Publication Date



Open access

Degree Type


Degree Name

Doctor of Philosophy (PHD)


Teaching and Learning (Education)

Date of Defense


First Committee Member

Marjorie Montague

Second Committee Member

Wendy Morrison

Third Committee Member

Batya Elbaum

Fourth Committee Member

Randall D. Penfield


The purpose of this study was to investigate population invariance of the true-score linking functions with respect to the ability subgroups (i.e., average-achieving students, low-achieving students, and students with learning disabilities). The mean/mean linking functions for five alternate forms of a curriculum-based math problem solving measure were based on the Rasch model. Most studies of curriculum-based measurement have reported only the reliability and validity of alternate forms of measures. This is necessary but insufficient for establishing alternate forms of curriculum-based measures. It is also necessary to establish equivalency of the forms. The present study was based on data from a previous study that developed equivalent forms of curriculum-based measures using Item Response Theory. The participants in the present study were 1,861 seventh- and eighth-grade students. Equatability indices were used to evaluate population invariance of the Rasch mean/mean linking functions over the ability subgroups. Results indicated that the Rasch mean/mean linking functions were population invariant for the ability subgroups across the five alternate forms. The differences between the linking functions computed on the ability subgroups and the linking function on the whole group were negligible for the five forms. Several implications and recommendations for future studies on population invariance of the linking functions with alternate forms of curriculum-based measures were discussed.


Curriculum-based Measure; Population Invariance