Nominal, Ordinal, Interval, and Ratio Typologies are Misleading

Abstract The psychophysicist S.S. Stevens developed a measurement scale typology that has dominated social statistics methodology for almost 50 years. During this period, it has generated considerable controversy among statisticians. Recently, there has been a renaissance in the use of Stevens's scale typology for guiding the design of statistical computer packages. The current use of Stevens's terminology fails to deal with the classical criticisms at the time it was proposed and ignores important developments in data analysis over the last several decades.

[1]  S. Shott,et al.  Nonparametric Statistics , 2018, The Encyclopedia of Archaeological Sciences.

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

[3]  M. Braga,et al.  Exploratory Data Analysis , 2018, Encyclopedia of Social Network Analysis and Mining. 2nd Ed..

[4]  John Law,et al.  Robust Statistics—The Approach Based on Influence Functions , 1986 .

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

[6]  Louis Narens,et al.  Measurement: The theory of numerical assignments. , 1986 .

[7]  James T. Townsend,et al.  Measurement Scales and Statistics: The Misconception Misconceived , 1984 .

[8]  Michael Stuart,et al.  Understanding Robust and Exploratory Data Analysis , 1984 .

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

[10]  Patrick M. O'Malley,et al.  A Guide for selecting statistical techniques for analyzing social science data , 1982, American Political Science Review.

[11]  David C. Hoaglin,et al.  Applications, basics, and computing of exploratory data analysis , 1983 .

[12]  Brian L. Joiner,et al.  Lurking Variables: Some Examples , 1981 .

[13]  Samuel Shye,et al.  Theory construction and data analysis in the behavioral sciences , 1980 .

[14]  J. Gaito Measurement scales and statistics: Resurgence of an old misconception. , 1980 .

[15]  W. W. Daniel Applied Nonparametric Statistics , 1978 .

[16]  Pertti J. Pelto,et al.  Anthropological research: Measurement, scales, and statistics , 1978 .

[17]  F. Mosteller,et al.  Data Analysis and Regression , 1978 .

[18]  Louis Guttman,et al.  What Is Not What in Statistics , 1977 .

[19]  Leo A. Goodman,et al.  A New Model for Scaling Response Patterns: An Application of the Quasi-Independence Concept , 1975 .

[20]  Vithala R. Rao,et al.  Conjoint Measurement- for Quantifying Judgmental Data , 1971 .

[21]  R. Causey Suppes Patrick and Zinnes Joseph L.. Basic measurement theory. Handbook of mathematical psychology , Volume I, edited by Luce R. Duncan, Bush Robert R., and Galanter Eugene, John Wiley and Sons, Inc., New York and London 1963, pp. 1–76. , 1971, Journal of Symbolic Logic.

[22]  T. Kuhn The Structure of Scientific Revolutions 2nd edition , 1970 .

[23]  C. H. Coombs,et al.  Mathematical psychology : an elementary introduction , 1970 .

[24]  L. Guttman A general nonmetric technique for finding the smallest coordinate space for a configuration of points , 1968 .

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

[26]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[27]  J. Kruskal Nonmetric multidimensional scaling: A numerical method , 1964 .

[28]  G. Box An analysis of transformations (with discussion) , 1964 .

[29]  John W. Tukey,et al.  Efficient Utilization of Non-Numerical Information in Quantitative Analysis General Theory and the Case of Simple Order , 1963 .

[30]  Eugene Galanter,et al.  Handbook of mathematical psychology: I. , 1963 .

[31]  T. Kuhn,et al.  The Structure of Scientific Revolutions. , 1964 .

[32]  R. Shepard The analysis of proximities: Multidimensional scaling with an unknown distance function. II , 1962 .

[33]  J. Tukey The Future of Data Analysis , 1962 .

[34]  R. Shepard The analysis of proximities: Multidimensional scaling with an unknown distance function. I. , 1962 .

[35]  N. Anderson Scales and statistics: parametric and nonparametric. , 1961, Psychological bulletin.

[36]  R. Luce,et al.  On the possible psychophysical laws. , 1959, Psychological review.

[37]  J. Tukey On the Comparative Anatomy of Transformations , 1957 .

[38]  S. Siegel,et al.  Nonparametric Statistics for the Behavioral Sciences , 2022, The SAGE Encyclopedia of Research Design.

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

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

[41]  Bartlett Ms The use of transformations. , 1947 .

[42]  M. Bartlett,et al.  The use of transformations. , 1947, Biometrics.

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

[44]  Gary R Lichtenstein [Letter to the Editor] , 1996, Nature.