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.

Despite flexibility waivers granted to states by the United States Department of Education from some provisions of the No Child Left Behind Act, our nation’s public schools continue to struggle to improve reading proficiency as measured by high stakes assessments. To reach state targets for reading proficiency schools must use data at the earliest point possible to inform instructional strategies and identify students at risk of failure. The response to intervention model holds promise for improving reading outcomes particularly for early elementary students. The effective use of reading curriculum based measures (R-CBM) to determine if instruction is adequate to produce students who score proficient or advanced on state mandated reading assessments is critical to achieving the goals for student learning. The population selected for this study included all third grade students from an East Tennessee school district. The third graders attended 13 schools and included 911 third grade students of which 770 students participated in the study. This included 372 male and 398 female students. Approximately 47% of the students were economically disadvantaged as determined by qualifying for free and reduced priced meals. The purpose of this study was to investigate the relationship between 4 predictor variables (fall R-CBM, winter R-CBM, spring R-CBM, and median R-CBM) and the Tennessee Comprehensive Assessment Program (TCAP) third grade reading and language arts assessment. Each data set included 4 R-CBM scores expressed in words read correctly and TCAP reading language arts scale scores. Gender and free and reduced price meals eligibility information for all third graders from the 2010-2011 school year were also collected. Results reflected a strong predictive relationship between the AIMSweb R-CBM and TCAP reading and language arts measure for third grade students. Zero order correlations in the multiple regression analysis ranged from .70 to .74 for the 4 predictor variables. A linear equation was developed to predict TCAP scores from a single R-CBM score (fall, winter, spring, and median). Based on this study practitioners may be able to establish goals for student reading that are strongly correlated with achieving proficiency on the TCAP reading and language arts assessment.

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