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Evidence Based on the Internal Structure of the Instrument: Factor Analysis

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Instrument Development in the Affective Domain

Abstract

Up to this point, the relationship between affective characteristics and their translation into mathematical structure has been largely theoretical. Chapter 4 is a notable departure from previous chapters in that all the methodological approaches and techniques require data collected from a sample of participants from the instrument developer’s target group. The purpose of Chapter 4 is to introduce the most effective and accepted methods for understanding the internal structure of instruments developed to measure affective characteristics. The internal structure of an instrument is the empirically defined mathematical relationship between the proposed latent construct(s) and the items observed variables in the instrument. This mathematical relationship is commonly understood as dimensionality—and the empirical evidence needed to understand the dimensionality of the proposed instrument can only be supplied by a sample of “real” subjects. Chapter 4 largely addresses with a family of techniques known as factor analysis. The chapter specifically discusses two techniques commonly employed in the process of understanding the internal structure of an instrument. The chapter provides an overview of both exploratory factor analysis and confirmatory factor analysis and explains their utility and usage within the instrument development process.

Measurement is the first step that leads to control and eventually to improvement. If you can’t measure something, you can’t understand it. If you can’t understand it, you can’t control it. If you can’t control it, you can’t improve it.

H. James Harrington

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Notes

  1. 1.

    The correlations represent the cosine of the angle between the two factors. Noting that the cosine curve can be used to calculate angles for various correlations, readers may wish to estimate the actual angle between axes. For example, when the correlation is zero, the angle is 90° (varimax).

  2. 2.

    Much of the discussion of model fit in confirmatory factor analysis models has been adapted from McCoach (2003). SEM isn’t just the School wide Enrichment Model anymore: Structural Equation Modeling (SEM) in gifted education. Journal for the Education of the Gifted, 27, 36–61.

  3. 3.

    The full CFA output for this example is contained in Appendix B.

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Authors and Affiliations

  1. Educational Psychology Department, University of Connecticut, Glenbrook Road, Unit 3064 249, Storrs, CT, 06269-3064, USA

    D. Betsy McCoach

  2. Alan Shawn Feinstein Graduate School, Johnson and Wales University, Quail Run Rd. 26, Storrs, CT, 06268, USA

    Robert K. Gable

  3. Department of Educational Psychology, University of Connecticut, Glenbrook Road, Unit 2064 249, Storrs, CT, 06269-2064, USA

    John P. Madura

Authors
  1. D. Betsy McCoach
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  2. Robert K. Gable
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  3. John P. Madura
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Correspondence to D. Betsy McCoach .

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McCoach, D.B., Gable, R.K., Madura, J.P. (2013). Evidence Based on the Internal Structure of the Instrument: Factor Analysis. In: Instrument Development in the Affective Domain. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7135-6_4

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