**ERIC Number:**ED523741

**Record Type:**Non-Journal

**Publication Date:**2011-Feb

**Pages:**43

**Abstractor:**As Provided

**Reference Count:**37

**ISBN:**N/A

**ISSN:**N/A

Evaluating Empirical Relationships among Prediction, Measurement, and Scaling Invariance. Research Report. ETS RR-11-06

Moses, Tim

Educational Testing Service

The purpose of this study was to consider the relationships of prediction, measurement, and scaling invariance when these invariances were simultaneously evaluated in psychometric test data. An approach was developed to evaluate prediction, measurement, and scaling invariance based on linear and nonlinear prediction, measurement, and scaling functions. The approach was used to evaluate the relationships among 12 pairs of tests in 6 datasets for gender invariance. The prediction, measurement, and scaling invariance results were found to be similar for most of the test relationships evaluated, in that all 3 invariances were more likely to be established for highly correlated tests than for less highly correlated tests. The invariance results appeared to be well summarized by intercept differences in the linear prediction, measurement, and scaling functions. The implications of the results were discussed with respect to the relationships among prediction, measurement, and scaling invariances described in prior theoretical and empirical research. Suggestions for extending theoretical and empirical invariance research were provided. Appended are: (1) Score-level assessment of prediction, measurement and scaling invariance for critical reading, where X is internal to (and highly correlated with) Y; (2) Score-level assessment of prediction, measurement and scaling invariance for English language, where X is internal to (and highly correlated with) Y; (3) Score-level assessment of prediction, measurement and scaling invariance for history, where X is internal to (and highly correlated with) Y; (4) Score-level assessment of prediction, measurement and scaling invariance for math, where X is internal to (and highly correlated with) Y; (5) Score-level assessment of prediction, measurement and scaling invariance for science, where X is internal to (and highly correlated with) Y; (6) Score-level assessment of prediction, measurement and scaling invariance for writing, where X is internal to (and highly correlated with) Y; (7) Score-level assessment of prediction, measurement and scaling invariance for English language, where X is external to (and less correlated with) Y; (8) Score-level assessment of prediction, measurement and scaling invariance for history, where X is external to (and less correlated with) Y; (9) Score-level assessment of prediction, measurement and scaling invariance for math to critical reading, where X is external to (and less correlated with) Y; (10) Score-level assessment of prediction, measurement and scaling invariance for math to writing, where X is external to (and less correlated with) Y; (11) Score-level assessment of prediction, measurement and scaling invariance for science, where X is external to (and less correlated with) Y; and (12) Score-level assessment of prediction, measurement and scaling invariance for writing to critical reading, where X is external to (and less correlated with) Y. (Contains 4 tables, 12 figures and 1 note.)

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**Publication Type:**Reports - Research

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**Educational Testing Service