Multivariate true score model for achievement and growth norms¶

Theory · All theories
Evidence · 3 claims (3 for) · 2 studies (2 associational), q2 · 1 of 2 report an effect size · 2 claims rest on one study

Description¶

The norming approach is "a model-based approach employing a multivariate true score model that factors out known imprecision of scores" from fall, winter, and spring test scores. Observed scores are decomposed into true scores and error scores with observed SEMs entering the model; true scores are assumed multivariate normal in the user population, with restricted maximum likelihood estimates obtainable from standard software such as HLM7 or SAS Proc Mixed. Predicted marginal distributions yield achievement norms per term and fall-to-spring growth norms, including conditional gains given a fall score.

Design Implications¶

Context¶

Requirements¶

• Observed standard errors of measurement for each term's score
• Joint normality of true scores in the user population

Constraints¶

• Inferences based on the model rely on the reasonableness of the joint normality assumption of score components for their validity

Target Learners¶

• Students in Grades 6–12 taking course-specific mathematics tests

Target Learning Objectives¶

• Normative interpretation of achievement status and fall-to-spring growth in course-specific mathematics

Claims¶

• Course Specific Norms Normality Supported [+M]
• Course Specific Term Score Correlations Above 090 [+M]
• Normality assumptions of the true score model appeared reasonable for the course-specific tests [+W]

Related Theories¶

• Multivariate true score model for building achievement and growth norms

Examples¶

• Course-specific MAP Growth Mathematics tests (Algebra 1, Geometry, Algebra 2)
• Course-specific MAP Growth tests (Algebra 1, Geometry, Algebra 2, Integrated Math 1–3, Biology/Life Science)

Key Sources¶

• Thum, Y. M., & He, W. (2019). Achievement and growth norms for course-specific MAP® Growth™ Algebra 1, Geometry, and Algebra 2 tests. NWEA Research Report. Portland, OR: NWEA. https://www.nwea.org/research/publication/achievement-and-growth-norms-for-course-specific-map-growth-algebra-1-geometry-and-algebra-2-tests/