Page:  of 334
 

be greater than expected from the error function. Second, the observed variation
may be in greater concordance with the invariance property than would be expected
from normal error functions. This situation will result in a profile similar to curve A
in

Figure 5.2
. The number of concordant scores would be greater, and the number
of discordant assessment scores would be fewer than expected from the error
function. It is assumed that two assessments result in Rasch scores that are in greater
concordance than expected from random error when three properties are present. (1)
The frequency of standardized difference scores centered about zero must be greater
than expected from random error alone, thereby indicating a larger than expected
frequency of concordant assessment scores. (2) The frequency of standardized
difference scores at the extreme ends of the distribution must be less than expected
from the error function, and these frequencies approach N(0, 1) asymptotically as the
value of the observed difference score increases. This suggests that the number of
discordant scores is less than expected from the error function. (3) The variance of
the standardized difference score should be significantly less than 1.0. This property
ensures that the dispersion of difference scores is less than expected from random
error alone.

The first two properties can be determined by examining the observed and
expected frequency distributions. The third property can be verified with an F max
assessment ( Winer, 1971). If any of the three properties are found not to be operant,
the score invariance property is not validated. Otherwise, the score invariance
property is operant, and the observed score differences are due at most to random
error.

The empirical research performed to date seem on the surface to validate the
invariance properties. However, certain problems exist concerning the indices used
in these studies, new indices have been presented in this book which directly test the
invariance properties. There is a need for simulations studies where the dimensional
and error structures are known before the final page is written on the topic of item
response theory.


Notes:
1. The least possible logit score in the case of the interval scale.
2. In the case of the three parameter model, where p = c.
3. The general two parameter as well as three parameter models do not
constrain the values of any parameter. However, events with negative or
zero discrimination indices are of no practical value.

-110-

Questia, a part of Gale, Cengage Learning. www.questia.com

Publication Information: Book Title: Assessment and Evaluation of Developmental Learning: Qualitative Individual Assessment and Evaluation Models. Contributors: Robert M. Hashway - author. Publisher: Praeger Publishers. Place of Publication: Westport, CT. Publication Year: 1998. Page Number: 110.
    
This feature allows you to create and manage separate folders for your different research projects. To view markups for a different project, make that project your current project.
This feature allows you to save a link to the publication you are reading or view all the publications you have put on your bookshelf.
This feature allows you to save a link to the page you are reading, which you can later return to from Projects.
This feature allows you to highlight words or phrases on the publication page you are reading.
This feature allows you to save a note you write on the publication page you are reading.
This feature allows you to create a citation to the page you are reading that you can paste into your paper. Highlight a passage to include that passage as a quotation.
This feature allows you to save a reference to a publication you are reading for your bibliography or generate a bibliography you can paste into your paper.
This feature allows you to print the page you are reading, including your notes or highlights (IE users must have "print background colors and image" setting selected.)
This feature allows you to look up words in encyclopedia.
  About Questia Tools
Close Window  
Questia's powerful research tools allow you to highlight, take notes, bookmark and even create instant citations and bibliographies. To use these features and save hours of work, you must create a Questia account.
Need a Questia account?
Sign up for a FREE trial now. Save time, stress and hassle, and get better grades with trusted, online research.

» Click here for our free trial

Already have a Questia account? Login now!
Error
Working...
Printing Preferences
Format for black and white printer: On Off
Print highlights: On Off
Print notes: On Off
Choose one of the options for printing:
Print this page (No Charge)
Print pages to