In article <[EMAIL PROTECTED]>
in sci.stat.edu, Donald Burrill <[EMAIL PROTECTED]> wrote:
>>On Mon, 1 Sep 2003, in reply to Eric Bohlman <[EMAIL PROTECTED]>'s
>>remark:
>>>Another way to put it is that the OP's original distribution is
>>>discrete, but he's approximating it with a continuous distribution,
>>>and the area under the appropriate part of the curve of a continuous
>>>distribution doesn't have to evenly divide that of a discrete one.
>
>Stan Brown <[EMAIL PROTECTED]> wrote:
>
>> I started to write that at first, but I don't think it's true. The
>> scores on the test may very well be continuous.
>
>You were right the first time, Stan. It is true: scores on a test are
>NOT continuous. Ever.
Sorry, I don't buy that. Think "partial credit". Scores on an esay
exam or an exam that involves working problems can be subdivided and
are not necessarily integers. They can be subdivided indefinitely --
in principle. (In practice I feel pretty confident that no grading
protocol would go to the ten-thousandth of a point.)
> (1) Scores on a test are nearly always the number of items correct, or
>a (usually linear) transformation thereof; and the number of items
>right is necessarily an integer, not a continuous measure.
Sure, for a multiple-choice test. I apologize if I missed it, but I
think we were told just "test", not multiple-choice test.
> (2) Even if the scores are transformed (via norms tables or otherwise)
>to some kind of "scaled score", there are a finite number of scores, not
>exceeding the number of items on the test nor the number of examinees in
>the data set.
True, but I don't see the relevance. If you have a sample of 10 deer
mice and record their weights, do you consider those weights _not_
part of a continuous distribution?
> (3) The scores are stored and and manipulated using digital computers;
>it is not possible for a digital instrument to deal with a continuous
>quantity except by approximation, and ALWAYS to a finite number of
>significant digits of precision. This would be true EVEN IF the
>original measuring instrument reported values on a continuum.
By that argument, there is no such thing as a continuous
distribution or continuous data. Sure, the universe is inherently
digital and discrete (as we known from the quantum theory), but for
all practical purposes ordinary things are continuous. Would you
seriously consider weight or time to be discrete random variables
just because the computer has only 18 digits of accuracy? Surely
not!
These points look so obvious that I fear either I'm completely
misunderstanding you or we're working from incompatible definitions.
--
Stan Brown, Oak Road Systems, Cortland County, New York, USA
http://OakRoadSystems.com/
It's not necessary to send me a copy of anything you post
publicly, but if you do please identify it explicitly to avoid
confusion.
.
.
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