Scales of measurements: An introduction and a selected bibliography

Stevens' (1946) distinctions among nominal, ordinal, interval and ratio measurements have had a marked influence on researchers of social, psychological and statistical sciences. This paper reviews those distinctions and includes some comments concerning the applicability of different statistical techniques to each scale. A detailed bibliography is also provided.

[1]  F. Lord.  Applications of Item Response Theory To Practical Testing Problems , 1980 .

[2]  Herbert Dingle,et al.  A THEORY OF MEASUREMENT , 1950, The British Journal for the Philosophy of Science.

[3]  Bernhardt Lieberman.  Contemporary Problems in Statistics: A Book of Readings for the Behavioural Sciences , 1972 .

[4]  R. Linn.  Educational measurement, 3rd ed. , 1989 .

[5]  L. L. Thurstone,et al.  The unit of measurement in educational scales. , 1927 .

[6]  Scott E. Maxwell,et al.  Measurement and Statistics: An Examination of Construct Validity. , 1985 .

[7]  K. Clayton,et al.  Introduction to Statistics for Psychology and Education , 1984 .

[8]  Jean-Claude Falmagne,et al.  A Probabilistic Theory of Extensive Measurement , 1980, Philosophy of Science.

[9]  Patrick Suppes,et al.  Foundational aspects of theories of measurement , 1958, Journal of Symbolic Logic.

[10]  John C. Baird,et al.  Fundamentals of scaling and psychophysics , 1978 .

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

[12]  Clyde M. Reese,et al.  A Comparison of Two Scales Measuring Attitudes towards Statistics , 1987 .

[13]  Louis Narens,et al.  Fundamental unit structures: A theory of ratio scalability☆ , 1979 .

[14]  T. Gregoire,et al.  Analysis of ordinal data to detect population differences. , 1987 .

[15]  W. J. Conover,et al.  Practical Nonparametric Statistics , 1972 .

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

[17]  F. J. Wall,et al.  Statistical Data Analysis Handbook , 1988 .

[18]  Joseph L. Zinnes,et al.  Theory and Methods of Scaling. , 1958 .

[19]  Manfred Droste,et al.  Ordinal scales in the theory of measurement , 1987 .

[20]  H. Raiffa,et al.  Some views on mathematical models and measurement theory. , 1954, Psychological review.

[21]  L. L. Thurstone,et al.  The absolute zero in intelligence measurement. , 1928 .

[22]  H. Blalock.  Conceptualization and Measurement in the Social Sciences , 1982 .

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

[24]  J. L. Price.  Handbook of Organizational Measurement , 1975 .

[25]  Henry Montgomery,et al.  Magnitude scales, category scales, and the general psychophysical differential equation , 1977 .

[26]  Ronald K. Hambleton,et al.  Applications of Item Response Theory , 1983 .

[27]  Robert L. Armstrong,et al.  The Midpoint on a Five-Point Likert-Type Scale , 1987 .

[28]  Karel Berka,et al.  Measurement: Its Concepts, Theories and Problems , 1982 .

[29]  P. Suppes.  Measurement, Empirical Meaningfulness, and Three-Valued Logic , 1969 .

[30]  Patrick Suppes,et al.  A Set of Independent Axioms for Extensive Quantities , 1969 .

[31]  E. Ghiselli.  Theory of psychological measurement , 1964 .

[32]  L. Thurstone.  Theory of attitude measurement. , 1929 .

[33]  Louis Narens,et al.  Utility-uncertainty trade-off structures☆ , 1976 .

[34]  Fritz Drasgow,et al.  Study of the measurement bias of two standardized psychological tests. , 1987 .

[35]  Mark L. Davison,et al.  Parametric statistics and levels of measurement. , 1988 .

[36]  P. Suppes,et al.  Decision making : an experimental approach , 1959 .

[37]  George W. Bohrnstedt,et al.  Level of Measurement , 1980 .

[38]  James D. Laing,et al.  Analysis of Ordinal Data , 2018, Statistical Analysis of Ecotoxicity Studies.

[39]  L. Guttman.  A basis for scaling qualitative data. , 1944 .

[40]  C. Bonjean,et al.  Sociological measurement : an inventory of scales and indices , 1969 .

[41]  R. Schulman,et al.  A test theory model for ordinal measurements , 1975 .

[42]  Alan Agresti,et al.  The Effect of Category Choice on Some Ordinal Measures of Association , 1976 .

[43]  G. Glass,et al.  Basic Statistics for the Behavioral Sciences , 1977 .

[44]  J. Gaito.  Non-Parametric Methods in Psychological Research , 1959 .

[45]  Bernard S. Phillips,et al.  Social Research: Strategy and Tactics. , 1967 .

[46]  Jan Faber,et al.  Consistent estimation of correlations between observed interval variables with skewed distributions , 1988 .

[47]  Nan M. Laird.  A NOTE ON CLASSIFYING ORDINAL-SCALE DATA , 1979 .

[48]  Daniel Katz,et al.  Research Methods in the Behavioral Sciences. , 1954 .

[49]  M. R. Novick,et al.  Statistical Theories of Mental Test Scores. , 1971 .

[50]  Eric W. Holman,et al.  Strong and weak extensive measurement , 1969 .

[51]  G. Masters,et al.  A comparison of latent trait and latent class analyses of Likert-type data , 1985 .

[52]  Earl R. Babbie,et al.  The practice of social research , 1969 .

[53]  W. G. Cochran.  The Comparison of Different Scales of Measurement for Experimental Results , 1943 .

[54]  J. Loevinger.  Objective Tests as Instruments of Psychological Theory , 1957 .

[55]  James Thomas Walker.  Using Statistics for Psychological Research: An Introduction , 1984 .

[56]  Frederic M. Lord.  Further Comment on "Football Numbers". , 1954 .

[57]  L. Crocker,et al.  Introduction to Classical and Modern Test Theory , 1986 .

[58]  S. S. Stevens,et al.  On the averaging of data. , 1955, Science.

[59]  H. Harman.  Modern factor analysis , 1961 .

[60]  C. Coombs.  A theory of data. , 1965, Psychology Review.

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

[62]  Hermann von Helmholtz,et al.  Counting and measuring , 2022 .

[63]  H. Kyburg.  Theory and measurement , 1984 .

[64]  S. S. Stevens,et al.  Psychophysics: Introduction to Its Perceptual, Neural and Social Prospects , 1975 .

[65]  Fritz Drasgow,et al.  Statistical power of differential validity and differential prediction analyses for detecting measurement nonequivalence. , 1984 .

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

[67]  Ken den Heyer,et al.  On the enduring untruth about measurement and parametric statistics. , 1980 .

[68]  Louis Narens,et al.  The algebra of measurement , 1976 .

[69]  Jean-Claude Falmagne,et al.  Statistical issues in measurement , 1985 .

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

[71]  G. Masters,et al.  Rating scale analysis , 1982 .

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

[73]  C H COOMBS,et al.  Psychological scaling without a unit of measurement. , 1950, Psychological review.

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

[75]  Robert L. Hamblin.  Ratio Measurement for the Social Sciences , 1971 .

[76]  M. E. Shaw,et al.  Scales for the measurement of attitudes , 1967 .

[77]  P. Gardner.  Scales and Statistics , 1975 .

[78]  Jacob Cohen.  A Coefficient of Agreement for Nominal Scales , 1960 .

[79]  J. Falmagne.  On a class of probabilistic conjoint measurement models: Some diagnostic properties☆ , 1979 .

[80]  W. W. Stine,et al.  Meaningful inference: The role of measurement in statistics. , 1989 .

[81]  R. Pagano.  Understanding Statistics in the Behavioral Sciences , 1981 .

[82]  Ronald K. Hambleton,et al.  LATENT TRAIT MODELS AND THEIR USE IN THE ANALYSIS OF EDUCATIONAL TEST DATA1,2,3 , 1977 .

[83]  M. Degroot,et al.  Probability and Statistics , 2021, Examining an Operational Approach to Teaching Probability.

[84]  Emin Babakus,et al.  The Sensitivity of Confirmatory Maximum Likelihood Factor Analysis to Violations of Measurement Scale and Distributional Assumptions , 1987 .

[85]  C. C. Craig,et al.  A First Course in Mathematical Statistics , 1947 .

[86]  Brian Ellis,et al.  Basic Concepts of Measurement. , 1966 .

[87]  Roger C. Pfaffenberger,et al.  Statistical Methods : For Business and Economics , 1977 .

[88]  P. Cozby,et al.  Methods in behavioral research , 1977 .

[89]  Burke Cj,et al.  Additive scales and statistics. , 1953 .

[90]  D. Krantz.  Conjoint measurement: The Luce-Tukey axiomatization and some extensions ☆ , 1964 .

[91]  G. A. Ferguson,et al.  Statistical analysis in psychology and education , 1960 .

[92]  S. Janson,et al.  On the Applicability of Truncated Component Analysis Based on Correlation Coefficients for Nominal Scales , 1978 .

[93]  H. T. Reynolds,et al.  Analysis of nominal data , 1977 .

[94]  Louis Narens,et al.  A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness , 1981 .

[95]  Jack Levin,et al.  Elementary Statistics in Social Research , 1974 .

[96]  Hilary Putnam,et al.  Replies and comments , 1991 .

[97]  Patrick Suppes,et al.  Studies in the Methodology and Foundations of Science: Selected Papers from 1951 to 1969 , 1969 .

[98]  V. L. Senders,et al.  Measurement and statistics , 1958 .

[99]  Dato N.M. De Gruijter,et al.  Advances in psychological and educational measurement , 1976 .

[100]  Eric W. Holman,et al.  A note on additive conjoint measurement , 1971 .

[101]  J. Gaito,et al.  Confusion of empirical and statistical aspects that lead to controversy , 1987 .

[102]  A. W. MacRae.  Measurement scales and statistics: What can significance tests tell us about the world? , 1988 .

[103]  Sanford Labovitz,et al.  The Assignment of Numbers to Rank Order Categories , 1970 .

[104]  William B. Michael,et al.  Psychological Scaling: Theory and Applications , 1961 .

[105]  H. Earl Hill,et al.  Applied techniques in statistics for selected industries : coatings, paints, and pigments , 1984 .

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

[107]  Larry B. Wallnau,et al.  Statistics for the Behavioral Sciences , 1985 .

[108]  John D. Kasarda,et al.  Ratio Measurement and Theoretical Inference in Social Research , 1979 .

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

[110]  Thomas P. Wilson,et al.  Critique of Ordinal Variables , 1971 .

[111]  Herman J. Loether,et al.  Descriptive and inferential statistics: An introduction , 1980 .

[112]  A. Jensen,et al.  Bias in Mental Testing , 1980 .

[113]  Charles L. Hulin,et al.  An empirical comparison of item response theory and hierarchical factor analysis in applications to the measurement of job satisfaction. , 1982 .

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

[115]  Kenneth A. Bollen,et al.  Ratio Variables in Aggregate Data Analysis , 1979 .

[116]  Norman Robert Campbell,et al.  An Account of the Principles of Measurement and Calculation , 1928, Nature.

[117]  Howard S. Gitlow,et al.  Discrimination Procedures for the Analysis of Nominally Scaled Data Sets , 1979 .

[118]  R. Luce,et al.  Simultaneous conjoint measurement: A new type of fundamental measurement , 1964 .

[119]  L. S. Prytulak,et al.  Critique of S. S. Stevens' Theory of Measurement Scale Classification , 1975 .

[120]  M. Tanner,et al.  Modeling ordinal scale disagreement. , 1985, Psychological bulletin.

[121]  B. Wright,et al.  Best test design , 1979 .

[122]  Louis Narens,et al.  Measurement without Archimedean Axioms , 1974, Philosophy of Science.

[123]  Bruce D. Spencer,et al.  Test Scores as Social Statistics: Comparing Distributions , 1983 .

[124]  Clinton I. Chase,et al.  Elementary Statistical Procedures , 1985 .

[125]  Robert J. Mislevy,et al.  Chapter 6: Recent Developments in Item Response Theory with Implications for Teacher Certification , 1987 .

[126]  R D Luce,et al.  Measurement Scales on the Continuum , 1987, Science.

[127]  G. D. Armstrong,et al.  Parametric statistics and ordinal data: a pervasive misconception. , 1981, Nursing research.

[128]  Louis Cohen,et al.  Statistics for Social Scientists , 1982 .

[129]  Susan E. Whitely,et al.  Multicomponent latent trait models for ability tests , 1980 .

[130]  Georg Rasch,et al.  Probabilistic Models for Some Intelligence and Attainment Tests , 1981, The SAGE Encyclopedia of Research Design.

[131]  Rainer Westermann.  Interval-scale measurement of attitudes: some theoretical conditions and empirical testing methods , 1983 .

[132]  W. Kristof,et al.  A FOUNDATION OF INTERVAL SCALE MEASUREMENT , 1967 .

[133]  Vicki F. Sharp,et al.  Statistics for the social sciences , 1979 .

[134]  Henry C. Byerly.  Realist Foundations of Measurement , 1972 .

[135]  Marty J. Schmidt,et al.  Understanding and using statistics: Basic concepts , 1975 .

[136]  R. Cléroux,et al.  The Comparison of Different Scales of Measurement in the Multivariate Normal Model: a Numerical Algorithm , 1975 .

[137]  S. S. Stevens,et al.  Handbook of experimental psychology , 1951 .

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

[139]  Louis Narens,et al.  On the scales of measurement , 1981 .

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

[141]  Harvey Goldstein,et al.  Dimensionality, bias, independence and measurement scale problems in latent trait test score models , 1980 .

[142]  Arnold Koslow.  Quantity and Quality: Some Aspects of Measurement , 1982, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association.

[143]  J. DuMond,et al.  An Introduction to Scientific Research , 1953 .

[144]  Gary L. Hansen,et al.  Response bias in sex-role attitude measurement , 1984 .

[145]  S. Bem.  The measurement of psychological androgyny. , 1974, Journal of consulting and clinical psychology.

[146]  C. O. Fraser.  Measurement in psychology , 1980 .

[147]  Paul F. Lazarsfeld,et al.  Continuities in the Language of Social Research , 1972 .

[148]  Rubens Ya.  Concepts of measurement. , 1979 .

[149]  Hubert M. Blalock,et al.  Measurement in the Social Sciences , 1974 .

[150]  Willem E. Saris.  A measurement model for psychophysical scaling , 1988 .

[151]  Sanford Labovitz,et al.  Some Observations on Measurement and Statistics , 1967 .

[152]  J. Gaito.  Scale classification and statistics. , 1960, Psychological review.

[153]  W. Hays.  Statistics for the social sciences , 1973 .

[154]  Delbert Miller,et al.  Handbook of research design and social measurement , 1993 .

[155]  Louis Narens,et al.  Symmetry, Scale Types, and Generalizations of Classical Physical Measurement , 1983 .

[156]  G. J. Boris Allan,et al.  Measurement scales and multivariate analysis , 1979 .

[157]  Louis M. Hsu.  On Scales of Measurement , 1980 .

[158]  Louis Narens,et al.  Classification of concatenation measurement structures according to scale type , 1985 .

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

[160]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[161]  L. Thurstone.  Attitudes Can Be Measured , 1928, American Journal of Sociology.

[162]  Clyde H. Coombs,et al.  A theory of psychological scaling , 1951 .

[163]  W. J. Youden.  Experimentation and Measurement , 1984 .

[164]  J. Vegelius,et al.  On Generalizations Of The G Index And The Phi Coefficient To Nominal Scales. , 1979, Multivariate behavioral research.

[165]  I. Onukogu,et al.  An Analysis of Variance of Nominal Data , 1985 .

[166]  E. W. Adams,et al.  Elements of a Theory of Inexact Measurement , 1965, Philosophy of Science.

[167]  R. Hambleton,et al.  Item Response Theory , 1984, The History of Educational Measurement.

[168]  R. Likert.  “Technique for the Measurement of Attitudes, A” , 2022, The SAGE Encyclopedia of Research Design.

[169]  D. Weiss,et al.  The Impossible Dream of Fechner and Stevens , 1981, Perception.

[170]  Mark L. Davison,et al.  Parametric statistics and levels of measurement : factorial designs and multiple regression , 1990 .

[171]  L. L. Thurstone,et al.  A mental unit of measurement. , 1927 .

[172]  Philip Ehrlich,et al.  Philosophical and Foundational Issues in Measurement Theory , 1994 .

[173]  Arnold Binder,et al.  Restrictions on statistics imposed by method of measurement: Some reality, much mythology , 1984 .

[174]  M. J. Allen.  Introduction to Measurement Theory , 1979 .

[175]  J. Gaito,et al.  Some issues in the measurement-statistics controversy. , 1986 .

[176]  Clyde H. Coombs,et al.  Psychology and mathematics : an essay on theory , 1983 .

[177]  William H. Angoff,et al.  Scales With Nonmeaningful Origins and Units of Measurement , 1962 .

[178]  Edwin S. Johnson,et al.  Research methods in criminology and criminal justice , 1981 .

[179]  Hoben Thomas,et al.  IQ, Interval Scales, and Normal Distributions. , 1982 .

[180]  Johann Pfanzag.  A general theory of measurement applications to utility , 1959 .

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

[182]  Hans Freudenthal,et al.  Mathematical Concepts of Elementary Measurement. , 1971 .

[183]  L. L. Thurstone,et al.  The measurement of opinion. , 1928 .

[184]  Magnus Stenbeck,et al.  Are Likert scales unidimensional , 1987 .

[185]  Linton C. Freeman,et al.  Order‐based statistics and monotonicity: A family of ordinal measures of association* , 1986 .

[186]  Sanford Labovitz,et al.  Statistical Usage In Sociology , 1972 .

[187]  Benjamin D. Wright,et al.  Solving measurement problems with the Rasch model. , 1977 .

[188]  J. Gaito,et al.  An empirical basis for the statement that measurement scale properties (and meaning) are irrelevant in statistical analyses , 1986 .

[189]  Patrick Suppes,et al.  Basic measurement theory , 1962 .

[190]  D. Krantz.  Measurement Structures and Psychological Laws , 1972, Science.

[191]  R. Glaser,et al.  A Methodological Analysis of the Inconsistency of Response to Test Items , 1949 .

[192]  Richard L. Daft,et al.  Administrative Intensity and Ratio Variables: The Case Against Definitional Dependency , 1979 .

[193]  T Heeren,et al.  Robustness of the two independent samples t-test when applied to ordinal scaled data. , 1987, Statistics in medicine.

[194]  Fritz Drasgow,et al.  A Decision-Theoretic Approach to the Use of Appropriateness Measurement for Detecting Invalid Test and Scale Scores , 1987 .

[195]  Gregory J. Moschetti.  Calculating Equity: Ordinal and Ratio Criteria. , 1979 .

[196]  John Robert Stockton.  Introduction to business and economic statistics , 1975 .

[197]  L L THURSTONE,et al.  The measurement of values. , 1960, Psychological review.

[198]  C. Alan Boneau.  A note on measurement scales and statistical tests. , 1961 .

[199]  K. Schuessler,et al.  Analysis of Ratio Variables: Opportunities and Pitfalls , 1974, American Journal of Sociology.

[200]  P. V. Rao,et al.  Measuring nominal scale agreement between a judge and a known standard , 1978 .

[201]  M Forrest,et al.  Ordinal scale and statistics in medical research. , 1986, British medical journal.

[202]  John H. Mueller,et al.  Statistical reasoning in sociology , 1977 .

[203]  W. W. Daniel.  Applied Nonparametric Statistics , 1979 .

[204]  Stanley E. Legum.  Jum C. Nunnally, Introduction to statistics for psychology and education. New York: McGraw Hill, 1975. , 1977 .

[205]  Paula M. Popovich,et al.  Attitudes toward Statistics: An Evaluation of Multiple Measures , 1988 .

[206]  J. Leeuw,et al.  Abstract Measurement Theory. , 1986 .

[207]  Johann Pfanzagl,et al.  Theory of measurement , 1970 .

[208]  Richard A. Behan,et al.  Football numbers (continued). , 1954 .

[209]  John P. Burgess,et al.  Why I am not a nominalist , 1983, Notre Dame J. Formal Log..

[210]  James A. Twaite.  Introductory statistics , 1979 .

[211]  F. Roberts.  Discrete Mathematical Models with Applications to Social, Biological, and Environmental Problems. , 1976 .