What Differential Weighting of Subsets of Items Does and Does Not Accomplish: Geometric Explanation
- Author(s):
- Carlson, James E.
- Publication Year:
- 2014
- Report Number:
- RR-14-20
- Source:
- ETS Research Report
- Document Type:
- Report
- Page Count:
- 18
- Subject/Key Words:
- Subscores, Variance, Subtests, Vector Geometry, Weighted Scores, Test Reliability, Test Validity
Abstract
A little-known theorem, a generalization of Pythagoras's theorem, due to Pappus, is used to present a geometric explanation of various definitions of the contribution of component tests to their composite. I show that an unambiguous definition of the unique contribution of a component to the composite score variance is present if and only if the component scores are uncorrelated. I further show the effect of differentially weighting the composites on the definitions of unique contributions and discuss some of the implications for composite score reliability and validity.
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- http://dx.doi.org/10.1002/ets2.12020