
> I have two units, one is supposed to be "improved" over the other.  I
> ran 200 tests on each unit, and recorded the number of successful
> tests out of each  group of ten tests.  I am trying to prove to
> myself whether one is actually better than the other, or that the
> differences are insignifigant, statistically.  Here is the raw data
>
> Successful tests
> out of ten tries
>
> unit1   unit2
> 10      10
> 3       2
> 5       10
> 10      9
> 10      6
> 0       0
> 7       9
> 10      10
> 8       8
> 0       5
> 7       6
> 2       6
> 9       8
> 7       10
> 8       9
> 10      10
> 4       10
> 0       1
> 3       3
>
> 113     132 out of 200  total # tests
> 57%     66% success rate
>
> Avg     5.947368421     6.947368421     Average
> St. Dev 3.703957106     3.341218743     St Dev
>
> Now on the surface Unit 2 looks slightly better than unit 1.
> However, the standard deviations are so large, maybe it is just a
> statistical fluke and next time unit 1 will look better.  Any body
> got enough math whizzing around their brain to tell?
>
> P.S. THe manufacturer says the tests should be 95% successful.  Yeah
> right.
>
> --Lawrence the Skeptical


All will depend on the kind of test.
If the group of 10 tests are exactly the same, then it is not 20 tests of
10, it was simply 200 tests, and the result is 113 x 132.

Statistics are very tricky.  Suppose the lotto number 35 was not drawn a
single time during the last 52 Saturdays, what are the chances of the ball
#35 to be drawn next Saturday?  Exactly the same as any other ball...
since
the past results does not interfere in the next draw, everytime happens to
be a fresh brand new opportunity to all the numbers.  Except of course if
the ball #35 is heavier, lighter, bigger, smaller, etc, what is not the
case, since they always replace the whole set of balls every Saturday for
new ones never used, exactly to avoid this kind of crazy thoughts.

If your result is basically 113 x 132, there is no tricky stat wizard that
will convince you otherwise, but in your place, I would love to see the
explanation why the Unit#2 made 10 in the first and third, and only 2 in
the second group of tests... that would be an interesting explanation...

Wagner.

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