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Psychometrika

, Volume 31, Issue 4, pp 545–561 | Cite as

Alpha factor analysis of infallible variables

  • Gene V Glass
Article

Abstract

The relationship between the factor pattern,F, derived from fallible (containing measurement error) observations on variables and the factor pattern,F*, derived from infallible observations on variables is investigated. A widely believed relationship betweenF andF*, viz.,F*=AF whereA is a diagonal matrix containing the inverses of the square roots of the reliabilities of the variables, is shown to be false for several factor analytic techniques. Under suitable assumptions, it is shown that for Kaiser and Caffrey's “alpha factor analysis”F* andF are related byF*=AF. Empirical examples for which the corresponding elements ofF* andAF are equal to two decimal places are presented. The implications of the equality ofF* andAF for alpha factor analysis are discussed.

Keywords

Measurement Error Public Policy Diagonal Matrix Statistical Theory Alpha Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Psychometric Society 1966

Authors and Affiliations

  • Gene V Glass
    • 1
  1. 1.University of IllinoisUSA

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