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<p class=MsoNormal><font size=2 color=blue face="Times New Roman"><span
style='font-size:10.0pt;color:blue'>There is Theo Dawson&#8217;s measure of
difficulty that yields stage of development for material.&nbsp; It is based on the
Model of Hierarchical Complexity and Skill Theory.&nbsp; It would be
interesting to see the correlation of these measures.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=blue face="Times New Roman"><span
style='font-size:10.0pt;color:blue'><o:p>&nbsp;</o:p></span></font></p>

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<p class=MsoNormal><font size=2 color=blue face="Times New Roman"><span
style='font-size:10.0pt;color:blue'>My best,</span></font><font color=blue><span
style='color:blue'><o:p></o:p></span></font></p>

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style='font-size:10.0pt;color:blue'><br>
<st1:place w:st="on"><st1:PlaceName w:st="on">Michael</st1:PlaceName> <st1:PlaceName
 w:st="on">Lamport</st1:PlaceName> <st1:PlaceType w:st="on">Commons</st1:PlaceType></st1:place>,
Ph.D.<br>
Assistant Clinical Professor<br>
Department of Psychiatry<br>
<st1:place w:st="on"><st1:PlaceName w:st="on">Harvard</st1:PlaceName> <st1:PlaceName
 w:st="on">Medical</st1:PlaceName> <st1:PlaceType w:st="on">School</st1:PlaceType></st1:place><br>
<st1:place w:st="on"><st1:PlaceName w:st="on">Beth</st1:PlaceName> <st1:PlaceName
 w:st="on">Israel</st1:PlaceName> <st1:PlaceName w:st="on">Deaconess</st1:PlaceName>
 <st1:PlaceName w:st="on">Medical</st1:PlaceName> <st1:PlaceType w:st="on">Center</st1:PlaceType></st1:place><o:p></o:p></span></font></p>

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  Huron Avenue</span></font></st1:address></st1:Street><font size=2 color=blue><span
style='font-size:10.0pt;color:blue'><o:p></o:p></span></font></p>

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  color=blue face="Times New Roman"><span style='font-size:10.0pt;color:blue'>Cambridge</span></font></st1:City><font
 size=2 color=blue><span style='font-size:10.0pt;color:blue'>, <st1:State
 w:st="on">MA</st1:State> <st1:PostalCode w:st="on">02138-1328</st1:PostalCode></span></font></st1:place><br>
<font size=2 color=blue><span style='font-size:10.0pt;color:blue'><a
href="mailto:commons@tiac.net">commons@tiac.net</a><br>
<a href="http://www.dareassociation.org/">http://www.dareassociation.org/</a><br>
617-497-5270 Telephone</span></font><font color=blue><span style='color:blue'><o:p></o:p></span></font></p>

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<p class=MsoNormal><font size=2 color=blue face="Times New Roman"><span
style='font-size:10.0pt;color:blue'>617-320-0896&nbsp; Cellular<br>
617-491-5270&nbsp; Facsimile</span></font><o:p></o:p></p>

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</span></font></div>

<p class=MsoNormal><b><font size=2 face=Tahoma><span style='font-size:10.0pt;
font-family:Tahoma;font-weight:bold'>From:</span></font></b><font size=2
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'>
rasch-bounces@acer.edu.au [mailto:rasch-bounces@acer.edu.au] <b><span
style='font-weight:bold'>On Behalf Of </span></b>Andrew Kyngdon<br>
<b><span style='font-weight:bold'>Sent:</span></b> Tuesday, October 30, 2007
4:54 PM<br>
<b><span style='font-weight:bold'>To:</span></b> Paul Barrett;
rasch@acer.edu.au<br>
<b><span style='font-weight:bold'>Subject:</span></b> RE: [Rasch] Not a Fan of
Lexiles?</span></font><o:p></o:p></p>

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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'>Dear Paul,<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'>A great firebrand post!
One major quibble, however, with what you said.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'>In the Lexile system,
measures of the difficulty of written prose text passages are NOT obtained from
either test scores, ratings, simulations or IRT model analyses of such data.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'>The Lexile theory argues
that the difficulty of written prose text is a functional composition of two
key cognitive variables &#8211; <i><span style='font-style:italic'>syntactic
complexity </span></i>and <i><span style='font-style:italic'>semantic rarity</span></i>.
&nbsp;Syntactic complexity is </span></font><font size=2 color=navy face=Arial><span
style='font-size:10.0pt;font-family:Arial;color:navy'>the complexity of the
sentence / thought unit structure of a written prose text passage. Semantic
rarity is the familiarity of the semantic units (words) which comprise a prose
text passage.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Each is assessed using a proxy variable.
For syntactic complexity. it is the natural logarithm of the mean sentence length
(LMSL). Why is this proxy used? Research in cognition has found that it is a
good proxy for the demand written prose text places upon Short Term Memory
(e.g. Crain &amp; Skankweiler, 1988). The longer a sentence is, the harder it
is to keep all the information in a sentence in STM. Thus text passages with
longer sentences are more difficult to comprehend.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>For semantic rarity, the proxy variable is
the mean natural logarithm of word frequency (MLWF). Why is this proxy used?
Stenner, Smith &amp; Burdick (1983) investigated over 50 variables, including
part of speech, number of letters, number of syllables, modal grade, word
content classification and various transformations of these variables. They
found MLWF was the best proxy for the likelihood a person has a word in their
mental lexicon. Moreover, reaction time and gaze duration studies have found
that people will look at rarer words for several hundred milliseconds longer
than commonly occurring words, suggesting rarer words are harder to locate and
retrieve from the mental lexicon. Thus text passages containing words which are
infrequently used will be more difficult to comprehend.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>The difficulty of a written prose text
passage <i><span style='font-style:italic'>i</span></i>, <i><span
style='font-style:italic'>D<sub>i</sub></span></i>, is a functional composition
of these proxies such that: <i><span style='font-style:italic'>D<sub>i</sub></span></i>
= (<i><span style='font-style:italic'>a</span></i> x LMSL) &#8211; (<i><span
style='font-style:italic'>b</span></i> x MLFW) &#8211; <i><span
style='font-style:italic'>c</span></i>. This expression, referred to as a <i><span
style='font-style:italic'>construct specification equation</span></i>, is a 5
variable simple polynomial conjoint structure (Krantz, Luce, Suppes &amp;
Tversky, 1971) where <i><span style='font-style:italic'>a</span></i>, <i><span
style='font-style:italic'>b</span></i> and <i><span style='font-style:italic'>c
</span></i>are real valued constants. The actual values of these constants are
proprietary; however, they result in <i><span style='font-style:italic'>D<sub>i</sub>
</span></i>being a scale in logit units.</span></font><font size=2 color=navy
face=Arial><span lang=EN-AU style='font-size:10.0pt;font-family:Arial;
color:navy'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'>Notice the complete
absence of &#8220;run of the mill&#8217; psychometry - test scores, IRT model
estimates, fit statistics, ratings, DIF, reliability coefficients and so on
&#8211; in the measurement of the difficulty of written prose text passages. <o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'>The biggest weakness of
the theory is the assumption of something more than monotone relationships
existing between proxy variables and the relevant psychological attributes
(Krantz &amp; Tversky, 1971). The theory of conjoint measurement (Krantz, et
al, 1971) can be used to address this issue. I have done this and found the
axioms to be satisfied using Karabatsos&#8217;s (2005) methods for the
probabilistic tests of deterministic axioms.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'>The Lexile theory argues
that the probability of comprehending a written prose text passage is a
non-interactive, additive function of the text&#8217;s difficulty and the
persons&#8217; reading ability. A suitable model for this is the Rasch (1960)
model. However, unlike conventional psychometry, we modify the Rasch model to
suit the theory. If a person&#8217;s ability is equal to the text difficulty,
we do not consider the person has successfully comprehended a text passage when
the response probability is only .5. A constant is therefore introduced into
the Rasch model such that when ability equals difficulty, the response
probability is .75. Note this modification does not destroy the raw score
sufficiency property (or any others) of the Rasch model. <o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'>This modified Rasch model
is Pr [Person<i><span style='font-style:italic'> v </span></i>comprehends text
passage<i><span style='font-style:italic'> i</span></i>] = exp(</span></font><i><font
size=2 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy;font-style:italic'>B<sub>v</sub> &#8211; D<sub>i </sub></span></font></i><font
size=2 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'>+ <i><span style='font-style:italic'>k</span></i>) / 1 + exp</span></font><font
size=2 color=navy face=Arial><span lang=EN-AU style='font-size:10.0pt;
font-family:Arial;color:navy'>(</span></font><i><font size=2 color=navy
face=Arial><span style='font-size:10.0pt;font-family:Arial;color:navy;
font-style:italic'>B<sub>v</sub> &#8211; D<sub>i</sub> </span></font></i><font
size=2 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'>+ <i><span style='font-style:italic'>k</span></i>), where <i><span
style='font-style:italic'>Bv</span></i> is the ability of person <i><span
style='font-style:italic'>v</span></i> and <i><span style='font-style:italic'>k</span></i>
is the aforementioned constant. Test scores enter the Lexile theory in the
estimation of person abilities. These come from tests consisting of Lexile
passage native items (text passages with a sentence &#8220;close&#8221;). Use
of the Rasch model puts the abilities on the same scale as the text difficulty
variable. Both then can use the same affine transformation to become
measurements in the Lexile scale.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Hence I consider your point:<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>&#8220;&#8230;there is
no substantive difference between probabilistic (latent variable) &nbsp;or
deterministic (raw score) scale scores. Which, by default, means all of the
Metametrics Lexile and Quantile work could have been achieved using conventional&nbsp;deterministic/actuarial
score algorithms (now there's a sobering thought).. &#8220;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>to be incorrect. One cannot arrive at the
measurement of text difficulty, as theorized in the Lexile system, following
conventional psychometric practice.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Cheers,<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Andrew<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>P.S. One serious problem with
connectionist models as theories of human thought processes &#8211; no
biological equivalent to the backpropagation algorithm. Does this mean
connectionism is merely another &#8220;unopened black box&#8221; theory of
psychology?<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Refs:<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Crain, S. &amp; Skankweiler, D. (1988).
Syntactic complexity and reading acquisition. In A. Davidson and G.M. Green
(Eds.), <i><span style='font-style:italic'>Linguistic complexity and text
comprehension: readability issues reconsidered</span></i>. <st1:place w:st="on"><st1:City
 w:st="on">Hillsdale</st1:City>, <st1:State w:st="on">N.J.</st1:State></st1:place>:
Erlbaum.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'>Karabatsos, G. (2005).
The exchangeable multinomial model as an approach to testing deterministic
axioms of choice and measurement. <i><span style='font-style:italic'>Journal of
Mathematical Psychology</span></i>, <i><span style='font-style:italic'>49</span></i>(1),
51-69.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'>Krantz, D.H.; Luce, R.D;
Suppes, P. &amp; Tversky, A. (1971). <i><span style='font-style:italic'>Foundations
of Measurement, Vol. I: Additive and polynomial representations</span></i>. <st1:place
w:st="on"><st1:State w:st="on">New York</st1:State></st1:place>: Academic
Press.</span></font><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'>Krantz, D.H. &amp;
Tversky, A. (1971). Conjoint measurement analysis of composition rules in
psychology. <i><span style='font-style:italic'>Psychological Review</span></i>,
<i><span style='font-style:italic'>78</span></i>(2), 151-169.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'>Rasch, G. (1960).&nbsp; <i><span
style='font-style:italic'>Probabilistic models for some intelligence and
attainment tests</span></i>. <st1:place w:st="on"><st1:City w:st="on">Copenhagen</st1:City></st1:place>:
Danish Institute for Educational Research.</span></font><font size=2
color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Stenner, A.J., Smith, M. &amp; Burdick, D.
S. (1983) Toward a theory of construct definition. <i><span style='font-style:
italic'>Journal of Education Measurement</span></i>, <i><span style='font-style:
italic'>20</span></i>, 305-315.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<div>

<p class=MsoNormal><st1:PersonName w:st="on"><font size=4 color=navy
 face=Arial><span style='font-size:14.0pt;font-family:Arial;color:navy'>Andrew
 Kyngdon</span></font></st1:PersonName><font size=4 color=navy face=Arial><span
style='font-size:14.0pt;font-family:Arial;color:navy'>, PhD</span></font><font
size=4 color=navy><span style='font-size:14.0pt;color:navy'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Senior Research Scientist</span></font><font
size=2 color=navy><span style='font-size:10.0pt;color:navy'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>MetaMetrics, Inc.</span></font><font
size=2 color=navy><span style='font-size:10.0pt;color:navy'><o:p></o:p></span></font></p>

<p class=MsoNormal><st1:Street tabIndex="0"
style="BACKGROUND-POSITION: left bottom; BACKGROUND-IMAGE: url(res://ietag.dll/#34/#1001); BACKGROUND-REPEAT: repeat-x"
w:st="on"><st1:address tabIndex="0"
 style="BACKGROUND-POSITION: left bottom; BACKGROUND-IMAGE: url(res://ietag.dll/#34/#1001); BACKGROUND-REPEAT: repeat-x"
 w:st="on"><font size=2 color=navy face=Arial><span style='font-size:10.0pt;
  font-family:Arial;color:navy'>1000 Park Forty Plaza Drive</span></font></st1:address></st1:Street><font
size=2 color=navy><span style='font-size:10.0pt;color:navy'><o:p></o:p></span></font></p>

<p class=MsoNormal><st1:place w:st="on"><st1:City tabIndex="0"
 style="BACKGROUND-POSITION: left bottom; BACKGROUND-IMAGE: url(res://ietag.dll/#34/#1001); BACKGROUND-REPEAT: repeat-x"
 w:st="on"><font size=2 color=navy face=Arial><span style='font-size:10.0pt;
  font-family:Arial;color:navy'>Durham</span></font></st1:City><font size=2
 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
 color:navy'> <st1:State tabIndex="0"
 style="BACKGROUND-POSITION: left bottom; BACKGROUND-IMAGE: url(res://ietag.dll/#34/#1001); BACKGROUND-REPEAT: repeat-x"
 w:st="on">NC</st1:State> <st1:PostalCode w:st="on">27713</st1:PostalCode> <st1:country-region
 tabIndex="0"
 style="BACKGROUND-POSITION: left bottom; BACKGROUND-IMAGE: url(res://ietag.dll/#34/#1001); BACKGROUND-REPEAT: repeat-x"
 w:st="on">USA</st1:country-region></span></font></st1:place><font size=2
color=navy><span style='font-size:10.0pt;color:navy'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Tel. 1 919&nbsp;354 3473</span></font><font
size=2 color=navy><span style='font-size:10.0pt;color:navy'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Fax. 1 919 547 3401</span></font><font
color=navy><span style='color:navy'><o:p></o:p></span></font></p>

<div>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>&nbsp;<o:p></o:p></span></font></p>

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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p>&nbsp;</o:p></span></font></p>

</div>

<blockquote style='border:none;border-left:solid black 1.5pt;padding:0in 0in 0in 4.0pt;
margin-left:3.75pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt'>

<div class=MsoNormal align=center style='text-align:center'><font size=2
color=black face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:black'>

<hr size=2 width="100%" align=center tabIndex=-1>

</span></font></div>

<p class=MsoNormal style='margin-bottom:12.0pt'><b><font size=2 color=black
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma;color:black;
font-weight:bold'>From:</span></font></b><font size=2 color=black face=Tahoma><span
style='font-size:10.0pt;font-family:Tahoma;color:black'>
rasch-bounces@acer.edu.au [mailto:rasch-bounces@acer.edu.au] <b><span
style='font-weight:bold'>On Behalf Of </span></b>renselange@earthlink.net<br>
<b><span style='font-weight:bold'>Sent:</span></b> Tuesday, October 30, 2007
5:28 AM<br>
<b><span style='font-weight:bold'>To:</span></b> Anthony James;
rasch@acer.edu.au<br>
<b><span style='font-weight:bold'>Subject:</span></b> Re: [Rasch] Fan</span></font><font
size=2 color=black face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:black'><o:p></o:p></span></font></p>

<p><font size=2 color=blue face=Arial><span lang=EN-AU style='font-size:10.0pt;
font-family:Arial;color:blue'>My take on this is &quot;so what&quot; as well.
Getting &quot;scores&quot; is hardly the main achievement of Rasch
modeling.&nbsp;There simply&nbsp;is little appreciable difference between raw
score sums&nbsp;and the Rasch model, as well as estimates obtained via one,
two, or three-parameter logistic models.</span></font><font size=2 color=black
face=Arial><span lang=EN-AU style='font-size:10.0pt;font-family:Arial;
color:black'> <o:p></o:p></span></font></p>

</blockquote>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>Hello Reese</span></font><font
size=1 color=black face=Arial><span lang=EN-AU style='font-size:9.0pt;
font-family:Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>There you have it in a
nutshell, why many scientists&nbsp;(vs psychometricians) concerned with
explaining substantive phenomena, sometimes using questionnaire data, are not
concerned with itemmetric models. </span></font><font size=1 color=black
face=Arial><span lang=EN-AU style='font-size:9.0pt;font-family:Arial;
color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>Edumetrics is frankly
&quot;technician work&quot;;&nbsp;the utility and benefits of probabilistic
modeling of item&nbsp;response data&nbsp;seems&nbsp;to be irrelevant to
explaining or predicting phenomenal outcomes more accurately.&nbsp;&nbsp;Whilst
other benefits might accrue to those primarily concerned with examinations,
licensing, or other such pragmatic ventures, as&nbsp;a scientist, you are
concerned with minimizing substantive error in any&nbsp;predictions you might
make on the basis of theory or&nbsp;even &quot;dustbowl&quot;
empiricism.&nbsp;&nbsp;</span></font><font size=1 color=black face=Arial><span
lang=EN-AU style='font-size:9.0pt;font-family:Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>As you state Reese,
there is no substantive difference between probabilistic (latent variable)
&nbsp;or deterministic (raw score) scale scores. Which, by default, means all
of the Metametrics Lexile and Quantile work could have been achieved using
conventional&nbsp;deterministic/actuarial score algorithms (now there's a
sobering thought).. </span></font><font size=1 color=black face=Arial><span
lang=EN-AU style='font-size:9.0pt;font-family:Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>Whether or not IRT is a
more &quot;efficient&quot; method of going about these activities seems to be
the issue - which is an important one neverthless. </span></font><font size=1
color=black face=Arial><span lang=EN-AU style='font-size:9.0pt;font-family:
Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>But what use is
&quot;efficiency&quot; when the magnitudes obtained are equivalent to just
summing up item responses? Person reliability can easily be computed without
any fuss using conventional item difficulties and rank order response
discrepancy (between item difficulty ranking and observed item responses). You
don't need a &quot;data model&quot; for this simple heuristic. Cross-validation
sorts out replicability.</span></font><font size=1 color=black face=Arial><span
lang=EN-AU style='font-size:9.0pt;font-family:Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>I'm not so sure IRT is
any more efficient at all than a sensible and intelligent approach to construct
assessment, except perhaps where edumetrics is concerned - but even here, where
are the advantages to be seen, and by whom?&nbsp;Are educational standards
improving because of IRT methods being applied?</span></font><font size=1
color=black face=Arial><span lang=EN-AU style='font-size:9.0pt;font-family:
Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>As far as I can see, the
only reason IRT came into existence was because Rasch and others
were&nbsp;fascinated with test theory, statistical data models, and fundamental
measurement, instead of the actual phenomena of interest, and capturing these
directly without the need for&nbsp;bucketloads of &nbsp;assumptions or
practically incomprehensible algebra and math.</span></font><font size=1
color=black face=Arial><span lang=EN-AU style='font-size:9.0pt;font-family:
Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>Indeed, what is apparent
(to me at least)&nbsp;is that&nbsp;the major source of
explanatory/predictive&nbsp;error&nbsp;is&nbsp;not in the
&quot;measurement&quot; metrics per se, but in the concepts we invoke to
explain phenomena, and how we actually try to measure or assess
&quot;magnitudes&quot; on them.</span></font><font size=1 color=black
face=Arial><span lang=EN-AU style='font-size:9.0pt;font-family:Arial;
color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>And, I haven't forgotten
my reply to Andrew or Moritz(!)&nbsp;- but I'm flat out on an interrater
discrepancy/reliability program right now - for the next 5 days or so - but I
couldn't resist replying to this as I've seen the same &quot;even though there
is no difference, this is still wonderful stuff&quot; statements in a recent
paper comparing Ideal Point unfolding models, dominance IRT, and simple raw
score methods ...</span></font><font size=1 color=black face=Arial><span
lang=EN-AU style='font-size:9.0pt;font-family:Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<div>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>Cherneyshenko, O.S.,
Stark, S., Drasgow, F., &amp; Roberts, B.W. (2007) Constructing personality
scales under the assumption of an Ideal Point response process: toward
increasing the flexibility of personality measures. <em><i><font face=Arial><span
style='font-family:Arial'>Psychological Assessment</span></font></i></em>, 19,
1, 88-106.&nbsp;</span></font><font size=1 color=black face=Arial><span
lang=EN-AU style='font-size:9.0pt;font-family:Arial;color:black'><o:p></o:p></span></font></p>

</div>

<div>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

</div>

<div>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>See page 103, Col 2, 2nd
para beginning &quot;Note also that examination&nbsp;of correlations .. &quot;
... which contains the sentence ... &quot;</span></font><font size=2
color=navy face=Arial><span lang=EN-AU style='font-size:10.0pt;font-family:
Arial;color:navy'>The use of ideal point methods, however, is unlikely to yield
increases in criterion-related validities</span></font><font size=2
color=black face=Arial><span lang=EN-AU style='font-size:10.0pt;font-family:
Arial;color:black'>&quot;</span></font><font size=1 color=black face=Arial><span
lang=EN-AU style='font-size:9.0pt;font-family:Arial;color:black'><o:p></o:p></span></font></p>

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<div>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

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<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>and then read the 1st
para of the discussion .. </span></font><font size=1 color=black face=Arial><span
lang=EN-AU style='font-size:9.0pt;font-family:Arial;color:black'><o:p></o:p></span></font></p>

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<div>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

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<div>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>Their argument, as far
as I can see, is more about the technicalities/differential pragmatic
benefits&nbsp;of test construction ...and the consequences on particular
measurement ranges within a scale. </span></font><font size=1 color=black
face=Arial><span lang=EN-AU style='font-size:9.0pt;font-family:Arial;
color:black'><o:p></o:p></span></font></p>

</div>

<div>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

</div>

<div>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>But, if the criterion
prediction remains the same - what is the achieved real-world&nbsp;or
scientific benefit? </span></font><font size=1 color=black face=Arial><span
lang=EN-AU style='font-size:9.0pt;font-family:Arial;color:black'><o:p></o:p></span></font></p>

</div>

<div>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

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<div>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>I have the feeling they
are discovering that the real problem is not with the technology of assessment,
but with the very nature of the constructs we try to assess.</span></font><font
size=1 color=black face=Arial><span lang=EN-AU style='font-size:9.0pt;
font-family:Arial;color:black'><o:p></o:p></span></font></p>

</div>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>However, this is not a
call to undo or dump IRT - as those like Metametrics, ACER, and others&nbsp;who
have generated impressive measurement and assessment systems around IRT are
testament to its functionality, utility, and profitability.&nbsp;</span></font><font
size=1 color=black face=Arial><span lang=EN-AU style='font-size:9.0pt;
font-family:Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>This is merely a statement
which says that it is just another way of &quot;modeling data&quot; and
constructing test scores which has proved to have no tangible advantages over
any other &quot;intelligent&quot; method of analyzing data to make important
decisions.</span></font><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>If you think think this
is unfair, consider the&nbsp;development of the
&quot;perceptron&quot;&nbsp;(The perceptron is a type of artificial neural
network invented in 1957 at the Cornell Aeronautical Laboratory by Frank
Rosenblatt .. Wikipedia). In 50 years look at what&nbsp;this simple
&quot;algorithm&quot; for a neural net has spawned .. an entire&nbsp;new
area&nbsp;of psychological science&nbsp;investigation &quot;connectionist
cognitive psychology&quot;, a neurophysiological model for developmental brain
networks and brain function,&nbsp;artificial intelligence, computational
biology,&nbsp;and literally physical working models of the development of human
intelligence, stock market trading algorithms, seriously accurate&nbsp;market
research/brand analysis&nbsp;prediction models, security camera person-feature
detection, biometric sensors, handwriting, and speech detection, etc, etc.. </span></font><font
size=1 color=black face=Arial><span lang=EN-AU style='font-size:9.0pt;
font-family:Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>And what has IRT spawned
in the same period? A&nbsp;few tests which are almost indistinguishable from
the old tests,&nbsp;hundreds of books and thousands of papers on test theory
and tiny one-shot applications for which CTT would have done the same job just
as well - and was probably doing so,&nbsp;and a few major-league companies who
sell the technology and some of its results to others.</span></font><font
size=1 color=black face=Arial><span lang=EN-AU style='font-size:9.0pt;
font-family:Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>If I am to do any work
as a psychological scientist - I want to be the inventor of&nbsp; a
&quot;perceptron&quot;, and not the inventor of yet another &quot;test
theory&quot; - which is why methods which predict or measure no better than
simple &quot;back of the matchbox&quot; algorithms or heuristics&nbsp;are not
given the &quot;time of day&quot; by those like myself who want to make big
strides in our science.&nbsp;</span></font><font size=1 color=black face=Arial><span
lang=EN-AU style='font-size:9.0pt;font-family:Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>So, in response
to:&quot;</span></font><font size=2 color=blue face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:blue'>The main problem here is
that non-IRT folks often do not (or cannot) even conceive of the possibilities
afforded by test / form equating, item / person fit and bias testing, Hence,
the advantages of all this appear rather &quot;academic&quot; ( read: useless).</span></font><font
size=2 color=black face=Arial><span lang=EN-AU style='font-size:10.0pt;
font-family:Arial;color:black'> &quot; ..</span></font><font size=1
color=black face=Arial><span lang=EN-AU style='font-size:9.0pt;font-family:
Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>You now have a better
idea why&nbsp;some like me really don't bother with IRT at all anymore - it's
virtually irrelevant to substantive progress in psychological science. And, if
you need to make decisions using test scores, why bother when a simple sum
score interpreted using representative population norms and other relevant and
somewhat more obvious item and scale statistics does &quot;the business&quot;
just as well as scores&nbsp;and indices associated with the &quot;latent variable&quot;
work which only a &quot;psychometric&nbsp; wizard&quot; can seemingly convey!</span></font><font
size=1 color=black face=Arial><span lang=EN-AU style='font-size:9.0pt;
font-family:Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>What made the neural net
so easy to &quot;sell&quot; was that it predicted valuable and substantive
outcomes for which no other model came close. That's why it was grabbed with
open arms by those &quot;non-academics and academics&quot; alike who looked at
the results and thought &quot; I've gotta have this &quot;. Sheesh, even
Shepard, Kruskal, Lingoes, and Guttman's non-metric Multidimensional Scaling
algorithms had a bigger impact in 10 years from their inception than IRT.</span></font><font
size=1 color=black face=Arial><span lang=EN-AU style='font-size:9.0pt;
font-family:Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>Until IRT, unfolding, or
any test theory model can produce that &quot;wow&quot; effect - they
will&nbsp;remain &quot;niche&quot;&nbsp;activities for a minority of
individuals in a tiny sub-domain of the social and human sciences.</span></font><font
size=1 color=black face=Arial><span lang=EN-AU style='font-size:9.0pt;
font-family:Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 color=black face=Arial><span lang=EN-AU
style='font-size:10.0pt;font-family:Arial;color:black'>Regards ... Paul</span></font><font
size=1 color=black face=Arial><span lang=EN-AU style='font-size:9.0pt;
font-family:Arial;color:black'><o:p></o:p></span></font></p>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

<div>

<p class=MsoNormal><font size=1 color=black face=Arial><span lang=EN-AU
style='font-size:9.0pt;font-family:Arial;color:black'>&nbsp;<o:p></o:p></span></font></p>

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