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Dear Anthony,<br>
<br>
I don't believe you can. Although item-based reliability coefficients
such as Cronbach Alpha or split-half in CTT are correlation-like, they
are actually r-squared values between true and observed scores. This
correlation becomes a reliability coefficient (i.e. r-squared) only
when one of the classical assumptions are met (strictly parallel,
essentially tau-equivalent, congeneric, etc.). When applied to
item-based approaches to reliability, these assumptions require that
items be interchangeable, at least to some degree. Your approach to
estimating item difficulty error by transposing the data matrix would
correspondingly require that <u>people</u> are interchangeable --
which, of course, contradicts the whole purpose of measurement,
discrimination or separation.<br>
<br>
(Note that the SEM equation you cited does require "reliability" to be
an r-squared value.)<br>
<br>
Best,<br>
Hoi<br>
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 style="color: rgb(0, 0, 0); font-size: 90%; font-family: times-roman;">_____________________________<br>
Hoi K. Suen<br>
Distinguished Professor<br>
Educational Psychology<br>
The Penn State University<br>
Website: <a href="http://suen.educ.psu.edu">suen.educ.psu.edu</a>
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<br>
<br>
Anthony James wrote:
<blockquote cite="mid:225281.96590.qm@web111414.mail.gq1.yahoo.com"
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        <div>Dear all,</div>
        <div>The standard error for perosn raw scores under CTT is
formulated as</div>
        <div>SEM<span
 style="font-size: 12pt; font-family: 'Times New Roman';" lang="EN-US">=SD*SQR<span
 style="font-size: 12pt; font-family: 'Times New Roman';" lang="EN-US">(<em>1-reliability</em>)</span></span></div>
        <div><span
 style="font-size: 12pt; font-family: 'Times New Roman';" lang="EN-US"><span
 style="font-size: 12pt; font-family: 'Times New Roman';" lang="EN-US">I
wanted to know if it is possible to estimate error for item
difficulties in CTT. </span></span></div>
        <div><span
 style="font-size: 12pt; font-family: 'Times New Roman';" lang="EN-US"><span
 style="font-size: 12pt; font-family: 'Times New Roman';" lang="EN-US">In
this formula if we replace SD of person raw scores with SD of item
p-values or item raw scores and then transpose the datafile and compute
interperson correlations for reliability and insert it in the formula, </span></span><span
 style="font-size: 12pt; font-family: 'Times New Roman';" lang="EN-US"><span
 style="font-size: 12pt; font-family: 'Times New Roman';" lang="EN-US">can
we say that we have estimated error in item difficulties?</span></span></div>
        <div><span
 style="font-size: 12pt; font-family: 'Times New Roman';" lang="EN-US"><span
 style="font-size: 12pt; font-family: 'Times New Roman';" lang="EN-US">I
know Im under the influence of the symmetry&nbsp;in Rasch, not sure if it
works under CTT.</span></span></div>
        <div><span
 style="font-size: 12pt; font-family: 'Times New Roman';" lang="EN-US"><span
 style="font-size: 12pt; font-family: 'Times New Roman';" lang="EN-US">Cheers</span></span></div>
        <div><span
 style="font-size: 12pt; font-family: 'Times New Roman';" lang="EN-US"><span
 style="font-size: 12pt; font-family: 'Times New Roman';" lang="EN-US">Anthony</span></span></div>
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