Measurement

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

Recent news on the Smoot unit of measurement

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.

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