Skip to main content
SpringerLink
Log in

Some Multivariate Developments in Nonparametric Statistics

  • Chapter
Handbook of Multivariate Experimental Psychology

Part of the book series: Perspectives on Individual Differences ((PIDF))

Abstract

The growing popularity of nonparametric statistics (Lehmann, 1975) is attested to by the proliferation of new techniques in the last couple of decades. Whereas early formulations of nonparametric statistics concentrated on uni- and bivariate techniques—a shortcoming that was identified by Siegel (1956)—in the last 20 years there has been a clear accent on their development for multivariate application. Although the multivariate implementation of nonparametric statistics is of central concern in this chapter, in order to provide a basis for an evaluation of these procedures it is necessary to deal first with some basic problems. Specifically, in this section two fundamental issues will be addressed: (1) the meaning of the term nonparametric and (2) its relation to the term distribution free, which is often used synonymously. Before beginning the discussion of nonparametric techniques, a brief overview of such critical terms as multivariate and nonparametric will be given.

This chapter was written while the author was Senior Research Scientist at the Max Planck Institute for Human Development and Education, Berlin, Federal Republic of Germany.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ashby, W. R. Measuring the internal informational exchange in a system. Cybernetica, 1965, 8, 5–22.

    Google Scholar 

  • Attneave, F. Applications of information theory to psychology. New York: Holt, 1959.

    Google Scholar 

  • Bishop, Y. M., Fienberg, S. E., and Holland, P. W. Discrete multivariate analysis: Theory and practice. Cambridge, Mass.: MIT Press, 1975.

    Google Scholar 

  • Bock, H. H. Explorative Datenanalyse. In N. Victor, W. Lehmacher, and W. van Eimeren (Eds.), Explorative Datenanalyse. Berlin: Springer, 1980.

    Google Scholar 

  • Bradley, J. V. Distribution-free statistical tests. Englewood Cliffs, N.J.: Prentice-Hall, 1968.

    Google Scholar 

  • Brandtstädter, J., and von Eye, A. Aussagenlogische Analyse von Kontingenztafeln I. Methodologische Vorüberlegungen. Trierer Psychologische Berichte,1982, 9, No. 6.

    Google Scholar 

  • Bredenkamp, J. Nonparametrische Prüfung von Wechselwirkungen. Psychologische Beiträge, 1974, 16, 398–416.

    Google Scholar 

  • Broekstra, G. Constraint analysis and structure identification, Annals of Systems Research, 1976, 5, 67–80.

    Google Scholar 

  • Broekstra, G. Constraint analysis and structure identification II. Annals of Systems Research, 1977a, 6, 1–20.

    Google Scholar 

  • Broekstra, G. Structure modeling. A constraint (information) analytic approach. In G. J. Klir (Ed.), Applied general systems research: Recent developments and trends. New York: Plenum Press, 1977b.

    Google Scholar 

  • Broekstra, G. On the representation and identification of structure systems. International Journal of Systems Science, 1978a, 9, 1271–1293.

    Google Scholar 

  • Broekstra, G. Symplifying data systems: An information theoretic analysis. In R. Trappl, G. J. Klir, and L. Ricciardi (Eds.), Progress in Cybernetics and Systems Research. Vol. III. New York: Wiley, 1978b.

    Google Scholar 

  • Broekstra, G. Two methods of constraint analysis. Progress in Cybernetics and Systems Research, 1980, 7, 13–23.

    Google Scholar 

  • Brunner, E., and Neumann, N. Rank tests for the 2 × 2 split plot design. Biometrical Journal,1988 (in press).

    Google Scholar 

  • Büning, H., and Trenkler, G. Nichtparametrische statistische Methoden. Berlin: de Gruyter, 1978.

    Google Scholar 

  • Cochran, W. G. Some methods for strengthening the common e-test. Biometrics, 1954, 10, 417–451.

    Google Scholar 

  • Cooley, W. W., and Lohnes, P. R. Multivariate data analysis. New York: Wiley, 1971.

    Google Scholar 

  • Cox, D. R., and Small, N. J. H. Testing multivariate normality. Biometrika, 1978, 65, 263–272.

    Google Scholar 

  • Desarbo, W. S. Gennclus: New models for general nonhierarchical clustering analysis. Psychometrika, 1982, 47, 449–475.

    Google Scholar 

  • Enke, H. Considering of certain relevant information in the analysis of contingency tables: A three-step procedure. Biometrical Journal, 1982, 24, 579–606.

    Google Scholar 

  • Erdfelder, E. Multivariate Rangvarianzanalyse: Ein nonparametrisches Analogon zur ein-und mehrfaktoriellen MANOVA. Trierer Psychologische Berichte, 1981, 8,No. 12.

    Google Scholar 

  • Froman, T., and Hubert, L. J. Application of prediction analysis to developmental priority. Psychological Bulletin, 1980, 87, 136–146.

    Google Scholar 

  • Ghosh, M., Grizzle, J. E., and Sen, P. K. Nonparametric methods in longitudinal series, Journal of the American Statistical Association, 1973, 68, 29–36.

    Google Scholar 

  • Gibbons, J. D. Nonparametric methods for quantitative analysis. New York: Holt, Rinehart & Winston, 1976.

    Google Scholar 

  • Gokhale, D. V., and Kullback, S. The information in contingency tables. New York: Dekker, 1978.

    Google Scholar 

  • Goodman, L. A., and Kruskal, W. H. Measures of association for cross classifications. Journal of the American Statistical Association, 1954, 49, 732–764.

    Google Scholar 

  • Goodman, L. A., and Kruskal, W. H. More about evaluation of formal theory. Journal of Mathematical Sociology, 1974a, 3, 209–211.

    Google Scholar 

  • Goodman, L. A., and Kruskal, W. H. Empirical evaluation of formal theory. Journal of Mathematical Sociology, 1974b, 3, 187–196.

    Google Scholar 

  • Häjek, P. Automatic listing of important observational statements I. Kybernetika, 1973a, 9, 187–205.

    Google Scholar 

  • Häjek, P. Automatic listing of important observational statements II. Kybernetika, 1973b, 9, 251–271.

    Google Scholar 

  • Häjek, P. Automatic listing of important observational statements III. Kybernetika, 1974, 10, 95–124.

    Google Scholar 

  • Hâjek, P., and Havränek, T. Mechanizing hypothesis formation: Mathematical foundation for a general theory. Berlin: Springer, 1978.

    Google Scholar 

  • Häjek, P., and Havränek, T. The GUHA method—Its aims and techniques (twenty-four questions and answers). International Journal of Man–Machine Studies, 1981, 10, 23–28.

    Google Scholar 

  • Häjek, P., and Sidak, Z. Theory of rank tests. Prague: Academia, 1971.

    Google Scholar 

  • Häjek, P., Havel, I., and Chytil, M. The GUHA method of automatic hypotheses determination. Computing, 1966, 1, 293–308.

    Google Scholar 

  • Hâjek, P., Havränek, T., and Chytil, M. K. Methoda GUHA: Automatickk tvorba hypotéz. Prague: Academia, 1983.

    Google Scholar 

  • Hartigan, J. A. Clustering algorithms. New York: Wiley, 1975.

    Google Scholar 

  • Härtner, R., Mattes, K., and Wottawa, H. Computergestützte Hypothesenagglutination zur Erfassung komplexer Zusammenhänge. EDV in Medizin und Biologie, 1980, 11, 53–59.

    Google Scholar 

  • Havränek, T. Statistical quantifiers in observational calculi: An application in GUHA methods. Theory and Decision, 1975, 6, 213–230.

    Google Scholar 

  • Havränek, T. Some comments on the GUHA procedures. In N. Viktor, W. Lehmacher, and W. van Eimeren (Eds.), Explorative Datenanalyse. Berlin: Springer, 1980.

    Google Scholar 

  • Havrânek, T. The GUHA method in the context of data analysis. International Journal of Man—Machine Studies, 1981a, 10, 265–282.

    Google Scholar 

  • Havrânek, T. Formal systems for mechanized statistical inference. International Journal of Man—Machine Studies, 1981b, 10, 333–350.

    Google Scholar 

  • Hildebrand, D. K., Laing, J. D., and Rosenthal, H. Prediction logic: A method for empirical evaluation of formal theory. Journal of Mathematical Sociology, 1974a, 3, 163–185.

    Google Scholar 

  • Hildebrand, D. K., Laing, J. D., and Rosenthal, H. Prediction logic and quasi-independence in empirical evaluation of formal theory. Journal of Mathematical Sociology, 1974b, 3, 197–209.

    Google Scholar 

  • Hildebrand, D. K., Laing, J. D., and Rosenthal, H. Prediction analysis in political research. American Political Science Review, 1976, 70, 509–535.

    Google Scholar 

  • Hildebrand, D. K., Laing, J. D., and Rosenthal, H. Prediction analysis of cross classifications. New York: Wiley, 1977.

    Google Scholar 

  • Hildebrand, D. K., Laing, J. D., and Rosenthal, H. Prediction analysis in economic models. In J. Kmenta and J. B. Ramsey (Eds.), Evaluation of economic models. New York: Academic Press, 1980.

    Google Scholar 

  • Holm, S., A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 1979, 6, 65–70.

    Google Scholar 

  • Ito, P. K. Robustness of ANOVA and MANOVA test procedures. In P. R. Krishnaiah (Ed.), Handbook of statistics. Vol. 1. Amsterdam: North-Holland, 1980.

    Google Scholar 

  • Kaskey, G., Kolman, B., Krishnaiah, P. R., and Steinberg, L. Transformations to normality. In P. R. Krishnaiah (Ed.), Handbook of statistics. Vol. 1. Amsterdam: North-Holland, 1980.

    Google Scholar 

  • Katz, B. M., and McSweeney, M. A multivariate Kruskal—Wallis test with post hoc procedures. Multivariate Behavioral Research, 1980, 15, 281–298.

    Google Scholar 

  • Krauth, J. Nichtparametrische Ansätze zur Auswertung von Verlaufskurven. Biometrische Zeitschrift, 1973, 15, 557–566.

    Google Scholar 

  • Krauth, J. Ein Vergleich der KFA mit der Methode der log-linearen Modelle. Zeitschrift für Sozialpsychologie, 1980, 11, 233–247.

    Google Scholar 

  • Krauth, J. Techniques of classification in psychology I: Factor analysis, multidimensional scaling, latent structure analysis. International Classification, 1981, 8, 126–132.

    Google Scholar 

  • Krauth, J. Techniques of classification in psychology II: Cluster analysis, typal analysis, configurai frequency analysis, discriminant analysis, regression analysis. International Classification, 1982, 9, 1–10.

    Google Scholar 

  • Krauth, J., and Lienert, G. A. KFA: Die Konfigurationsfrequenzanalyse und ihre Anwendung in Psychologie und Medizin. Freiburg: Alber, 1973.

    Google Scholar 

  • Krauth, J., and Lienert, G. A. Nonparametric two-sample comparison of learning curves based on orthogonal polynomials. Psychological Research, 1978, 40, 159–171.

    Google Scholar 

  • Krauth, J., and Lienert, G. A. Multivariate nonparametric techniques in psychological research. Psychologische Beiträge, 1981, 23, 226–241.

    Google Scholar 

  • Krippendorff, K. A spectral analysis of relations. Paper presented at the International Congress of Communication Sciences, Berlin, May 1977.

    Google Scholar 

  • Krippendorff, K., PARTITI: A spectral analysis of relations with partitioning option. Unpublished FORTRAN program, University of Pennsylvania, 1978.

    Google Scholar 

  • Krippendorff, K. An algorithm for identifying structural models of multivariate data. International Journal of General Systems, 1981, 7, 1–17.

    Google Scholar 

  • Krippendorff, K. Regression analysis using information theory. Paper presented at the 26th Annual Conference of the Society for General Systems Research, Washington, D.C., 1982.

    Google Scholar 

  • Krueger, H. P. Zur Anwendungsindikation von nonparametrischen Prädiktionsverfahren. Zeitschrift für Sozialpsychologie, 1979, 10, 94–104.

    Google Scholar 

  • Kruskal, W. H., and Wallis, W. A. Use of ranks in one criterion variance analysis. Journal of the American Statistical Association, 1952, 47, 583–621.

    Google Scholar 

  • Ku, H. H., Varner, R. M., and Kullback, S. On the analysis of multidimensional contingency tables. Journal of the American Statistical Association, 1971, 66, 55–64.

    Google Scholar 

  • Kullback, S. Information theory and statistics. New York: Wiley, 1959.

    Google Scholar 

  • Lancaster, H. O. The chi-squared distribution. New York: Wiley, 1969.

    Google Scholar 

  • Lehmacher, W. A more powerful simultaneous test procedure in configurai frequency analysis. Biometrical Journal, 1981, 23, 429–436.

    Google Scholar 

  • Lehmacher, W., and Lienert, G. A. Die Konfigurationsfrequenzanalyse XVI. Neue Tests gegen Typen und Syndrome. Zeitschrift für Klinische Psychologie und Psychotherapie, 1982, 30, 5–11.

    PubMed  Google Scholar 

  • Lehmann, E. L. Nonparametrics. San Francisco: Holden-day, 1975.

    Google Scholar 

  • Lienert, G. A. Die “Konfigurationsfrequenzanalyse” als Klassifikationsmethode in der klinischen Psychologie. In M. Irle (Ed.), Bericht über den 26. Kongress der Deutschen Gesellschaft für Psychologie in Tübingen 1968. Göttingen: Hogrefe, 1969.

    Google Scholar 

  • Lienert, G. A. Verteilungsfreie Methoden in der Biostatistik. Vol. 1 ( 2nd ed. ). Meisenheim am Glan: Hain, 1973.

    Google Scholar 

  • Lienert, G. A. Verteilungsfreie Methoden in der Biostatistik. Tafelband. Meisenheim am Glan: Hain, 1975.

    Google Scholar 

  • Lienert, G. A. Verteilungsfreie Methoden in der Biostatistik. Vol. 2. Meisenheim am Glan: Hain, 1978.

    Google Scholar 

  • Lienert, G. A., and Krauth, J. Die Konfigurationsfrequenzanalyse IX. Auswertung multivariater klinischer Versuchspläne (Teil 1). Zeitschrift für klinische Psychologie und Psychotherapie, 1974a, 22, 3–17.

    PubMed  Google Scholar 

  • Lienert, G. A., and Krauth, J. Die Konfigurationsfrequenzanalyse IX. Auswertung multivariater klinischer Versuchspläne (Teil 2). Zeitschrift für klinische Psychologie und Psychotherapie, 1974b, 22, 108–121.

    PubMed  Google Scholar 

  • Lienert, G. A., and Krauth, J. Configurai frequency analysis as a statistical tool for defining types. Educational and Psychological Measurement, 1975, 35, 231–238.

    Google Scholar 

  • Lindner, K. Eine exakte Auswertungsmethode zur Konfigurationsfrequenzanalyse. Psychologische Beiträge, 1984, 26, 393–415.

    Google Scholar 

  • Mittenecker, E., and Raab, E. Informationstheorie für Psychologen. Göttingen: Hogrefe, 1973.

    Google Scholar 

  • Moore, A. S. The effect of dependence on chi-squared tests of fit. The Annals of Statistics, 1982, 10, 1163–1171.

    Google Scholar 

  • Opp, K. D. Methodologie der Sozialwissenschaften. Reinbek: Rowohlt, 1970.

    Google Scholar 

  • Paivio, A. D. Imagery and verbal processes. New York: Holt, Rinehart & Winston, 1971.

    Google Scholar 

  • Plackett, R. L. Multidimensional contingency tables, a survey of models and methods. Bulletin of the International Institute of Statistics, 1969, 43, 133–142.

    Google Scholar 

  • Pokorny, D., and Havränek, T. On some procedures for identifying sources of independence in contingency tables. In L. C. A. Corsten and J. Hermans (Eds.), Compstat 1978: Proceedings in Computational Statistics. Würzburg: Physica, 1978.

    Google Scholar 

  • Pratt, J. W., and Gibbons, J. D. Concepts of nonparametric theory. Berlin, Springer, 1981.

    Google Scholar 

  • Puri, M. L., and Sen, P. K. Nonparametric methods in multivariate analysis. New York: Wiley, 1971.

    Google Scholar 

  • Quade, D. Nonparametric analysis of covariance by matching. Biometrics, 1982, 38, 579–611.

    Google Scholar 

  • Randless, R. H., and Wolfe, D. A. Introduction to the theory of nonparametric statistics. New York: Wiley, 1979.

    Google Scholar 

  • Rasch, D., Herrendörfer, G., Bock, J., and Busch, K. Verfahrensbibliothek Versuchsplanung und -auswertung. Vol. 1. East Berlin: Deutscher Landwirtschaftsverlag, 1978a.

    Google Scholar 

  • Rasch, D., Herrendörfer, G., Bock, J., and Busch, K. Verfahrensbibliothek Versuchsplanung und -auswertung. Vol. 2. East Berlin: Deutscher Landwirtschaftsverlag, 1978b.

    Google Scholar 

  • Rasch, D., Herrendörfer, G., Bock, J., and Busch, K. Verfahrensbibliothek Versuchsplanung und -auswertung. Vol. 3. East Berlin: Deutscher Landwirtschaftsverlag, 1981.

    Google Scholar 

  • Roeder, B. KFA-Programm, Version 3. Dortmund: Pädagogische Hochschule Ruhr, 1976.

    Google Scholar 

  • Samar, V. J., and Hoppe, C. NMANOVA: Non-parametric multivariate one-way analysis of variance. Applied Pschological Measurement, 1981, 5, 516.

    Google Scholar 

  • Sen, P. K. Nonparametric simultaneous inference for some MANOVA models. In P. R. Krishnaiah (Ed.), Handbook of statistics. Vol. 1. Amsterdam: North-Holland, 1980.

    Google Scholar 

  • Shannon, C. E., and Weaver, W. The mathematical theory of communication. Urbana: University of Illinois Press, 1949.

    Google Scholar 

  • Siegel, S. Nonparametric statistics. New York: McGraw-Hill, 1956.

    Google Scholar 

  • Tukey, J. W. Exploratory data analysis. Vol. 1. Reading, Mass.: Addison-Wesley, 1970.

    Google Scholar 

  • von Eye, A. Die Assoziationsstrukturanalyse auf informationstheoretischer Basis. Zeitschrift für klinische Psychologie und Psychotherapie, 1981, 29, 216–227.

    Google Scholar 

  • von Eye, A. On the equivalence of the information theoretic transmission measure to the common x 2-statistic. Biometrical Journal, 1982, 24, 391–398.

    Google Scholar 

  • von Eye, A. Structure identification using nonparametric models. In J. R. Nesselroade and A. von Eye (Eds.), Individual development and social change: Explanatory analysis. New York: Academic Press, 1985, pp. 125–154.

    Google Scholar 

  • von Eye, A., and Brandtstädter, J. Systematizing the results of configurai frequency analysis by minimizing Boolean functions. In H. Caussinus, P. Ettinger, and J. R. Mathieu (Eds.), Compstat 1982, Part II: Short Communications, summaries of posters. Vienna: Physica, 1982.

    Google Scholar 

  • von Eye, A., and Brandtstädter, J. Aussagenlogische Analyse von Kontingenztaftln II. Statistische Evaluation. Trierer Psychologische Berichte, 1983, 10,No. 2.

    Google Scholar 

  • von Eye, A., and Brandtstädter, J. Aussagenlogische Analyse von Kontingenztafeln III. Mehrdimensionale Designs. Trierer Psychologische Berichte, 1984, 11,No. 6.

    Google Scholar 

  • von Eye, A., and Brandtstädter, J. Evaluating developmental hypotheses using statement calculus and nonparametric statistics. In P. B. Baltes, D. L. Featherman, and R. M. Lerner (eds.). Life-span development and behavior. Vol. 8. Hillsdale, N.J.: Erlbaum, 1988.

    Google Scholar 

  • von Eye, A., and Lienert, G. A. Die Konfigurationsfrequenzanalyse XX. Typen und Syndrome zweiter Ordnung (Komplextypen). Zeitschrift für klinische Psychologie und Psychotherapie, 1984, 32, 345–355.

    Google Scholar 

  • Ward, J. H. Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 1963, 58, 236–244.

    Google Scholar 

  • Weaver, W. Recent contributions to the mathematical theory of communication. In C. E. Shannon and W. Weaver (Eds.), The mathematical theory of communication. Urbana: University of Illinois Press, 1949.

    Google Scholar 

  • Wise, U. E. Multinominal probabilities and the x 2 and the X 2 distributions. Biometrika, 1963, 50, 145–154.

    Google Scholar 

  • Wottawa, H. Allgemeine Aussagen in der psychologischen Forschung: eine Fiktion. In W. Michaelis (Ed.), Bericht über den 32. Kongress der Deutschen Gesellschaft für Psychologie in Zürich 1980. Vol. 1. Göttingen: Hogrefe, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Individual and Family Studies, College of Health and Human Development, The Pennsylvania State University, University Park, Pennsylvania, 16802, USA

    Alexander von Eye

Authors
  1. Alexander von Eye
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Pennsylvania State University, University Park, Pennsylvania, USA

    John R. Nesselroade

  2. University of Hawaii at Manoa, 96844, Honolulu, Hawaii, USA

    Raymond B. Cattell

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Plenum Press, New York

About this chapter

Cite this chapter

von Eye, A. (1988). Some Multivariate Developments in Nonparametric Statistics. In: Nesselroade, J.R., Cattell, R.B. (eds) Handbook of Multivariate Experimental Psychology. Perspectives on Individual Differences. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0893-5_11

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-0893-5_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8232-7

  • Online ISBN: 978-1-4613-0893-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation