Multivariate true score model for achievement and growth norming

Research Method · All research methods
Evidence · 5 claims (5 for) · 4 studies (4 associational), q2 · 1 of 4 report an effect size · 4 claims rest on one study

Description

The report uses a model-based approach in which observed scores are decomposed into true scores and error scores, with the standard error of measurement introduced so that imprecision of observed scores is accounted for. The article states it uses "a multivariate true score model that accounts for the known imprecision of scores" to generate both achievement norms per term and between-term growth norms. True scores are assumed to have a multivariate normal sampling distribution, and the joint distribution of predicted fall, winter, and spring scores provides the basis for the norms.

Accounts

• Multivariate true score model for building achievement and growth norms: The report uses a model-based approach in which observed scores are decomposed into true scores and error scores, with the standard error of measurement introduced so that imprecision of observed scores is accounted for. The article states it uses "a multivariate true score model that accounts for the known imprecision of scores" to generate both achievement norms per term and between-term growth norms. True scores are assumed to have a multivariate normal sampling distribution, and the joint distribution of predicted fall, winter, and spring scores provides the basis for the norms. (Wei He (2022))
• Multivariate true score model for deriving achievement and growth norms: The norming procedure is a model-based approach from the course-specific MAP Growth Mathematics norming study (Thum & He, 2019). It uses "a multivariate true score model that accounts for the known imprecision of scores from the fall, winter, and spring terms", introducing each score's standard error of measurement into the model. True scores are assumed multivariate normal, and the estimated joint distribution of predicted fall, winter, and spring scores provides the basis for marginal achievement norms and conditional growth norms. (Wei He (2022))
• Model-based multivariate true score norming procedure: The norming approach, employed previously in the course-specific MAP Growth Mathematics norming study (Thum & He, 2019), uses "a multivariate true score model that accounts for the known imprecision of scores from the fall, winter, and spring terms." Observed scores are decomposed into true scores and error scores, with each score's standard error of measurement introduced into the model. True scores are assumed multivariate normal, and the resulting joint distribution of predicted fall, winter, and spring scores provides the basis for achievement norms (marginal distributions) and growth norms (between-term gains). (Wei He et al. (2026))

Claims

• Normality assumptions of the true score model appeared reasonable for the course-specific tests [+W]
• Q-Q plots, CDF curves, and residual checks support the joint normality assumption underlying the multivariate true score model for the course-specific tests. [+W]
• The multivariate normality assumption of the true score model was judged reasonable for all domains and grades [+W]
• The multivariate normality assumption of the norming model was judged met for all domains and grades, despite some tail deviations in Q-Q plots [+W]
• True-score-model correlations between term scores exceed 0.90 for almost all course-specific tests [+W]

Related Research Methods

• Mental-age score conversion and norming method

Key Sources

• Wei He. (2022). Achievement and Growth Norms for Course-Specific MAP® Growth™ Tests. NWEA Research Report. https://www.nwea.org/research/publication/achievement-and-growth-norms-for-course-specific-map-growth-tests/
• Wei He, NWEA Psychometric Solutions. (2022). Achievement and Growth Norms for English MAP Reading Fluency Foundational Skills. NWEA. https://www.nwea.org/research/publication/achievement-and-growth-norms-for-english-map-reading-fluency-foundational-skills/
• Wei He, NWEA Psychometrics and Analytics. (2026). Achievement and Growth Norms for Spanish MAP Reading Fluency Foundational Skills. NWEA. https://www.nwea.org/research/publication/achievement-and-growth-norms-for-spanish-map-reading-fluency-foundational-skills-report/

Page metadata

Field	Value
type	research-method
id	multivariate-true-score-model-for-achievement-and-growth-norming
aliases	model-based-multivariate-true-score-norming-procedure
title	Multivariate true score model for achievement and growth norming
description	The report uses a model-based approach in which observed scores are decomposed into true scores and error scores, with the standard error of measurement introduced so that imprecision of observed scores is accounted for.
status	review
moved_from	theory/multivariate-true-score-model-norming, theory/multivariate-true-score-norming-model
generated	by process:sweep-kinds on 2026-10-10
trust	unverified — no one has confirmed this page's content
sources	2 — wei-he-2022, wei-he-2026

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