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Syllabus
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Data
FYA

Data Theory


An introduction to the measurement and construction of data. As you may realize, data is not simply "collected." It is constructed. And data can be constructed from data, as when we build indices and multi-item scales.

 

 

Topics

  • Cases and variables

  • Vectors and matrices

  • Scales of measurement

  • meaningfulness

  • data construction

  • brief mention of scaling, such as

    thurstone, guttman, likert, magnitude

Handouts

  • Borgatti. Notes on measurement. [html]
  • Sarle. Measurement Theory: Frequently Asked Questions. [html]

Optional

  • Wikipedia. Weight. [html]
  • Trochim. Unidimensional scaling [php] (skim -- will be covered in depth later)

Related Modules

 

 

Readings

  • Dawes, R.M. 1977. "Suppose we measured height with rating scales instead of rulers." Applied Psychological Measurement 1(2):267-273 [^pdf]
  • S. S. Stevens (1946), Science 103, 677 [^pdf]
  • Luce and Narens. Science. [^pdf]
  • Luce. Meaningfulness and invariance. [^pdf]
  • Zegers, F. E., & ten Berge, J. M. F. (1985). A family of association coefficients for metric scales. Psychometrika, 50(1), 17-24 [PDF] (just skim)

Quotations

  • “after a century of theory and research on psychological test scores, for most test scores we still have no idea whether they really measure something, or are no more than relatively arbitrary summations of item responses”
    --- Borsboom, 2005

FYA

 

Bibliography


 

Formal measurement theory

  • Stevens, S.S. 1951. Mathematics, measurement and psychophysics. In
    Handbook of Experimental Psychology, ed. S.S. Stevens, New York: Wiley. 

  • D. H. Krantz, R. D. Luce, P. Suppes, A. Tversky, 1971. Foundations of Measurement. (Academic Press, New York, 1971)

  • F. S. Roberts. 1979. Measurement Theory. (Addison-Wesley, Reading, MA, 1979).

  • L. Narens, Abstract Measurement Theory (MIT Press, Cambridge, MA, 1985)

  • Narens. Measurement, Theory of. [pdf]

  • Suppes, P. and Zinnes, J.L. 1963. Basic measurement theory. In Handbook of Mathematical Psychology, Vol. 1, ed. R.D. Luce, R.R. Bush and E. Galanter, New York: Wiley.

  • Luce, R. D., Krantz, D. H., Suppes, P., and Tversky, A. (1990), Foundations of measurement, Vol. III: Representation, axiomatization, and invariance, New York: Academic Press.
  • Suppes, P., Krantz, D. H., Luce, R. D., and Tversky, A. (1989), Foundations of measurement, Vol. II: Geometrical, threshold, and probabilistic respresentations, New York: Academic Press.

Statistics and Measurement

  • Hand, D.J. (1996), "Statistics and the theory of measurement," with discussion, J. of the Royal Statistical Society, Series A, 159, 445-492 [^pdf]

Arguments against measurement level in statistics

  • Lord, F.M. (1953), "On the Statistical Treatment of Football Numbers," American Psychologist, 8, 750-751
  • Velleman, P.F., and Wilkinson, L. (1993), "Nominal, Ordinal, Interval, and Ratio Typologies Are Misleading," The American Statistician, 47, 65-72.

On data construction

  • Bernard, H. R., P. J. Pelto, O. Werner, J. Boster, A. K. Romney, A. Johnson, C. R. Ember, and A. Kasakoff. 1986. The construction of primary data in cultural anthropology. Current Anthropology 27:382-395.

Send mail to sborgatti@uky.edu with questions or comments about this web site. Copyright © 2008 by Steve Borgatti. Last modified: 08/11/09.

 

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