What Differential Weighting of Subsets of Items Does and Does Not Accomplish: Geometric Explanation | Zendy

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What Differential Weighting of Subsets of Items Does and Does Not Accomplish: Geometric Explanation

Author(s) -

Carlson James E.

Publication year - 2014

Publication title -

ets research report series

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.235

H-Index - 5

ISSN - 2330-8516

DOI - 10.1002/ets2.12020

Subject(s) - weighting , generalization , component (thermodynamics) , mathematics , variance (accounting) , uncorrelated , reliability (semiconductor) , variance components , statistics , composite number , pure mathematics , mathematical analysis , algorithm , medicine , physics , power (physics) , accounting , quantum mechanics , business , radiology , thermodynamics

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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