> 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 Matt¹s
>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
having been in the measurement field for more than 1/2 my life ... i have
some feel for and appreciation of ... the notion of measurement error
(whether this is a principle of math ... or not) ...
reliability is all about that ... reliability of the measured value ... the
measured jump of 21 feet ... can we depend on this to be correct and if
not, how "off" could it be from a bad measurement standpoint ...
so, this question interests me not so much from the standpoint of what
specifically IT is measuring ... but, from the standpoint of what makes a
decent question ... or a poor one
this kind of item is one that gives "tests" some of the bad name they get
in a case like this, we have to look at the question being asked ... ie,
the stem ... and first list out what are "facts" of the stem and what are
"logical inferences" that an examinee could make (maybe should make)
let's assume up front that the objective of the item really is ... concept
of measurement error ... that is, when folks take measurements ... they can
be wrong ... and wrong either way but, consider the following in this case
FACTS
1. you are given that the jumps were measured to the nearest foot
2. you are given that the jumps were measured accurately
LOGICAL INFERENCES on the part of the examinee
1. this is a contest ... broad jump ... and a tape measure was used that
had at least inch subdivisions ... or even greater (ever see a tape measure
at a track meet only with FOOT tick marks? ever have in your hand, a tape
measure that is 25 feet or 50 feet ... that did NOT have at least inch or
probably FINER subdivisions?)
2. contests are important so ... the measurers are assumed to be doing
their best to read "jumps" accurately ... if they don't ... they get water
bottles tossed at them by the irate parents
3. typical tapes could be extended in a somewhat slack mode ... when
extended to make the measurement ... but there is a limit to how TAUT or
lengthened they can be made to go ... so, if an error is likely to occur
(forget the fact that "accurate" is given in the stem) ... then it would be
most likely and sensibly in the slackened condition ... which means the
measured jump would be recorded LONGER than it should be ...
given the FACTS and what i believe to be sensible inferences one can and
should make in a broad jump contest which this is assumed to be like ...
would lead me as a measurement person ... to say this:
if the tape were extended in the taut(est) condition ... AND, measurements
were done accurately ... then if the landing mark were really between 20.5
and 21 ... we assume it will be rounded up/reported as 21 ... max error 1/2
foot ... or ... if the landing mark fell between just less than 21.5 and 21
... it would be rounded down or reported to be 21 ... this max gap sensibly
would be 1 foot
however, if the tape were slackened ... either a little or a lot, whether
it be measurer's error or not ... for a particular measurement (which
means it is not an accurate measurement by definition but, lets let that
slide for a moment) ... then the gap (and hence max error) between the tape
mark and the landing mark becomes harder to discern ... perhaps impossible
to discern
because ... we don't know how much slack there might be in the tape
but, regardless, it will be seen by the measurer as being LONGER than it
really is ...
thus, under the slackened condition ... errors could make the measurment
longer than it should be ... but, in the taut condition ... the error is
not likely to make the measurement shorter than it should be ...
the liklihood of an LONGER error (if anything) is much greater than the
liklihood of a SHORTER error
if in the taut condition ... the MINIMUM "max" error could sensibly be
called (rounding of course considered) 1 foot ... between the two ACTUAL
jumps ... BUT WHAT COULD THE SENSIBLE MAXIMUM MAX ERROR BE BETWEEN THE 2
ACTUAL JUMPS?
i say that this canNOT be sensibly determined from the facts and logical
inferences made in the question ... and while i now say that choice C would
be a "possible choice" it should actually read (C: One jump could be up to
1 foot longer than the other <<<< could be 1 foot ... but not could be UP
TO 1 foot) for the MIN MAX ... choice D of 2 feet is NOT a good choice
either (nor can any be deduced) for the MAX MAX error in the actual jumps
thus, i now don't believe C is correctly stated ... and therefore is not
correct ... and D is not correct because we cannot determine what might be
the largest error that could be made ... it might be 1.3 feet or 1.7 ... or
2.1 ... but we do NOT know that the max error could or would be 2 feet
bottom line:
A and B are incorrect for sure ... C is not good ... and D can't be proved
to be correct
none of the choices is correct ... C is probably the BEST choice but still
not a good one
this might be a good question for assessing an inappropriate objective ...
or, an inappropriate question to test a legitimate objective
but as it stands ... it surely is a poor item that fails to keep straight
... appropriateness of the item GIVEN some objective
==============================================================
dennis roberts, penn state university
educational psychology, 8148632401
http://roberts.ed.psu.edu/users/droberts/drober~1.htm
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