# [Rasch] Units of measurement in the social sciences

Andrew Kyngdon akyngdon at lexile.com
Wed Oct 24 00:20:32 EST 2007

```Hi Paul,

You've raised an important point of which much attention has been paid
at MetaMetrics. There are a few issues here.

Firstly, we report Lexiles in whole numbers. For theoretical text
difficulties we round to the nearest 10 Lexiles and persons to the
out at 806.32L. We round this to 805L. If a Harry Potter book comes out
at 1007.15L we round to 1010L (incidentally, we found that J.K Rowling
steadily increased the text difficulty of her novels during the course
of the Harry Potter series).

Secondly, there is a theory misspecification error of 64L (Stenner,
Burdick, Sanford & Burdick, 2006). This is an estimate of the Root Mean
Square Error (RMSE) obtained when the ensemble means of prose text
passages or "text slices" are regressed on the Lexile theory.

What this means is that a prose text consisting of N passages has an
expected error of 64L divided by the square root of N. Shorter prose
texts thus have a higher expected error than longer ones. For example, a
short, 500 word periodical with 4 passages will have an expected error
of 64 / (4^1/2) = 32L. A Harry Potter novel of 900 text slices has an
expected error term of 64 / (900^1/2) = 2L. We have found that most
books have expected errors in the single digits. For example, the novel
"A Clockwork Orange" has a text difficulty of 1260L and an expected
error of 3L (Stenner, et al, 2006).

Thirdly, we have found that person reading measures from hour long
reading tests have an error of around 90L. This is about half a logit,
which is consistent with the error of reading tests since time
immemorial.

On a related issue, we recently obtained data using an instructional
software application based on the Lexile Framework for Reading. We found
that forecasted text comprehension rates (as percentages of correct
responses) matched observed comprehension rates to 3 decimal places.

I hope this helps. Feel free to ask more questions.

Best, Andrew

Ref.:

Stenner, A.J.; Burdick, H.; Sanford, E.E. and Burdick, D.S. (2006) How
accurate are Lexile text measures? Journal of Applied Measurement, 7(3),
307-322.

Andrew Kyngdon, PhD

Senior Research Scientist

MetaMetrics, Inc.

1000 Park Forty Plaza Drive

Durham NC 27713 USA

Tel. 1 919 354 3473

Fax. 1 919 547 3401

3rd International Conference in Rasch measurement,

January 22-24 2008, Perth, Australia

http://www.education.uwa.edu.au/__data/page/115936/Rasch_conference_v12.
pdf

________________________________

From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On
Behalf Of Paul Barrett
Sent: Monday, October 22, 2007 5:43 PM
To: rasch at acer.edu.au
Subject: RE: [Rasch] Units of measurement in the social sciences

________________________________

From: rasch-bounces at acer.edu.au
[mailto:rasch-bounces at acer.edu.au] On Behalf Of Andrew Kyngdon
Sent: Tuesday, October 23, 2007 10:06 AM
To: rasch at acer.edu.au
Subject: RE: [Rasch] Units of measurement in the social sciences

My two cents...

...The unit of measurement in the Lexile reading scale is
defined as 1/1000th of the difference in comprehensibility between basal
primer texts and Grolier's (1986) Encyclopaedia (Stenner, 1986).

Hello Andrew

Out of interest, what is the degree of precision of measurement of this
unit? i.e. to what level of precision can the unit be measured (0, 1, 2,
3, 5 decimal places etc.)

Regards ... Paul

Paul Barrett, Ph.D.

2622 East 21st Street | Tulsa, OK  74114

Chief Research Scientist

Office | 918.749.0632  Fax | 918.749.0635

pbarrett at hoganassessments.com

hoganassessments.com <http://www.hoganassessments.com/>

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