\doc\web\99\15\stddev.txt
Date forwarded: Sat, 9 Oct 1999 16:55:56 -0400 (EDT)
Date sent: Sat, 9 Oct 1999 14:02:44 -0700 (PDT)
From: La Griffe du Lion
Subject: Re: [Upstream] WASL Closes Race Gap Or Just Bogus??
To: upstream-list@cycad.com
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Forwarded by: upstream-list@cycad.com
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Arthur,
1) I suppose it does seem a bit like magic, but I'm afraid the answer
to your question is rather technical. I actually did not calculate
standard deviations from your data, but rather the difference between
group means (in SD units), the usual way to specify group differences.
If you are really interested, go to "Women and Minorities in Science."
http://members.xoom.com/griffedulion/women_and_minorities_in_science.htm
Look at the two paragraphs following equation (5). There I explain in
detail how to calculate, i.e, closely estimate, mean differences from
"pass rates." I do it there for male-female differences, and the "pass
rates" are percentages above SAT thresholds. However, the two problems
are formally identical, and the same algorithm can be implemented in
the present context.
As I have set up the computational machinery to solve this problem, I
can do it very quickly -- a few minutes at most. If you have similar
data, just send it to me. I will help you out.
2) With respect to your 10 percent across the board improvement rate,
if this means 10 percent improvement for *each* group, I guarantee it
will be impossible unless a)group differnces are erased or b)tests are
scored differently for each group. The first is without precedent, the
second too uncivilized for even a school superintendent.
Alternatively, 10 percent improvement for an entire school system can
be engineered easily. I suspect this is what you are observing.
Best, Griffe
--- arthurhu@halcyon.com wrote:
> How did you figure out the Std Dev from the figures I gave?
> I thought the office did not give this data out, how can
> you compute it from the pass rates?
>
> What hit me over the head is that this test growth is too
> close to the fanciful "projections" chart they also gave out
> which showed a nice straight line from the 1997 80% flunk rate
> up to the desired 80% pass rate. When the actual test conforms
> to this, it seems to be just as much as UC claimed not to have
> admissions quotas, even though their number of blacks exactly
> matched or exceeded their stated numeric goals of 8% black
> and 15% Hispanic.
>
> I believe this test is being constructed to give an across
> the board 10% test improvement rate. The difficulty of the
> problems is known, even though officials deny that any of the
> 4th grade problems violate grade level guidelines which is
> obvious to anyone who does a simple comparison. This is even
> more remarkable given that two of the most difficult problems
> were removed from the 1999 test because they were taken from
> sample booklets.
>
> As far as I know, no other state has shown improvement that
> grows exactly according to the stated improvement quotas that
> were set out as "goals". Oregon's tests remain at a 50%
> flunk level, and Virginia is still way off from going from 0%
> of schools passing to 80% of schools passing.
>
> As far as I've picked up, a standards "committee" decides
> the first year how many problem need to be correct for
> each level of "standards" based performance, this number
> remains constant and the wizards constructing the test
> use "scientific" methods to insure the tests are equally
> difficult from year to year, even though current SPI
> Terry Bergeson has admitted some tests were more difficult
> in some years than others, at least in a writing task.
>
> How you can claim the test is equally difficult from year
> to year, but it can vary from year to year is beyond me.
>
> If somebody can give me a foolproof argument that these
> tests are bogus, that might win the election for the
> Superintendent of Public Instruction in 2000.
>
> On 1999-10-08 upstream-list@cycad.com said:
> >There are several issues here:
> >1) Projecting scores:
> >Extrapolation without a guiding model ranks way up on the scale
> of
> >human egotism. Nevertheless, it is possible to make some
> predictions
> >about the WASL math passing rates down the road, though the
> >predictions will take the form of 'what if' games.
> >We must first identify what is constant in the WASL pass rates
> >already observed. It is simply this: In standard units, the 1997,
> >1998 and 1999 passing rates quoted by Hu show no significant
> change
> >with time in racial or ethnic differences. We can closely
> estimate
> >these differences from the passing rate data alone, with the
> >following result:
> >With little spread over three years, Asians averaged a negligible
> >0.027 SD below whites. Also with little spread, blacks and
> Hispanics
> >lagged 0.85 SD and 0.89 SD, respectively, behind whites. If we
> must
> >project, at least do it by preserving these differences.
> >If, for example, in 2003 whites were to pass at the 85 percent
> level
> >(Hu's extrapolation), blacks would be expected to pass at the
> 57.5
> >percent level (not 35 percent). Hispanics would pass at about the
> >55.9 percent level, and Asians at the 84.4 percent level (not 72
> >percent). We can safely predict, that if and when the 80 percent
> >passing goal is achieved by whites, blacks will pass at about a
> 50
> >percent rate.
> >It would defy reason to construct an exam which would show, say,
> a
> >10 percent increase in pass rates *across the board*. It cannot
> be
> >done. If one group were to improve by 10 percent, the others
> would
> >improve by different proportions.
> >2) Is the passing bar being lowered?
> >There is no way to tell from these data alone whether the bar is
> >being lowered or whether students are improving, or some
> >combination of both. Note, however, that a trivial exam can
> falsely
> >give the appearance of erasing an ethnic gap. Based on group
> >differences consistent with WASL results, if a test is
> constructed
> >such that 99 percent of whites pass, then 93 percent of blacks
> >would pass. The "Reduction" of this gap to 6 points would in fact
> >represent no closure whatsoever.
> Arthur Hu "Fairness in Diversity" Kirkland WA
> http://www.leconsulting.com/arthurhu/
>
> Net-Tamer V 1.11P - Registered
>
> ---
>
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=====
La Griffe du Lion
http://members.xoom.com/griffedulion/index.html
__________________________________________________
In 1998, more than a million college-bound high school seniors took
the SAT I mathematical reasoning test, 541,962 men and 630,817 women.
Men averaged 529.6 (SD = 114.1). Women averaged 494.5 (SD = 107.8).
Since the two distributions have slightly different standard
deviations, we computed the gap as the difference in the means
divided by the root mean square of the two SDs, obtaining a
male-female math gap of 0.32 SD.
Go to my essay, "Women and Minorities in Science."
http://members.xoom.com/griffedulion/women_and_minorities_in_science.htmThere
you will find how to do the calculation. Instead of "male" use "white"
or "asian"; instead of "female" put in "black" or any other group. I've
quoted the relevant passage below.
"Assuming a normalized Gaussian probability density centered on zero,
(2) may be solved numerically for lamda, the number of standard
deviations the threshold score is displaced from the mean score of
PsubM. ... Knowing lamda, (5) may be solved numerically for Delta, the
gap between the male and female means."
I wrote a routine for MAPLE to do the calculation. Though MAPLE is a
symbolic processor, I have not used that capability, so most math
packages can be taught to do this calculation. Just in case you have
access to MAPLE, I have attached the program. Call it YOURNAME.ms and
MAPLE will interpret it.
Griffe
P.S. If blacks in Seattle are at the bottom of the barrel, and whites
do unusually well, shouldn't the difference between their means be
extra large rather than extra small as in the G4 Seattle 1993 CTBS
norm?