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Nonlinear Growth? No problem. Score Equating in JMP® using Common Measure, Linearly-Smoothed Equipercentile Equating

In Psychometrics, researchers often equate scores from two homogeneous tests to interpret patterns of growth. In our analysis to equate the DIBELS Next® Composite Score across time of year, we ran into several challenges with conventional methods of equating. The Composite shares few of the same subtests, and those subtests are given three months apart and contain ceiling and floor effects. Traditional methods of equating proved inadequate due to growth, floor, and ceiling effects. For our solution, we combined the shared subtests into an intermediate link (an internal anchor), and equated the Composites first to the intermediate link, and then to each other using equipercentile equating. Next, we fit a linear regression to the equipercentile fit between the floor and ceiling effects where the relationship was clearly linear. Finally, we extended the fit through the score range. We repeated this analysis for all grades, equating our results from one time point to the next. The result was a scaled score where zero on the beginning of year Composite was less than zero on the end of year scale - an interpretable result for evaluating growth.

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