skip to main content skip to footer

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.

Read More