April 24 – Measurement and Meaning


  • Clyde H. Coombs, Robyn M. Dawes, and Amos Tversky, “Psychological Measurement Theory” (Chapter 2), Mathematical Psychology: An Elementary Introduction, Prentice-Hall, Inc., 1970, pp. 7-30
    • The authors write (p. 17) that “no measurement theory for intelligence is available.” What reasons do they have for saying this?
    • The chapter ends with the following statement: “Only when the assumptions of the theory are satisfied by the data can measurement be obtained.” In practice, empirical researchers often make measurements even when their data do not fit a measurement theory. Can you think of an example? What use are such measurements?
  • Jean-Claude Falmagne, “Measurement Theory and the Research Psychologist”, Psychological Science 3(2):88-93, 1992
    • One question that came up in class was why statements that are scale-dependent (e.g. about ratios on a Fahrenheit or Celsius scale) are not meaningful. Falmagne gives a god analysis of this in his section on “The Meaningfulness of Scientific Statements and Models” (p. 92). He concludes: “opening the door to nonmeaningful models would unavoidably transform the citadel science into a clamorous Tower of Babel. Scientists from different circles (or countries) would end up spending precious time in fruitless controversies regarding essentially identical, but very different looking, models for the same data.”

Slides: http://www.stanford.edu/class/symsys130/SymSys130-4-24-2013.ppt.pdf. Some key points:

  • Psychologists were challenged in the mid-20th Century to show that their field could admit what Norman R. Campbell called “extensive measurement”, i.e. measurements that can be represented on an interval scale. Measurement theory shows that there are psychological quantities, such as loudness, that can be measured in this way.
  • For more on proper scoring rules, see the Wikipedia articles on “Scoring Rules” and the “Brier Score”. I mangled the explanation a bit in class. The Brier score only applies to a set of mutually exclusive events over which a probability distribution is laid by someone from whom the probabilities are being elicited (commonly called a “judge” in the parlance of psychology).
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