In article <[EMAIL PROTECTED]>,
[EMAIL PROTECTED] (Robert J. MacG. Dawson) wrote:
<Snip>
> Interesting. If it's 8.4 degrees Fahrenheit at which he
> switches, no conclusion could be drawn for *any* sample size because
the
> recorded value would not be a monotonic function of actual
temperature.
> ; if the change takes place at 8.4C the sample size might be
> insufficient, but as the scale is monotone (the MCAS score is) valid
> conclusions could be drawn from a large enough sample (the ubiquitous
> central limit theorem!) - with the understanding that they were not in
> general conclusions about the arithmetic mean temperature, but about
> another measire of location.
>
> However, we have to understand that in the absence of a
well-defined
> ONE-parameter family of alternatives (eg, shift, scale, etc) or a
class
> of distributions such as the symmetric distributions for which
> "location" is hard to define in any other way, the assumption that
> "score increasing" must mean "arithmetic mean of scores increasing" is
> arbitrary.
>
> -Robert Dawson
I should have made the cutoff in my hypothetical -40 degrees, the point
at which the Celsius and Fahrenheit scales match. I corrected this in
another post on this thread.
I still think that using two different linear transformations
creates a major problem in interpreting what the mean scaled score
means. The scales on the MCAS tests and my hypothetical (with a -40
degree cutoff) would be monotonic (ordinal), and the median would remain
a valid indication of central location. I am not certain about how the
mean could be interpreted. It is the mean that is being used for the
evaluation of school performance.
State-wide, about one-third to half the test scores on any test would be
based on the non-proficient scaling and one third to half on the
proficient scaling. As described in today's Boston Globe,
students must pass the English and math tests to graduate in 2003, but
34% of the 10th grade students state-wide are failing the math and 45%
are failing the English MCAS. Yesterday the MA Dept. of Education
passed a resolution that will allow failing students to retake the exam
5 times:
http://www.boston.com/dailyglobe2/024/metro/MCAS_retest_plan_approved+.s
html
--
Eugene D. Gallagher
ECOS, UMASS/Boston
Sent via Deja.com
http://www.deja.com/
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
