[Rasch] Error in CTT p-values

Hoi Suen HoiSuen at psu.edu
Sat Jul 25 03:10:30 EST 2009

Dear Anthony,

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 
_people_ are interchangeable -- which, of course, contradicts the whole 
purpose of measurement, discrimination or separation.

(Note that the SEM equation you cited does require "reliability" to be 
an r-squared value.)


Hoi K. Suen
Distinguished Professor
Educational Psychology
The Penn State University
Website: suen.educ.psu.edu <http://suen.educ.psu.edu>

Anthony James wrote:
> Dear all,
> The standard error for perosn raw scores under CTT is formulated as
> SEM=SD*SQR(/1-reliability/)
> I wanted to know if it is possible to estimate error for item 
> difficulties in CTT.
> 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, can we say that we have estimated error in item difficulties?
> I know Im under the influence of the symmetry in Rasch, not sure if it 
> works under CTT.
> Cheers
> Anthony
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