The effects of different degrees of smoothing on
the results of equipercentile equating in the random
groups design using a postsmoothing method based
on cubic splines were investigated. A computer-based
procedure was introduced for selecting a desirable
degree of smoothing. The procedure was based on
two criteria: (1) that the equating function is reasonably
smooth, as evaluated by the second derivatives
of the cubic spline functions, and (2) that the equated
score distributions are close to that of the old form.
The equating functions obtained from smoothing the
equipercentile equivalents by a fixed smoothing degree and a degree selected by the computer-based
procedure were evaluated in computer simulations for
four tests. The results suggest that no particular fixed
degree of smoothing always led to an optimal degree
of smoothing. The degrees of smoothing selected by
the computer-based procedure were better than the
best fixed degrees of smoothing for two of the four
tests studied; for one of the other two tests, the degrees
selected by the computer procedure performed
better or nearly as well as the best fixed degrees.
Index terms: computer simulation, cubic spline, equating, equipercentile equating, smoothing.
Zeng, Lingjia. (1995). The optimal degree of smoothing in equipercentile equating with postsmoothing. Applied Psychological Measurement, 19, 177-190. doi:10.1177/014662169501900205
The optimal degree of smoothing in equipercentile equating with postsmoothing.
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