Типологии номинальных, ординальных, интервальных и относительных шкал вводят в заблуждение. (Перевод В. И. Хоменко)
Выражение признательности
Перевод выполнен в рамках конкурса переводовобъявленного журналом «Социология4М» в 2011 г.
Аннотация
Разработанная психофизиком С. С. Стивенсом типология измерительных шкал доминирует в социальной статистике на протяжении без малого 50 лет. В течение этого времени данная типология неизменно оставалась предметом активной полемики. Недавно типология шкал Стивенса пережила свой ренессанс, связанный с разработкой компьютерных статистических пакетов. Однако ныне терминологию Стивенса используют без учета как классической критики, сопровождавшей ее появление, так и достижений в области анализа данных, которые появились в последние десятилетия.
Ключевые слова:
анализ данных, типы данных, измерительные шкалы, шкалирование
Литература
Stevens S.S. On the Theory of Measurement Scales // Science. 1946. No. 103. P. 677–680.
Суппес П., Зинес Дж. Основы теории измерений // Психологические измерения / Под ред. Л.Д. Мешалкина. М.: МИР, 1967.
СтивенсС.С. Математика, измерение и психофизика // Экспериментальная психология / Под ред. С. Стивенса. М.: Иностр. лит., 1960. С. 19–99.
Luce R.D. On the Possible Psychophysical Laws // Psychological Review. 1956. No. 66. P. 81–95.
Blalock H.M.Jr. Social Statistics. N.Y.: McGraw-Hill, 1960.
Sigel S. Nonparametric Statistics for the Behavioral Sciences. N.Y.: McGrawHill, 1956.
Andrews F.M., Klem L., Davidson T.N., O’Malley P.M., Rodgers W.L. A Guide for Selecting Statistical Techniques for Analyzing Social Science Data. Ann Arbor: Univ. of Michigan; Institute for social research, 1981.
Lord F. On the Statistical Treatment of Football Numbers // American Psychologist. 1953. No. 6. P. 750–751.
Baker B.O., Hardyck C.D., Petrinovich L.F. Weak Measurements vs. Strong Statistics: an Empirical Critique of S.S. Stevens’s Proscriptions on Statistics // Educational and Psychological Measurement. 1966. No. 26. P. 291–309.
Borgatta E.F., Bohrnstedt G.F. Level of Measurement – Once Over Again // Sociological Methods and Research. 1980. No. 9. P. 147–160.
Guttman L. What Is Now What in Statistics // The Statistician. 1977. No. 26. P. 81–107.
Tukey J.W. Data Analysis and Behavioral Science of Learning to Bear the Quantitative Man’s Burden by Shunning Badmandments // The Collected Works of John W. Tukey / Ed. by L.V. Jones. Belmont, CA: Wadsworth, 1961. Vol. 3. P. 391–484.
Krantz D.H., Luce R.D., Suppes P., Tversky A. Foundations of Measurement. N.Y.: Academic press, 1971. Vol. 1.
Luce R.D., Krantz D.H., Suppes P., Tversky A. Foundations of Measurement. N.Y.: Academic press, 1990. Vol. 3.
Narens L., Luce R.D. Measurement: the Theory of Numerical Assignments. Reading, MA: Addison-Wesley, 1986.
Roberts F.S. Measurement Theory. Reading, MA: Addison-Wesley, 1979.
Zumbo B. D., Zimmerman D. W. Levels of Measurement and the Relation Between Parametric and Nonparametric Tests. Working Paper 91-1. Edumetrics Research Group, University of Ottawa.
Gaito J. Measurement Scales and Statistics: Resurgence of an Old Misconception // Psychological Bulletin. 1980. No. 87. P. 564–567.
Townsend J. T., Ashby F. G. Measurement Scales and Statistics: the Misconception Misconceived // Psychological Bulletin. 1984. No. 96. P. 394–401.
Michel J. Measurement scales and Statistics: a Clash of Paradigms // Psychological Bulletin. 1986. No. 100. P. 398–407.
Tukey J.W. The Future of Data Analysis // The Collected Works of JohnW.Tukey / Ed. by L.V. Jones. Belmont, CA: Wadsworth, 1961. Vol. 3. P. 187–389.
Мостеллер Ф, Тьюки Дж. Анализ данных и регрессия. М: Финансы и статистика, 1982.
Bartlet M.S. The Use of Transformation // Biometrics. 1947. No. 3. P. 39–52.
Tukey J.W. On the Comparative Anatomy of Transformations // Annals of Mathematical Statistics. 1957. No. 28. P. 602–632.
Box G.E.P., Cox D.R. An Analysis of Transformations // Journal of the Royal Statistical Society. 1963. No. 26. P. 211–252.
Hoaglin D.C. Transformations in Everyday Experience // Chance. 1988. No. 1. P. 40–45.
Abelson R.P., Tukey J.W. Efficient Utilization of Non-numerical Information in Quantitative Analysis: General Theory and the Case of Simple Order // Annals of Mathematical Statistics. 1963. No. 34. P. 1347–1369.
Shepard R.N. The Analysis of Proximities: Multidimensional Scaling with an Unknown Distance Function // Psychometrika. 1962. No. 27. P. 125–139.
Kruskal J.B. Nonmetrik Multidimensional Scaling: a Numerical Method // Psychometrika. 1964. No. 29. P. 115–129.
Guttman L. A General Nonmetric for Finding the Smallest Coordinate for a Configuration of Points // Psychometrika. 1968. No. 33. P. 469–506.
Joiner B.F. Lurking Variables: Some Examples // The American Statistician. 1981. No. 35. P. 227–233.
Rozenboom W.W. Scaling Theory and the Nature of Measurement // Synthese. 1966. No. 16. P. 170–233.
Goodman L.A. A New Model for Scaling Response Patterns: an Application of Quasi-independent Concept // Journal of the American Statistical Association. 1975. No. 70. P. 755–768.
Shye S. Partial Order Scalogram Analysis // Theory Construction and Data Analysis in the Behavioral Sciences / Ed. by S. Shye. San Francisco: Jossey-Bass, 1978.
Green P.E., Rao V.R. Conjoint Measures for Quantifying Judgmental Data // Journal of Marketing Research. 1971. No. 8. P. 355–363.
Anderson N.H. Scales and Statistics: Parametric and Nonparametric // Psychological Bulletin. 1961. No. 58. P. 305–316.
Хампель Ф., Рончетти Э., Рауссеу П., Штаэль В. Робастность в стати- стике: подход на основе функций влияния. М.: Мир, 1989.
Hoaglin D.C., Mosteller F., Tukey J.W. Understanding Robust and Exploratory Data Analysis. N.Y.: John Wiley, 1983.
Тьюки Дж. Анализ данных наблюдений: разведочный анализ / Под ред. В.М. Писаренко. М.: Мир, 1981.
Velleman P.W., Hoaglin D.C. Applications, Basics and Computing of Exploratory Data Analysis. Boston: Duxbury press, 1981.
Savage I.R. Nonparametric Statistics // Journal of the American Statistical Association. 1957. No. 52. P. 331–334.
Sigel S. Nonparametric statistics for the behavioral sciences. N.Y.: McGrawHill, 1956.
Bacon F. Novum Organum // The works of Francis Bacon / Ed. by J. Spedding, R.L. Ellis, D.D. Heath. Belmont; N.Y., 1868. Vol. 8.
Кун Т. Структура научных революций. М.: Прогресс, 1977.
Суппес П., Зинес Дж. Основы теории измерений // Психологические измерения / Под ред. Л.Д. Мешалкина. М.: МИР, 1967.
СтивенсС.С. Математика, измерение и психофизика // Экспериментальная психология / Под ред. С. Стивенса. М.: Иностр. лит., 1960. С. 19–99.
Luce R.D. On the Possible Psychophysical Laws // Psychological Review. 1956. No. 66. P. 81–95.
Blalock H.M.Jr. Social Statistics. N.Y.: McGraw-Hill, 1960.
Sigel S. Nonparametric Statistics for the Behavioral Sciences. N.Y.: McGrawHill, 1956.
Andrews F.M., Klem L., Davidson T.N., O’Malley P.M., Rodgers W.L. A Guide for Selecting Statistical Techniques for Analyzing Social Science Data. Ann Arbor: Univ. of Michigan; Institute for social research, 1981.
Lord F. On the Statistical Treatment of Football Numbers // American Psychologist. 1953. No. 6. P. 750–751.
Baker B.O., Hardyck C.D., Petrinovich L.F. Weak Measurements vs. Strong Statistics: an Empirical Critique of S.S. Stevens’s Proscriptions on Statistics // Educational and Psychological Measurement. 1966. No. 26. P. 291–309.
Borgatta E.F., Bohrnstedt G.F. Level of Measurement – Once Over Again // Sociological Methods and Research. 1980. No. 9. P. 147–160.
Guttman L. What Is Now What in Statistics // The Statistician. 1977. No. 26. P. 81–107.
Tukey J.W. Data Analysis and Behavioral Science of Learning to Bear the Quantitative Man’s Burden by Shunning Badmandments // The Collected Works of John W. Tukey / Ed. by L.V. Jones. Belmont, CA: Wadsworth, 1961. Vol. 3. P. 391–484.
Krantz D.H., Luce R.D., Suppes P., Tversky A. Foundations of Measurement. N.Y.: Academic press, 1971. Vol. 1.
Luce R.D., Krantz D.H., Suppes P., Tversky A. Foundations of Measurement. N.Y.: Academic press, 1990. Vol. 3.
Narens L., Luce R.D. Measurement: the Theory of Numerical Assignments. Reading, MA: Addison-Wesley, 1986.
Roberts F.S. Measurement Theory. Reading, MA: Addison-Wesley, 1979.
Zumbo B. D., Zimmerman D. W. Levels of Measurement and the Relation Between Parametric and Nonparametric Tests. Working Paper 91-1. Edumetrics Research Group, University of Ottawa.
Gaito J. Measurement Scales and Statistics: Resurgence of an Old Misconception // Psychological Bulletin. 1980. No. 87. P. 564–567.
Townsend J. T., Ashby F. G. Measurement Scales and Statistics: the Misconception Misconceived // Psychological Bulletin. 1984. No. 96. P. 394–401.
Michel J. Measurement scales and Statistics: a Clash of Paradigms // Psychological Bulletin. 1986. No. 100. P. 398–407.
Tukey J.W. The Future of Data Analysis // The Collected Works of JohnW.Tukey / Ed. by L.V. Jones. Belmont, CA: Wadsworth, 1961. Vol. 3. P. 187–389.
Мостеллер Ф, Тьюки Дж. Анализ данных и регрессия. М: Финансы и статистика, 1982.
Bartlet M.S. The Use of Transformation // Biometrics. 1947. No. 3. P. 39–52.
Tukey J.W. On the Comparative Anatomy of Transformations // Annals of Mathematical Statistics. 1957. No. 28. P. 602–632.
Box G.E.P., Cox D.R. An Analysis of Transformations // Journal of the Royal Statistical Society. 1963. No. 26. P. 211–252.
Hoaglin D.C. Transformations in Everyday Experience // Chance. 1988. No. 1. P. 40–45.
Abelson R.P., Tukey J.W. Efficient Utilization of Non-numerical Information in Quantitative Analysis: General Theory and the Case of Simple Order // Annals of Mathematical Statistics. 1963. No. 34. P. 1347–1369.
Shepard R.N. The Analysis of Proximities: Multidimensional Scaling with an Unknown Distance Function // Psychometrika. 1962. No. 27. P. 125–139.
Kruskal J.B. Nonmetrik Multidimensional Scaling: a Numerical Method // Psychometrika. 1964. No. 29. P. 115–129.
Guttman L. A General Nonmetric for Finding the Smallest Coordinate for a Configuration of Points // Psychometrika. 1968. No. 33. P. 469–506.
Joiner B.F. Lurking Variables: Some Examples // The American Statistician. 1981. No. 35. P. 227–233.
Rozenboom W.W. Scaling Theory and the Nature of Measurement // Synthese. 1966. No. 16. P. 170–233.
Goodman L.A. A New Model for Scaling Response Patterns: an Application of Quasi-independent Concept // Journal of the American Statistical Association. 1975. No. 70. P. 755–768.
Shye S. Partial Order Scalogram Analysis // Theory Construction and Data Analysis in the Behavioral Sciences / Ed. by S. Shye. San Francisco: Jossey-Bass, 1978.
Green P.E., Rao V.R. Conjoint Measures for Quantifying Judgmental Data // Journal of Marketing Research. 1971. No. 8. P. 355–363.
Anderson N.H. Scales and Statistics: Parametric and Nonparametric // Psychological Bulletin. 1961. No. 58. P. 305–316.
Хампель Ф., Рончетти Э., Рауссеу П., Штаэль В. Робастность в стати- стике: подход на основе функций влияния. М.: Мир, 1989.
Hoaglin D.C., Mosteller F., Tukey J.W. Understanding Robust and Exploratory Data Analysis. N.Y.: John Wiley, 1983.
Тьюки Дж. Анализ данных наблюдений: разведочный анализ / Под ред. В.М. Писаренко. М.: Мир, 1981.
Velleman P.W., Hoaglin D.C. Applications, Basics and Computing of Exploratory Data Analysis. Boston: Duxbury press, 1981.
Savage I.R. Nonparametric Statistics // Journal of the American Statistical Association. 1957. No. 52. P. 331–334.
Sigel S. Nonparametric statistics for the behavioral sciences. N.Y.: McGrawHill, 1956.
Bacon F. Novum Organum // The works of Francis Bacon / Ed. by J. Spedding, R.L. Ellis, D.D. Heath. Belmont; N.Y., 1868. Vol. 8.
Кун Т. Структура научных революций. М.: Прогресс, 1977.
