# [Rasch] Re:Urgent question about high stakes and normality

iasonas lambrianou liasonas at lycos.com
Sun Jan 29 21:32:21 EST 2006

```Thanks Agustin,

I get the point, however, i missed to say that different people get
different tests e.g. one may take maths, history and science and somebody
else may take maths, english and biology. Then, we need to aggregate the
scores on each subject to get an 'overall' score. I know that you cannot
aggregate scores from different tests, not to mention comparing aggregate
scores from different combinations of tests. However, this is a political
requirement and we cannot change it. We just have to do what is less
worse under these political decisions. So, we take the z-scores of each
test, and then we add the z-scores and we transform this to a scale from
1-20. So, in effect, we have (z score on test1) + (z score on test 2) +
(z score on test 3). As I said before, different people get different
tests. Question 1: Are z scores are meaningful only if the distribution
of scores is normal? If not, do we need to normalise the distribution of
raw scores in order to get meaningful z scores (to aggregate)? If yes, is
this transformation ln(x/100-x) appropriate?

Sorry for not clarifying these issues,

Jason

----- Original Message -----
From: "Agustin Tristan"
To: "iasonas lambrianou" , "-Rasch"
Subject: [Rasch] Re:Urgent question about high stakes and normality
Date: Sat, 28 Jan 2006 10:07:33 -0800 (PST)

Hello Asonas!Normal distribution is something you MUST have? Why do
you think that normality is a required characteristic of the
particular population that you have tested? How are the mean and
standard deviation? How are the skewness and kurtosis parameters?
Please tell.I cannot qualify the scores of the students as "strange",
as I dont't have additional information, but if you're normalizing
something that is not normal, why are you interested to transform
them until you get a normal distribution? You may sort the students
according to their ability even if it is not normal distributed and
if your test is a good one.What if your score distribution is
multimodal? are you against that? high stakes tests may produce
skewed or bimodal distributions, not normal, specially if teachers
and the scholar program is looking to improve the results of the
students.It is clear that many populations behave as a normal
distribution in various tests,but not necessarily in all tests.In
(are your items distributed according to a normal or to a uniform
distribution?).And mainly, the most important of all, you must know
if the test satisfies the specifications of validity, this is more
important than normality of the distribution of the students.In
brief: I am most interested in other things than normality, and
certainly not in obtaining a "beautiful" picture of my students, I
need before all to have a good test and get a "good" picture of the
students. I can send you my picture, if the camera is a good one, and
if I have a good picture, you must see an ugly man, I really don't
expect a "beautiful" picture of myself, but a good one. Do I have to
retouch my picture to have a "beautiful" man in my picture and say
that I'm "normal"?Hope this helpsRegardsAgustin Tristan

asonas lambrianou <liasonas at lycos.com> wrote:

Dear friends,
I have a very urgent question, anyone who can contribute, please
do so

We use the t-scores (z scores) of the examinees on high stakes
tests to sort them according to their ability.
When the distribution of the raw scores deviates a lot from the
normal, then the t-scores look a bit 'strange'. Do you also agree
that t-scores can not be used when the distribution deviates
substantially from the normal?
Also, I can transform the raw scores using y=ln(x/(100-x)) and
the distribution of the raw scores becomes normal. Then, I can
get more 'beautiful' t scores (z scores). Am I allowed to use
this transformation and then get the t scores?

Thanks

Jason

> ----- Original Message -----
> From: "Mike Linacre (RMT)"
> To: rasch at acer.edu.au
> Subject: [Rasch] Different models: counts to scale conversion
> Date: Mon, 23 Jan 2006 14:58:51 -0600
>
>
> Not sure about the contrast "log-scaled" vs. "Rasch-scaled"
>
> Georg Rasch based his theory on the Poisson model, which is a
Rasch
> model and is a log-scaling model. It seems the actual contrast
is
> between a Rasch-Poisson model and a Rasch rating-scale-type
model.
>
> Mike L.
>
> Earlier remark:
> > When I was predicting the amount of money that a counselor
was
> > going to be sued for a bad outcome based the hierarchical
> > complexity of the informed consent procedure. Log money did
the
> > best. Right behind it by just a little worse .96 versus .94
was
> > Rasch scaled money. The value of money has been argued to
> > require loging for years.
>
> _______________________________________________
> Rasch mailing list
> Rasch at acer.edu.au
> http://listserv3.acer.edu.au/mailman/listinfo/rasch

>

Dr. Iasonas Lamprianou
CFAS, School of Education
The University of Manchester
Oxford Road, Manchester M13 9PL, UK
Tel. 0044 161 275 3485
iasonas.lamprianou at man.ac.uk

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Dr. Iasonas Lamprianou
CFAS, School of Education
The University of Manchester
Oxford Road, Manchester M13 9PL, UK
Tel. 0044  161 275 3485
iasonas.lamprianou at man.ac.uk

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