The effectiveness of smoothing the bivariate
distributions of common and noncommon item
scores in the frequency estimation method of
common-item equipercentile equating was examined.
The mean squared error of equating was
computed for several equating methods and sample
sizes, for two sets of population bivariate distributions
of equating and nonequating item scores
defined using data from a professional licensure
exam. Eight equating methods were compared: five
equipercentile methods and three linear methods.
One of the equipercentile methods was unsmoothed
equipercentile equating. Four methods of
smoothed equipercentile (SEP) equating were considered
: two based on log-linear models, one based
on the four-parameter beta binomial model, and
one based on the four-parameter beta compound
binomial model. The three linear equating methods
were the Tucker method, the Levine Equally Reliable
method, and the Levine Unequally Reliable
method. The results indicated that smoothed
distributions produced more accurate equating
functions than the unsmoothed distributions, even
for the largest sample size. Tucker linear equating
produced more accurate results than SEP equating
when the systematic error introduced by assuming
a linear equating function was small relative to the
random error of the methods of SEP
equating. Index terms: common-item equating,
equating, log-linear models, smoothing, strong true
Hanson, Bradley A..
A comparison of bivariate smoothing methods in common-item equipercentile equating.
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