> 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

> 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

> 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.

> 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 <@spam@wagnerKILLspamUSTR.NET>
> Sent by: pic microcontroller discussion list <KILLspamPICLISTKILLspamMITVMA.MIT.EDU>
> 04/17/2003 01:07 PM
> Please respond to pic microcontroller discussion list
>
>
>         To:     RemoveMEPICLISTTakeThisOuTMITVMA.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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