Fundamental characteristics and statistical analysis of ordinal variables: a review

Quality and Quantity

Volumn 51, Issue 1, 2017, Pages 435-458

  Lalla, Michele ^a  

^a UNIVERSITY OF MODENA AND REGGIO EMILIA   (Italy)

Author keywords

Feeling thermometer; Fuzzy sets; Likert scale; Measurement; Semantic differential; Stapel scale

Indexed keywords

EID: 85009206216     PISSN: 00335177     EISSN: 15737845     Source Type: Journal    
DOI: 10.1007/s11135-016-0314-5     Document Type: Article

References (89)

1. Agresti, A.: Categorical Data Analysis. John Wiley & Sons, New York (1990)
2. Aiello, F., Attanasio, M.: How to transform a batch of simple indicators to make up a unique one?. In: Atti della XLII Riunione Scientifica: Sessioni Plenarie e Specializzate, pp. 327–338. SIS, 9–11 giugno. University of Bari, Bari, IT (2004)
3. Aitchison, J., Silvey, S.D.: The generalization of probit analysis to the case of multiple responses. Biometrika 44(1/2), 131–140 (1957)
4. Alvarez, R.M., Bailey, D., Katz, J.N.: An empirical bayes approach to estimating ordinal treatment effects. Polit. Anal. 19(1 Winter), 20–31 (2011)
5. Amemiya, T.: Qualitative response models: a survey. J. Econ. Lit. 19(4), 1483–1538 (1981)
6. ANES, American National Election Studies: Pre- post- election study. Survey Research Center (S473) (1964) http://www.electionstudies.org/studypages/1964prepost/int1964.txt
7. Babbie, E.: The Practice of Social Research. Cengage Learning, 12th edn. Wadsworth, Belmont (2010)
8. Bernardi, L.: Misurazione e valutazione: le difficoltà di una coppia alle prime esperienze in comune. In: Bertin, G. (ed.) Valutazione e sapere sociologico. Metodi e tecniche di gestione dei processi decisionali, pp. 69–82. Franco Angeli, Milano (1995)
9. Bernardi, L., Capursi, V., Librizzi, L.: Measurement awareness: the use of indicators between expectations and opportunities. In: Atti della XLII Riunione Scientifica: Sessioni Plenarie e Specializzate, pp. 315–326. SIS, 9–11 giugno. University of Bari, Bari, IT (2004)
10. Bernberg, R.E.: Socio-psychological factors in individual morale: I. The prediction of specific indicators. J. Soc. Psychol. 36(1), 73–82 (1952)
11. Bollen, K.A.: Structural Equations with Latent Variables. John Wiley & Sons, New York (1989)
12. Cacciola, S., Marradi, A.: Contributo al dibattito sulle scale Likert basato sull’analisi di interviste registrate. In: Marradi, A. (ed.) Costruire il dato. Sulle tecniche di raccolta delle informazioni nelle scienze sociali, pp. 63–102. Franco Angeli, Milano (1988)
13. Campostrini, S., Ghellini, G., Tuzzi, A.: Con senso di misura. Riflessi statistici da alcuni allievi di Lorenzo Bernardi. CLEUP, Padova (2015)
14. Cantril, H., Free, L.A.: Hopes and fears for self and country: the self-anchoring striving scale in cross-cultural research. Am. Behav. Sci. 6(2, Supplement: Oct.), 1–30 (1962)
15. Conover, W.J.: Practical Nonparametric Statistics, 3rd edn. John Wiley & Sons, New York (1999)
16. Coombs, C.H.: Psychological scaling without a unit of measurement. Psychol. Rev. 57(3), 145–158 (1950)
17. Coombs, C.H.: Theory and method of social measurement. In: Festinger, L., Katz, D. (eds.) Research Methods in the Behavioral Sciences, pp. 471–535. Dryden, New York (1953)
18. Crespi, I.: Use of a scaling technique in surveys. J. Market. 25(July), 69–72 (1961)
19. Crespi, L.P.: Public opinion toward conscientious objectors: II. Measurement of national approval-disapproval. J. Psychol. 19(2), 209–250 (1945a)
20. Crespi, L.P.: Public opinion toward conscientious objectors: III. Intensity of social rejection in stereotype and attitude. J. Psychol. 19(2), 251–276 (1945b)
21. Das, S.: Quantifying fuzziness due to the scale of measurement in response systems. Fuzzy Sets Syst. 132(3), 317–333 (2002)
22. Das, S.: On measuring imprecision in human response due to respondent and attribute and its utility in questionnaire design. Int. J. Uncertain. Fuzz. 14(2), 155–173 (2006)
23. Domingo-Ferrer, J., Torra, V.: Extending microaggregation procedures using defuzzification methods for categorical variables. Proceedings of first International IEEE symposium on intelligent systems, Verna, Sept. pp. 44–49 (2002)
24. Dubois, D., Prade, H. (eds.): Fundamentals of Fuzzy Sets. Kluwer Academic Publ, Boston (2000)
25. Dubois, D., Prade, H., Gil, M.A., Grzegorzewsky, P., Hryniewicz, O. (eds.): Soft Methods for Handling Variability and Imprecision. Springer-Verlag, Heidelberg (2008)
26. Farebrother, R.W.: A class of shrinkage estimators. J. R. Stat. Soc. B 40(1), 47–49 (1977)
27. Gilula, Z., Krieger, A.M., Ritov, Y.: Ordinal association in contingency tables: some interpretive aspects. J. Am. Stat. Assoc. 83(402), 540–545 (1988)
28. Goodman, L.A.: Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika 61(2), 215–231 (1974)
29. Goodman, L.A.: Simple models for the analysis of association in cross-classifications having ordered categories. J. Am. Stat. Assoc. 74(367), 537–552 (1979)
30. Greene, W.H.: Econometric Analysis, 5th edn. Prentice Hall, Upper Saddle River (2003)
31. Guttman, L.A.: The basis for scalogram analysis. In: Stouffer, S. (ed.) Measurement and Prediction, pp. 60–90. Princeton University Press, New York (1950)
32. Guttman, L.A.: A general nonmetric technique for finding the smallest coordinate space for a configuration of points. Psychometrika 33(4), 469–506 (1968)
33. Hagenaars, J.A., McCutcheon, A.L.: Applied Latent Class Analysis. Kluwer, Dordrecht (2002)
34. Hand, D.J.: Measurement theory and practice. The world through quantification. Arnold, London (2004)
35. Hoaglin, D.C., Mosteller, F., Tukey, J.W.: Understanding Robust and Exploratory Data Analysis. John Wiley & Sons, New York (1983)
36. Hofacker, C.F.: Categorical judgment scaling with ordinal assumptions. Multivar. Behav. Res. 19(1), 91–106 (1984)
37. Hofmans, J., Theuns, P., Van Acker, F.: Combining quality and quantity. A psychometric evaluation of the self-anchoring scale. Qual. Quant. 43(5), 703–716 (2009)
38. Jöreskog, K.G.: A general method for estimating a linear structural equation system. In: Goldberger, A.S., Duncan, O.D. (eds.) Structural Equation Models in the Social Sciences, pp. 85–112. Seminar Press, New York (1973)
39. Jöreskog, K.G.: New developments in LISREL: analysis of ordinal variables using polychoric correlations and weighted least squares. Qual. Quant. 24(4), 387–404 (1990)
40. Jöreskog, K.G.: On the estimation of polychoric correlations and their asymptotic covariance matrix. Psychometrika 59(3), 381–389 (1994)
41. Jöreskog, K.G., Sörbom, D.: Advances in Factor Analysis and Structural Equation Models. Abt books, Cambridge (1979)
42. Juster, F.T.: Prediction and consumer buying intentions. Am. Econ. Rev. 50(2), 604–617 (1960)
43. Juster, F.T.: Consumer buying intentions and purchase probability: an experiment in survey design. J. Am. Stat. Assoc. 61(315), 658–696 (1966)
44. Kampen, J., Swyngedouw, M.: The ordinal controversy revisited. Qual. Quant. 34(1), 87–102 (2000)
45. Khurshid, A., Sahai, H.: Scales of measurement: an introduction and selected bibliography. Qual. Quant. 27(3), 303–323 (1993)
46. Kilpatrick, F.P., Cantril, H.: Self-anchoring scaling: a measure of individuals’ unique reality worlds. J. Individ. Psychol. 16(2), 158–173 (1960)
47. Lalla, M.: Le scale ordinali e i relativi problemi operativi. In: Campostrini, S., Ghellini, G., Tuzzi, A. (eds.) Con senso di misura Riflessi statistici da alcuni allievi di Lorenzo Bernardi, pp. 35–52. CLEUP, Padova (2015)
48. Lalla, M., Facchinetti, G., Mastroleo, G.: Ordinal scales and fuzzy set systems to measure agreement: an application to the evaluation of teaching activity. Qual. Quant. 38(5), 577–601 (2004)
49. Lalla, M., Ferrari, D., Pirotti, T.: Fuzzy inference systems to analyze ordinal variables—the case of evaluating teaching activity. In: Proceedings of the international conference on fuzzy computation theory and applications. SciTePress—Science and Technology Publications Digital Library, Setubal, pp. 25–36 (2014)
50. Landenna, G., Marasini, D.: Metodi statistici non parametrici. il Mulino, Bologna (1990)
51. Likert, R.: A technique for the measurement of attitudes. Archives of Psychology 140, 1–55 (1932)
52. Lord, F.M.: On the statistical treatment of football members. Am. Psychol. 8(12), 750–751 (1953)
53. Marradi, A.: Termometri con vincolo di ordinabilità: il «gioco della torre» consente di aggirare la tendenza alla desiderabilità sociale? Sociologia e ricerca sociale 57, 49–59 (1998)
54. Marradi, A.: Metodologia delle scienze sociali. il Mulino, Bologna (2007)
55. Mantel, N.: Chi square tests with one degree of freedom: extensions of the Mantel-Haenszel procedure. J. Am. Stat. Assoc. 58(303), 690–700 (1963)
56. McCullagh, P.: Regression models for ordinal data (with discussion). J. R. Stat. Soc. B 42(2), 109–142 (1980)
57. McKelvey, R.D., Zavoina, W.: A statistical model for the analysis of ordinal level dependent variables. J. Math. Sociol. 4(1), 103–120 (1975)
58. Niederée, R.: There is more to measurement than just measurement: measurement theory, symmetry, and substantive theorizing. J. Math. Psychol. 38(4), 527–594 (1994)
59. Nowakowska, M.: Methodological problem of measurement of fuzzy concepts in the social sciences. Behav. Sci. 22(2), 107–115 (1977)
60. Osgood, C.E.: The nature of measurement and meaning. Psychol. Bull. 49(3), 197–237 (1952)
61. Osgood, C.E., Suci, G.J., Tannenbaum, R.H.: The Measurement of Meaning. University of Illinois Press, Urbana (1957)
62. Pearson, K.: On a new method of determining correlation between a measured character A, and a character B, of which only the percentage of cases wherein B exceeds (or falls short of) a given intensity is recorded for each grades of A. Biometrika 7(1/2), 96–105 (1909)
63. Pesarin, F.: Multivariate Permutation Tests: With Application in Biostatistics. John Wiley & Sons, Chichester (2001)
64. Pesarin, F., Salmaso, L.: Permutation Tests for Complex Data: Theory, Applications and Software. John Wiley & Sons, Chichester (2010)
65. Prytulac, L.S.: A critique of S. S. Stevens’ theory of measurement scale classification. Percept. Motor Skills 41(1), 3–28 (1975)
66. Ricolfi, L.: Operazioni di ricerca e scale. Rassegna italiana di sociologia XXVI(2), 189–227 (1985)
67. Savage, I.R.: Nonparametric statistics. J. Am. Stat. Assoc. 52(279), 331–344 (1957)
68. Smithson, M.J.: Fuzzy Set Analysis for Behavioral and social sciences. Springer, Heidelberg (1987)
69. Smithson, M.J.: Fuzzy set theory and the social sciences: the scope for applications. Fuzzy Sets Syst. 26(1), 1–21 (1988)
70. Siegel, S., Castellan Jr, N.J.: Nonparametric Statistics for the Behavioral Science. McGraw-Hill, New York (1988)
71. Stevens, S.S.: On the theory of scale measurement. Science 103(2684), 677–680 (1946)
72. Stevens, S.S.: Mathematics, measurement, and psychophysics. In: Stevens, S.S. (ed.) Handbook of Experimental Psychology, pp. 1–49. Wiley & Sons, New York (1951)
73. Symeonaki, M., Michalopoulou, C., Kazani, A.: A fuzzy set theory solution to combining likert items into a single overall scale (or subscales). Qual. Quant. 49(2), 739–762 (2015)
74. Tanaka, H.: Fuzzy data analysis by possibilistic linear models. Fuzzy Sets Syst. 24(3), 363–375 (1987)
75. Thurstone, L.L.: A law of comparative judgment. Psychol. Rev. 34(4), 273–286 (1927a)
76. Thurstone, L.L.: The method of paired comparison for social values. J. Abnorm. Soc. Psychol. 21(4), 384–397 (1927b)
77. Thurstone, L.L.: Attitudes can be measured. Am. J. Sociol. 33(4), 529–554 (1928)
78. Tukey, J.W.: Exploratory Data Analysis. Addison-Wesley, Reading (1977)
79. Van Leekwijck, W., Kerre, E.E.: Defuzzification: criteria and classification. Fuzzy Sets Syst. 108(1), 159–178 (1999)
80. Velleman, P.F., Wilkinson, L.: Ordinal, interval, and ratio typologies are misleading. Am. Stat. 47(1), 65–72 (1993)
81. Viertl, R.: Statistical Methods for Fuzzy Data. John Wiley and Sons, New Delhi (2011)
82. Von Altrock, C.: Fuzzy logic and neurofuzzy applications in business and finance. Prentice Hall PTR, Upper Saddle River (1997)
83. Weisberg, H.F., Rusk, J.G.: Dimensions of candidate evaluation. Am. Polit. Sci. Rev. 64(4), 1167–1185 (1970)
84. Westermann, R.: Interval-scale measurement of attitudes: some theoretical conditions and empirical testing methods. Br. J. Math. Stat. Psychol. 36(2), 228–239 (1983)
85. White, M.: Psychological technique and social problems. Southwest. Polit. Soc. Sci. Q. 7, 58–73 (1926)
86. Wilson, T.P.: Critique of ordinal variables. Soc. Forces 49(3), 432–444 (1971)
87. Yang, M., Lin, T.: Fuzzy least-squares linear regression analysis for fuzzy input–output data. Fuzzy Sets Syst. 126(3), 389–399 (2002)
88. Yu, J.H., Albaum, G., Swenson, M.: Is a central tendency error inherent in the use of semantic differential scales in different cultures? Int. J. Market Res. 45(2), 213–228 (2003)
89. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)