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On Scales of Measurement in Autism Spectrum Disorders (ASD) and Beyond: Where Smitty Went Wrong

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Abstract

The author examined critically three beliefs of S.S. Stevens pertaining to his quadripartite system of scales of measurement: (1) There are four scales of measurement in common usage (2) These scales and the scientific disciplines that use them can be incrementally graded for levels of reliability and validity or accuracy such that: Nominal scale variables produce the lowest levels of reliability and accuracy; with successively improving levels for Ordinal, Equal Interval, and Equal Ratio scales; and (3) The scale upon which a variable is measured determines the type of statistical test that one is permitted to apply. It was shown that each of the three beliefs is fundamentally flawed.

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References

  • Bartko, J. J. (1966). The intraclass correlation coefficient as a measure of rater agreement. Psychological Reports, 19, 3–11.

    Article  PubMed  Google Scholar 

  • Bartko, J. J. (1976). On various intraclass correlation cofficients. Psychological Bulletin, 83, 762–765.

    Article  Google Scholar 

  • Bolanowski, S. J., & Gescheider, (Eds.). (1991). Ratio scaling of psychological magnitude: In honor of the memory of S.S. Stevens. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Buchler, J. (1940). Philosophical writings of Peirce. New York: Dover.

    Google Scholar 

  • Cicchetti, D. V. (1976). Assessing inter-rater reliability for rating scales: Resolving some basic issues. British Journal of Psychiatry, 129, 452–456.

    Article  PubMed  Google Scholar 

  • Cicchetti, D. V., Bronen, R., Spencer, S., Haut, S., Berg, A., Oliver, P., et al. (2006). Rating scales, scales of measurement, and issues of reliability: Resolving some critical issues for clinicians. Journal of Nervous and Mental Disease, 194, 564–567.

    Article  Google Scholar 

  • Cicchetti, D. V., Showalter, D., & Tyrer, P. (1985). The effect of number of rating scale categories upon levels of inter-rater reliability: A Monte Carlo investigation. Applied Psychological Measurement, 9, 31–36.

    Article  Google Scholar 

  • Cohen, J. (1960). Α coefficient of agreement for nominal scales. Educational and Psychological Measurement, 23, 37–46.

    Google Scholar 

  • Cohen, J. (1968). Weighted kappa: Nominal scale agreement with provision for scaled disagreement or partial credit. Psychological Bulletin, 70, 213–220.

    Google Scholar 

  • Colman, A. M., & Preston, C. C. (2000). Optimal number of response categories in rating scales: Reliability, validity, discriminating power, and respondent preferences. Acta Psychologica, 104, 1–15.

    Article  PubMed  Google Scholar 

  • Coombs, C. H. (1953). Theory and methods of social measurement. In L. Festinger, D. Katz (Eds.), Research methods in the behavioral sciences, (pp. 471–535). Hillside, NJ: Lawrence Erlbaum Associates.

  • Embretson, S. E., & Hershberger, S. L. (1999). The new rules of measurement: What every psychologist should know. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Fleiss, J. L. (1975). Measuring agreement between two judges on the presence or absence of a trait. Biometrics, 31, 651–659.

    Article  PubMed  Google Scholar 

  • Fleiss, J. L., & Cohen, J. (1973). The equivalence of weighted kappa and the intraclass correlation coefficient as measures of agreement. Educational and Psychological Measurement, 33, 613–619.

    Article  Google Scholar 

  • Freeman, L. C. (1965). Elementary applied statistics. New York: Wiley.

    Google Scholar 

  • Grimm, L. G., & Yarnold, P. R. (1995). Reading and understanding multivariate statistics. Washington, D.C.: American Psychological Association.

    Google Scholar 

  • Guttman, L. (1941). The quantification of a class of attributes: A theory and method of scale construction. In P. Horst, et al. (Eds.), The prediction of personal adjustment, (pp. 319–348). New York: Social Science Research Council, Bulletin 48.

  • Kraemer, H. C., Kazdin, A. E., Offord, D. R., Kessler, R. C., Jensen, P. S., & Kupfer, D. J. (1997). Coming to terms with the concept of risk. Archives of General Psychiatry, 64, 337–343.

    Article  Google Scholar 

  • McNemar, Q. (1955). Psychological statistics (2nd ed.). New York: Wiley.

    Google Scholar 

  • Miller, G. A. (1975). Stanley Smith Stevens, 1906–1973: A biographical memoir. Washington, D.C.: New York Academy of Sciences.

    Google Scholar 

  • Rice, I. L., & Wagstaff, A. K. (1967). Client voice quality and expressive style as indexes of productive psychotherapy. Journal of Consulting Psychology, 3, 557–563.

    Article  Google Scholar 

  • Sholten, A. Z., & Borsboom, D. (2009). A re-analysis of Lord’s treatment of football numbers. Journal of Mathematical Psychology, 53, 69–75.

    Article  Google Scholar 

  • Sparrow, S. S., Cicchetti, & Balla, D. A. (2008). Vineland II: A revision of the Vineland adaptive behavior scales: III. Expanded form: Circle Pines, MN: American Guidance Service.

  • Sparrow, S. S., Cicchetti, & Balla, D. A. (2005). Vineland II: A revision of the Vineland adaptive behavior scales: I. Survey/caregiver form (2nd ed.). Circle Pines, MN: American Guidance Service.

    Google Scholar 

  • Sparrow, S. S., Cicchetti, & Balla, D. A. (2006). Vineland II: A revision of the Vineland adaptive behavior scales: II. Teacher report form (2nd ed.). Circle Pines, MN: American Guidance Service.

    Google Scholar 

  • Stevens, S. S. (1946). On the theory of scales of measurement. Science, 10, 677–680.

    Article  Google Scholar 

  • Stevens, S. S. (1951). Mathematics, measurement, and psychophysics. In S. S. Stevens (Ed.), Handbook of experimental psychology (pp. 1–49). New York: Wiley.

    Google Scholar 

  • Stevens, S. S. (1968). Measurement, statistics, and the schemapiric view. Science, 161, 849–856.

    Article  PubMed  Google Scholar 

  • Weiss, D. (1986). The discriminating power of ordinal data. Journal of Social Behavior and Personality, 1, 381–389.

    Google Scholar 

  • Wright, B. D. (1999). Fundamental measurement for psychology. In S. E. Embretson & S. L. Hershberger (Eds.), The new rules of measurement. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Yule, G. U. (1912). On the methods of measuring two attributes. Journal of the Royal Statistical Society, 75, 579–642.

    Article  Google Scholar 

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Correspondence to Domenic V. Cicchetti.

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Cicchetti, D.V. On Scales of Measurement in Autism Spectrum Disorders (ASD) and Beyond: Where Smitty Went Wrong. J Autism Dev Disord 44, 303–309 (2014). https://doi.org/10.1007/s10803-012-1486-z

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