Measurement theory: Frequently asked questions

What is measurement theory? What is measurement? Why should I care about measurement theory? What are permissible transformations? What are levels of measurement? What about binary (0/1) variables? Is measurement level a fixed, immutable property of the data? Isn't an ordinal scale just an interval scale with error? What does measurement level have to do with discrete vs. continuous? Don't the theorems in a statistics textbook prove the validity of statistical methods without reference to measurement theory? Does measurement level detemine what statistics are valid? But measurement level has been shown empirically to be irrelevant to statistical results, hasn't it? What are some more examples of how measurement level relates to statistical methodology? Are there other theories of measurement? What's the bottom line? References

[1]  David J. Hand,et al.  Statistics and the theory of measurement , 1996 .

[2]  A. Tversky,et al.  Foundations of Measurement, Vol. I: Additive and Polynomial Representations , 1991 .

[3]  I. Jolliffe,et al.  Nonlinear Multivariate Analysis , 1992 .

[4]  P. McCullagh.  Analysis of Ordinal Categorical Data , 1985 .

[5]  C. West Churchman,et al.  Measurement: Definitions and Theories , 1960 .

[6]  D. Bartholomew,et al.  Statistics and the theory of measurement - Discussion , 1996 .

[7]  Patrick Suppes,et al.  Foundations of Measurement, Vol. II: Geometrical, Threshold, and Probabilistic Representations , 1989 .

[8]  Frederic M. Lord,et al.  On the Statistical Treatment of Football Numbers. , 1953 .

[9]  S. S. Steivens.  Measurement, Statistics, and the Schemapiric View , 1968 .

[10]  Leonard R. Sussman,et al.  Nominal, Ordinal, Interval, and Ratio Typologies are Misleading , 1993 .

[11]  J. Flynn.  Massive IQ gains in 14 nations: What IQ tests really measure. , 1987 .

[12]  A. Tversky,et al.  Foundations of Measurement, Vol. III: Representation, Axiomatization, and Invariance , 1990 .

[13]  J. Michell.  Measurement scales and statistics: A clash of paradigms. , 1986 .

[14]  M. Hill,et al.  Nonlinear Multivariate Analysis. , 1990 .

[15]  H. Jeffreys.  The Logic of Modern Physics , 1928, Nature.

[16]  Gary Michael Maranell,et al.  Scaling: A Sourcebook for Behavioral Scientists , 1974 .

[17]  S S Stevens,et al.  On the Theory of Scales of Measurement. , 1946, Science.

[18]  S. S. Stevens.  Mathematics, measurement, and psychophysics. , 1951 .

[19]  Merrilee H. Salmon.  Introduction to the Philosophy of Science , 1992 .

[20]  J. Michell.  An introduction to the logic of psychological measurement , 1995 .

[21]  U. Neisser.  RISING SCORES ON INTELLIGENCE TESTS , 1997 .

[22]  Robert Klee,et al.  Introduction to the Philosophy of Science: Cutting Nature at Its Seams , 1996 .

[23]  Curtis D. Hardyck,et al.  Weak Measurements vs. Strong Statistics: An Empirical Critique of S. S. Stevens' Proscriptions nn Statistics , 1966 .

[24]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .