Abstract
Rescaling of nominal- and ordinal-scaled data to interval-scaled data is an important preparatory step prior to applying parametric statistical tests. Without rescaling, the analyst typically must resort to non-parametric tests that are less robust statistically than the metric counterparts. Multi-dimensional scaling (MDS) is a procedure that can be used to perform the desired rescaling. This paper utilizes MDS to transform nonmetric data from the IAN (Interactive Autism Network) and illustrates the application of the results to autism. Two simulated distributions were created from the MDS procedure to determine the best transformation. The tests reveal that either a normal or uniform distribution is acceptable with the uniform distribution performing marginally better than the normal.
Chapter PDF
Similar content being viewed by others
Keywords
References
IAN (Interactive Autism Network) (homepage on the Internet), Kennedy Krieger Institute, Baltimore (2007-2008), http://www.ianproject.org (cited November 13, 2008)
Cooper, D.R., Schindler, P.S.: Business Research Methods, 9th edn. Mc-Graw Hill Irwin, New York (2006)
DeVellis, R.F.: Scale Development Theory and Applications, 2nd edn. Sage Publications, Thousand Oaks (2003)
Green, P.E., Tull, D.S.: Research for Marketing Decisions, 4th edn. Prentice-Hall, Inc., Englewood Cliffs (1978)
Dawis, R.V.: Scale Construction. Journal of Counseling Psychology 34(4), 481–489 (1987)
Edwards, A.L.: Techniques of Attitude Scale Construction. Appleton-Century-Crofts, Inc., New York (1957)
Dunn-Rankin, P.: Scaling Methods. Lawrence Erlbaum Associates Publishers, Hillsdale (1983)
Thurstone, L.L.: A law of comparative judgment. Psychological Review 34, 273–286 (1927)
Thurstone, L.L.: The method of paired comparisons for social values. Journal of Abnormal and Social Psychology 21, 384–400 (1927)
Thurstone, L.L.: Psychophysical analysis. American Journal of Psychology 38(3), 368–389 (1927)
Andrich, D., Luo, G.: A hyperbolic cosine latent trait model for unfolding dichotomous single-stimulus responses. Applied Psychological Measurement 17(3), 253–276 (1993)
Andrich, D.: Relationships between the Thurstone and Rasch approaches to item scaling. Applied Psychological Measurement 2(3), 449–460 (1978)
Wright, B.D., Masters, G.N.: Rating Scale Analysis. Mesa Press, Chicago (1982)
McCartney, K., Burchinal, M.R., Bub, K.L.: Best Practices in Quantitative Methods for Developmentalists. Blackwell Publishing, Boston (2006)
Sapp, M.: Basic Psychological Measurement, Research Designs, and Statistics without Math. Charles C. Thomas Publisher, Ltd., Springfield (2006)
Harwell, M.R., Gatti, G.G.: Rescaling ordinal data to interval data in educational research. Review of Educational Research 71(1), 105–131
Kruskal, J.B., Wish, M.: Multidimensional Scaling. Sage Publications, Beverly Hills (1978)
Shepard, R.N.: The analysis of proximities: multidimensional scaling with an unknown distance function. Psychometrika 27, 125–140, 219–246 (1962)
Kruskal, J.B.: Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29(1), 1–27 (1964)
SAS Software (homepage on the Internet). Business Intelligence Software and Predictive Analytics, Cary, NC (2008), http://www.sas.com (cited November 13, 2008)
Abdi, H.: Bonferroni and Sidak corrections for multiple comparisons. In: Salkind (ed.) Encyclopedia of Measurement and Statistics, Sage, Thousand Oaks (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Engle, K.M., Forgionne, G.A. (2009). Rescaling Non-metric Data to Metric Data Using Multi-Dimensional Scaling. In: Aykin, N. (eds) Internationalization, Design and Global Development. IDGD 2009. Lecture Notes in Computer Science, vol 5623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02767-3_27
Download citation
DOI: https://doi.org/10.1007/978-3-642-02767-3_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02766-6
Online ISBN: 978-3-642-02767-3
eBook Packages: Computer ScienceComputer Science (R0)