The metric transformations of the ability scales involved
in three equating techniques-external anchor
test, internal anchor test, and a pooled groups procedure
-were investigated. Simulated item response data
for two unique tests and a common test were obtained
for two groups that differed with respect to mean ability
and variability. The obtained metrics for various
combinations of groups and tests were transformed to
a common metric and then to the underlying ability
metric. The results showed that there was reasonable
agreement between the transformed obtained metrics
and the underlying ability metric. They also showed
that the largest errors in the ability score statistics occurred
under the external anchor test procedure and
the smallest under the pooled procedures. Although
the pooled procedure performed well, it was affected
by unequal variances in the two groups of examinees.
Baker, Frank B. (1984). Ability metric transformations involved in vertical equating under item response theory. Applied Psychological Measurement, 8, 261-271. doi:10.1177/014662168400800302
Baker, Frank B..
Ability metric transformations involved in vertical equating under item response theory.
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