1. BOY Composite ↔ MOY Composite
Nonlinear Growth? No problem.
Score Equating in JMP using Common Measure, Linearly-Smoothed Equipercentile Equating
Elizabeth N Dewey, MS, Senior Research Analyst/Statistician & Roland H Good III, PhD,  President and Associate Director of Research and Development
Dynamic Measurement Group, the authors of DIBELS
New Method - The Equating Procedure
Abstract
BOY Composite ↔ MOY Composite
BOY Composite ↔
BOY Link ≅
MOY Link
MOY Composite
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.
We equipercentile equate the composite score to an intermediate score that is scale equivalent across the year. The Composite scores are transformed onto the link's scale, and connect the Composites from different times of year.
Step 1
Step 2
Step 3
Step 4
Percentile ranks were calculated for each composite score and linking metric.
The Composite scores and the linking metrics from the same time of year were equated using equipercentile equating.
The results from step 2 were concatenated, and a spline regression was fit to fill in the gaps in the Composites.
A linear regression was fit to the equipercentile equating function within the 8th and 98th percentile.
For our solution, we combined the shared subtests into an intermediate link, 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.
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.
Traditional Methods
Results
The linear equating function does not account for the effects of learning that occur within the three months between administrations.
The equipercentile equating function accounts for learning, but forces the solution through the floor and ceiling.  
In early grades, skills evolve rapidly, and so a measure that is given at the beginning of the year may not be appropriate by the end of the year. By design, DIBELS Next evaluates those skills that are time-wise appropriate, and the same measures are comparable across time of year and grade levels (with some exceptions due to grade-level reading materials). However, the Composite score is not comparable, because its subtests vary across the school year. Thus, in grades K-2, the beginning-of-year Composite is not directly comparable to the end-of-year Composite.
But the equated Composite scores are comparable. With these results, we can now chart growth across three of the most formative grade levels, and provides another tool to identify students who may need educational intervention.
References
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). New Jersey: Lawrence Erlbaum.