Behavior Research Methods

, Volume 41, Issue 3, pp 901–908 | Cite as

Nominal analysis of “variance”

  • David J. Weiss


Nominal responses are the natural way for people to report actions or opinions. Because nominal responses do not generate numerical data, they have been underutilized in behavioral research. On those occasions in which nominal responses are elicited, the responses are customarily aggregated over people or trials so that large-sample statistics can be employed. A new analysis is proposed that directly associates differences among responses with particular sources in factorial designs. A pair of nominal responses either matches or does not; when responses do not match, they vary. That analogue to variance is incorporated in the nominal analysis of “variance” (Nanova ) procedure, wherein the proportions of matches associated with sources play the same role as do sums of squares in an anova . The Nanova table is structured like an ANOVA table. The significance levels of the N ratios formed by comparing proportions are determined by resampling. Fictitious behavioral examples featuring independent groups and repeated measures designs are presented. A Windows program for the analysis is available.


Medical Student American Statistical Association Nominal Data Artificial Data Symptom Effect 
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  1. Agresti, A. (1990). Categorical data analysis. New York: Wiley Interscience.Google Scholar
  2. Anderson, N. H. (1961). Scales and statistics: Parametric and nonparametric. Psychological Bulletin, 58, 305–316. doi:10.1037/h0042576CrossRefPubMedGoogle Scholar
  3. Bock, R. D. (1975). Multivariate statistical methods in behavioral research. New York: McGraw-Hill.Google Scholar
  4. Chen, Z., & Kuo, L. (2001). A note on the estimation of the multinomial logit model with random effects. American Statistician, 55, 89–95.CrossRefGoogle Scholar
  5. Cohen, J. (1968). Multiple regression as a general data-analytic system. Psychological Bulletin, 70, 426–443. doi:10.1037/h0026714CrossRefGoogle Scholar
  6. Dyke, G. V., & Patterson, H. D. (1952). Analysis of factorial arrangements when the data are proportions. Biometrics, 8, 1–12.CrossRefGoogle Scholar
  7. Edgington, E. S., & Onghena, P. (2007). Randomization tests (4th ed.). Boca Raton, FL: Chapman & Hall/CRC.Google Scholar
  8. Fasolo, B., McClelland, G. H., & Lange, K. (2005). The effect of site design and interattribute correlations on interactive Web-based decisions. In C. P. Haugtvedt, K. Machleit, & R. Yalch (Eds.), Online consumer psychology: Understanding and influencing behavior in the virtual world (pp. 325–344). Mahwah, NJ: Erlbaum.Google Scholar
  9. Fienberg, S. E. (2000). Contingency tables and log-linear models: Basic results and new developments. Journal of the American Statistical Association, 95, 643–647.CrossRefGoogle Scholar
  10. Gini, C. (1939). Variabilità e concentrazione: Vol. 1 di. Memorie di metodologia statistica. Milano: Giuffrè.Google Scholar
  11. Goodman, L. A. (1971). The analysis of multidimensional contingency tables: Stepwise procedures and direct estimation methods for building models for multiple classifications. Technometrics, 13, 33–61.CrossRefGoogle Scholar
  12. Grizzle, J. E. (1971). Multivariate logit analysis. Biometrics, 27, 1057–1062.CrossRefPubMedGoogle Scholar
  13. Haberman, S. J. (1982). Analysis of dispersion of multinomial responses. Journal of the American Statistical Association, 77, 568–580.CrossRefGoogle Scholar
  14. Jain, D., Vilcassim, N., & Chintagunta, P. (1994). A random-coefficients logit brand-choice model applied to panel data. Journal of Business & Economic Statistics, 12, 317–328.CrossRefGoogle Scholar
  15. Keppel, G. (1991). Design and analysis: A researcher’s handbook. Upper Saddle River, NJ: Prentice Hall.Google Scholar
  16. LaPiere, R. T. (1934). Attitudes and actions. Social Forces, 13, 230–237.CrossRefGoogle Scholar
  17. Lewis, D., & Burke, C. J. (1949). The use and misuse of the chi-square test. Psychological Bulletin, 46, 433–489. doi:10.1037/h0059088CrossRefPubMedGoogle Scholar
  18. Light, R. J., & Margolin, B. H. (1971). An analysis of variance for categorical data. Journal of the American Statistical Association, 66, 534–544.CrossRefGoogle Scholar
  19. Lord, F. M. (1953). On the statistical treatment of football numbers. American Psychologist, 8, 750–751.CrossRefGoogle Scholar
  20. Luce, R. D. (1959). Individual choice behavior: A theoretical analysis. New York: Wiley.Google Scholar
  21. Matheson, G. (2006). Intervals and ratios: The invariantive transformations of Stanley Smith Stevens. History of the Human Sciences, 19, 65–81. doi:10.1177/0952695106066542CrossRefGoogle Scholar
  22. McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In P. Zaremba (Ed.), Frontiers in economics (pp. 105–142). New York: Academic Press.Google Scholar
  23. Oden, G. C. (1977). Fuzziness in semantic memory: Choosing exemplars of subjective categories. Memory & Cognition, 5, 198–204.Google Scholar
  24. Onukogu, I. B. (1985). An analysis of variance of nominal data. Biometrical Journal, 27, 375–383. doi:10.1002/bimj.4710270404CrossRefGoogle Scholar
  25. Pesarin, F., & De Martini, D. (2002). On unbiasedness and power of permutation tests. Metron, 60, 3–19.Google Scholar
  26. Rodgers, J. L. (2000). The bootstrap, the jackknife, and the randomization test: A sampling taxonomy. Multivariate Behavioral Research, 34, 441–456.CrossRefGoogle Scholar
  27. Shaffer, J. P. (1973). Defining and testing hypotheses in multidimensional contingency tables. Psychological Bulletin, 79, 127–141. doi:10.1037/h0033865CrossRefGoogle Scholar
  28. Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103, 677–680. doi:10.1126/science.103.2684.677CrossRefGoogle Scholar
  29. Stevens, S. S. (1951). Mathematics, measurement, and psychophysics. In S. S. Stevens (Ed.), Handbook of experimental psychology (pp. 1–41). New York: Wiley.Google Scholar
  30. Weiss, D. J. (2006). Analysis of variance and functional measurement: A practical guide. New York: Oxford University Press.Google Scholar

Copyright information

© Psychonomic Society, Inc. 2009

Authors and Affiliations

  1. 1.California State UniversityLos Angeles

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