In article <[EMAIL PROTECTED]>,
[EMAIL PROTECTED] (Donald Burrill) wrote:
> On Sat, 28 Oct 2000, Martin Boulger (impersonating haytham siala)
wrote:
>
> > I have to mark scripts based on a marking scheme thus:
>
> How much of the ensuing paragraph comprises requirements externally
> imposed upon you and not subject to your control, what conditions are
> debatable, and which ones are your own choice?
>
> > 10 questions of equal weighting, grade each answer from A to F.
>
> Is this data as presented, or is part of your task the grading of
each
> question? If the latter, do you get to mark the questions _de_novo_,
or
> do you receive a collection of numerical values to be classified into
> the categories A to F? Do the categories A to F comprise 6
categories
> (as the sequel seems to imply), or are they modifiable by (e.g.) +
and -
> (and ++ and -- ?) suffixes?
>
> Frankly, I always prefer to work with the original raw scores (from
which
> I presume the initial letter-grades for the ten questions were
derived,
> and in the process coarsened). But my responses below are based on
an
> assumption that the only information available to you are the letter
> grades for each question.
>
> > So each question, obviously, counts for 10%.
>
> In one sense, yes: "equal weighting", in the usual sense, would
imply
> this if you understand the process to entail a weighted sum of the 10
> question-grades. It is, however, possible (if perhaps not usual) to
> devise grading schemata that give equal importance to each question
but
> do not entail _adding_ the separate grades.
>
> > Given a random set of grades how do I work out a final grade?
>
> Interesting question! Why, I wonder, would anyone be given a
_random_
> set of grades? Usually one would have all the papers for a
particular
> course (or section of a course), or all the marks previously assigned
to
> those enrolled, or some systematically chosen subset thereof, I
should
> think.
>
> > I considered allocating for each question 10% for an "A", 8% for
an"B"
> > through to 0% for an F. I can add up the grades for each question
to
> > get a grade out of 100%.
>
> Yes, you can do this. I would not use the symbol "%", though. You
can
> by this means produce a total score whose maximum is 100 points, but
it
> is not all clear that this score would properly represent a per
centum of
> anything at all, let alone anything interesting.
>
> > However, only 70% or above = an "A", 60 - 69 a "B", 50 - 59 a "C",
> > 40 - 49 a "D" and 30 - 39 = "E" below this is an F.
>
> Why? Is this scheme imposed on you, or is this just your arbitrary
> choice of cutting points for recoding the total score?
>
> > So my idea doesn't work (and wouldn't be very accurate anyway).
>
> In what sense(s) does it not work? (Apart from some obvious
> dysfunctions, like 10 B's on the original questions magically turning
> into an A for the overall grade, which some folks might not consider
> reasonable.) As for accuracy, what kind of accuracy do you want to
> attain, and how do you wish to define "accuracy"?
>
> > Any clues to a statistical technique appropriate for this problem?
>
> Not without summat more in the way of detail, including what I
suspect to
> be a whole bunch of hidden assumptions. (What, for instance, do the
> original 10 questions represent? They might be different domains on
a
> single final examination; or a chronological series of midterm tests
in
> some course of study; or some peculiar combination of these; or
> something entirely else. Depending, I'd have different proposals for
> how to handle the aggregation process.)
>
> You might begin by considering how you want the results to turn out.
> One way of operationalizing "equal weight" is to report each case's
> marks in lexicographical order, e.g. AAAAB BBBCD for any case that
> has four As, four Bs, one C and one D, ignoring which particular
> question earned each of these marks. Now consider the table of
possible
> marks (or, if you prefer, restrict your attention to the actual
> distribution of marks you have to deal with; but better, I think, to
> consider the population first, then the sample). I report some of
them, in
> groups of five for readability:
>
> AAAAA AAAAA
> AAAAA AAAAB
> AAAAA AAAAC
> AAAAA AAAAD
> AAAAA AAAAE
> AAAAA AAAAF
> AAAAA AAABB
> . . .
>
> EFFFF FFFFF
> FFFFF FFFFF
>
> For which of these patterns ought the output to be "A"? ... "B"?
Etc.?
>
> This is perhaps easier to contemplate in the abstract if we consider
the
> task for four marks to be aggregated (instead of ten). The 126
possible
> patterns are these:
>
> AAAA AACF ABCE ACDF BBBB BBFF BDEE CCEE DDDE
> AAAB AADD ABCF ACEE BBBC BCCC BDEF CCEF DDDF
> AAAC AADE ABDD ACEF BBBD BCCD BDFF CCFF DDEE
> AAAD AADF ABDE ACFF BBBE BCCE BEEE CDDD DDEF
> AAAE AAEE ABDF ADDD BBBF BCCF BEEF CDDE DDFF
> AAAF AAEF ABEE ADDE BBCC BCDD BEFF CDDF DEEE
> AABB AAFF ABEF ADDF BBCD BCDE BFFF CDEE DEEF
> AABC ABBB ABFF ADEE BBCE BCDF CCCC CDEF DEFF
> AABD ABBC ACCC ADEF BBCF BCEE CCCD CDFF DFFF
> AABE ABBD ACCD ADFF BBDD BCEF CCCE CEEE EEEE
> AABF ABBE ACCE AEEE BBDE BCFF CCCF CEEF EEEF
> AACC ABBF ACCF AEEF BBDF BDDD CCDD CEFF EEFF
> AACD ABCC ACDD AEFF BBEE BDDE CCDE CFFF EFFF
> AACE ABCD ACDE AFFF BBEF BDDF CCDF DDDD FFFF
>
> Of these, there are some that would generally be agreed to
represent "A"
> work overall (AAAA and AAAB surely, probably AAAC and AABB, maybe
AAAD?)
> (and similarly for "B", "C", etc.); and some that are less easy to
> categorize into a set of six ranks (e.g., AAAF in the above list).
> Once one has wrapped one's mind around the underlying task, it may
be
> more straightforward (if no less tedious!) to devise an algorithm
that
> approximates that categorization acceptably. Simple arithmetic is
> unlikely to be subtle enough, though.
> (And of course, even for simple arithmetic it is unclear
whether
> the grading scheme should be treated as an equal-interval scale. I
would
> argue that it shouldn't.)
>
> I don't suppose this has made what you thought you were about any
> easier; sorry about that! On the other hand, I didn't read you as
> asking (at least, not explicitly) for "easier".
> -- DFB.
> ---------------------------------------------------------------------
-
> Donald F. Burrill
[EMAIL PROTECTED]
> 348 Hyde Hall, Plymouth State College,
[EMAIL PROTECTED]
> MSC #29, Plymouth, NH 03264 (603) 535-
2597
> Department of Mathematics, Boston University
[EMAIL PROTECTED]
> 111 Cummington Street, room 261, Boston, MA 02215 (617) 353-
5288
> 184 Nashua Road, Bedford, NH 03110 (603) 471-
7128
>
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