On 16 Jan 2001 09:01:18 -0800, [EMAIL PROTECTED] (Robert J.
MacG. Dawson) wrote:
>
>
> Rich Ulrich wrote:
>
> > Construing the language as precisely as possible, but being careful to
> > take into account the full language of the question and the
> > multiple-choice answers, what do you think the correct answer is?
> >
> > Do you think the question is actually OK? Is the wording good enough
> > as it stands? Or, as worded, could there be a legitimate uncertainty
> > about which answer is correct?
> >
> > BEGIN QUESTION TEXT
> >
> > 37. When Matt's and Damien's broad jumps were measured accurately to
> > the nearest foot, each measurement was 21 feet. Which statement best
> > describes the greatest possible difference in the lengths of Matt�s
> > jump and Damien's jump?
> >
> > A. One jump could be up to 1/4 foot longer than the other.
> > B. One jump could be up to 1/2 foot longer than the other.
> > C. One jump could be up to 1 foot longer than the other.
> > D. One jump could be up to 2 feet longer than the other.
> >
> > END QUESTION TEXT
>
>
> I guess I don't see any problem with this. "Accurately to the nearest
> foot" does not mean the same thing as "to within one foot" or "to an
> accuracy/tolerance of plus or minus one foot" which I suppose yields the
> canonical wrong answer. The use of the word "nearest" is crucial.
>
Maybe I won't convince anyone, but I do want to try once more....
One Theme (a little bit relevant) is the wording of questions.
Another Theme is a technical one about how sloppy we all tend to be,
when we make assumptions about accuracy of measurement.
Here are some strings of words... DO these suggest round-off errors?
"If Matt scored 121 on an IQ test and Damien scored 123 on the same
test, what is the maximum difference in their IQs?"
- This reads BAD to me, because I know that IQs are fuzzy numbers.
At the best, Matt-today is apt to be 4 points different from
Matt-tomorrow, so there's 5 or 6 points to expect from 2 people who
measure exactly the same. If you want to know about whether the
testee understands ROUNDOFF, you don't introduce ontological doubts,
i.e., What is reality?
- Folks *do* accept and pretend to understand some numbers like
this. If you are testing for math-content, it is not fair to require
that knowledgeable testees ignore or draw on what else they know.
Now, if you are testing for IQ in the disguise of testing for math, it
*might* be useful to see how well people figure out what the question
is supposed to be (but I do have my doubts about that sort of Q).
- Testing for math, it is fair for you to ask for conclusions about
numbers, NOT about "sizes." (Not every 14-year old will draw the
distinction, but quite a few of them ought to be capable of it.)
"Please measure the child's height accurately to the nearest
millimeter."
- Measuring with that precision can be tough. You might have to be
taught how to do it by protocol; or you might not achieve an accuracy
which is quite as good as the expert's. I think that is a reasonable
request -- or a reasonable description, even if the potential is not
quite met 100%. That is: I think someone could ask for it, and it
could be useful in a close, daily study of growth; replication (for
reliability and validity-testing) would show a VERY frequent error of
1 (or 2) millimeters.
"Please use the tape measure in the usual way and write down the size
of the waist, accurately to the nearest millimeter."
- I find a lot of resistance from people, in trying to get them to
*think* of measurements in units that are shaky. When they are
pushing the limits of what can be measured, experimental physicists
are thoroughly aware that you need to specify both an estimate and its
precision. But ordinary folk seem to (a) think that you can round-off
to a number with no discernable "error", and - consistent with that -
(b) refuse to contemplate measuring the soft-tissue of the waist in
millimeters.
Semantically, I tend to draw a distinction -- which seems
to be, a distinction between the overtones of the ADVERB
and the ADJECTIVE (unless I am being fooled by the -ly).
If you asked for my waist size, "accurate" to a millimeter,
I would have to demur, pleading the lack of definition or rules.
If I had been measuring, and now you asked, measure
"accurately" to a millimeter, I would have no difficulty in agreeing
to read a measurement that finely. But other people seem to choke on
the concept. I'm not claiming that I have found the most appropriate
words, but I don't think this gap is all my fault.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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