Open AccessWhat 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.