In article <[EMAIL PROTECTED]>,
[EMAIL PROTECTED] wrote:
<Snip>
> - I don't know what the authors say, but (on their behalf)
> I suggest that maybe the funny range was selected in order
> to avoid ignorant comparisons that public tests are prone to.
> That is, from these scores, you won't be tempted to say
> that 'one school is doing 50% better.'
>
> --
> Rich Ulrich, [EMAIL PROTECTED]
> http://www.pitt.edu/~wpilib/index.html
You make a good point, that choosing this hideous scale makes it
difficult to apply ratio-level measurements to these scores. I
posted a note on this thread earlier today pointed out the odd
way that the Dept. of Education scales the scores. Students
get a raw score, usually on about a 75-90 points possible, then
a panel decides what "proficiency" is. Then, the scores are scaled
to make one year like another. Two different linear regressions
are used, with the intersection being the not-proficient vs.
proficient breakpoint
For each exam in each year, there are different y intercepts
and slopes listed to convert to scaled scores.
Scaled score =1.59 raw score +177.25 if raw score <38.83
Scaled score =2.65 raw score +136.19 if raw score >38.83
Now, a school's performance is based on the average of these
scaled scores. By using these different scalings, the DOE has
changed an interval-scaled variable (with a 1:1 correspondence
to percentage of correct answers) into an ordinal scale. Unless
the variables are at least interval scale, it is no longer
appropriate to even take averages of these scores.
Imagine this as an MCAS question:
A scientist has two thermometers, one Fahrenheit and the other Celsius.
When the temperature is less than 8.4 degrees, the scientist
uses the Celsius scale. When the temperature is more than
8.4 degrees, he uses the Fahrenheit scale. In 1998, he took 40
measurements of the temperature. In the two following years, he
took 40 more measurements of the temperature each year.
The mean temperature was one degree less in 1998 than the mean
of the 1999 and 2000 temperatures. Should the scientist:
a) Conclude that the temperature is getting colder
b) Conclude that the temperature is about the same
c) Conclude that the temperature is getting warmer
d) Not conclude anything since it is meaningless to average
degrees Farhenheit and degrees Celsius in this way.
--
Eugene D. Gallagher
ECOS, UMASS/Boston
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