Re: Statistics Question

[Victor Steinbok <Victor.Steinbok@VERIZON.NET>]

At 12:36 PM -0800 1/28/02, Ed Levine wrote:
> To: ARN-L
>
> My statistical comprehension is apparently (based on NY State's definition)
> only a "2" (Does Not Meet Standard).  In an effort to understand what
> "norm-referenced" means, I have a (perhaps naive) question.
>
> Don't the people who construct standardized, norm-referenced exams seek to
> atttain a bell-shaped curve when they norm the tests on a sample
> group prior to
> selling the test to the public?
>
> And, how is a rectangular (AKA "uniform") distribution possible if a test is
> "properly" normed?
>
> Thanks in advance to the person or persons who help me out of this quandary.

Gerry might have answered the question to your satisfaction already,
but I'll take a crack. Distribution by percentile is ALWAYS uniform
(rectangular), since the same number of students (in theory) classify
for each percentile rank. The scores do not correspond to percentiles
in the same fashion--they are stretched out at the top and bunched up
in the middle, resulting in something resembling a bell-curve
scenario.

Incidentally, I am wondering if the bell-shaped distribution is
expected for ALL norm-referenced tests. Certainly, SAT might be
expected to be skewed toward the low end, as 200 does not represent
the lowest scores, just a cut-off score for the lowest performing
population. In other words, people who get a 0 a 3 or a 10 all get
the same 200 score and the number of such people is sub-1%, unlike
the scores at the top of the scale. Perhaps I am just interpreting
the SAT scale in correctly.

       VS-)

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