Publication Date



Open access

Degree Type


Degree Name

Doctor of Philosophy (PHD)


Kinesiology and Sport Sciences (Education)

Date of Defense


First Committee Member

Randall D. Penfield - Committee Chair

Second Committee Member

Nicholas D. Myers

Third Committee Member

Batya Elbaum

Fourth Committee Member

Kent Burnett


The study of measurement invariance in polytomous items that targets individual score levels is known as differential step functioning (DSF; Penfield, 2007, 2008). DSF methods provide specific information describing the manifestation of the invariance effect within particular score levels and therefore serve a diagnostic role in identifying the individual score levels involved in the item's invariance effect. The analysis of DSF requires the creation of a set of dichotomizations of the item response variable. There are two primary approaches for creating the set of dichotomizations to conduct a DSF analysis. The first approach, known as the adjacent categories approach, is consistent with the dichotomization scheme underlying the generalized partial credit model (GPCM; Muraki, 1992) and considers each pair of adjacent score levels while treating the other score levels as missing. The second approach, known as the cumulative approach, is consistent with the dichotomization scheme underlying the graded response model (GRM; Samejima, 1997) and includes data from every score level in each dichotomization. To date, there is limited research on how the cumulative and adjacent categories approaches compare within the context of DSF, particularly as applied to a real data set. The understanding of how the interpretation and practical outcomes may vary given these two approaches is also limited. The current study addressed these two issues. This study evaluated the results of a DSF analysis using both the adjacent categories and cumulative dichotomization schemes in order to determine if the two approaches yield similar results and interpretations of DSF. These approaches were applied to data from a polytomously scored alternate assessment administered to children with significant cognitive disabilities. The results of the DSF analyses revealed that the two approaches generally led to consistent results, particularly in the case where DSF effects were negligible. For steps where significant DSF was present, the two approaches generally guide analysts to the same location of the item. However, several aspects of the results rose questions about the use of the adjacent categories dichotomization scheme. First, there seemed to be a lack of independence of the adjacent categories method since large DSF effects at one step are often paired with large DSF effects in the opposite direction found in the previous step. Additionally, when a substantial DSF effect existed, it was more likely to be significant using the cumulative approach over the adjacent categories approach. This is likely due to the smaller standard errors that lead to greater stability of the cumulative approach. In sum, the results indicate that the cumulative approach is preferable over the adjacent categories approach when conducting a DSF analysis.


Test Validity; Alternate Assessments; Differential Step Functioning; Differential Item Functioning