A General Least Squares Solution for Successive Intervals | Psychometrika | Cambridge Core (original) (raw)

Abstract

A general least squares solution for successive intervals is presented, along with iterative procedures for obtaining stimulus scale values, discriminal dispersions, and category boundaries. Because provisions for weighting were incorporated into the derivation, the solution may be applied without loss of rigor to the typical experimental matrix of incomplete data, i.e., to a data matrix with missing entries, as well as to the rarely occurring matrix of complete data. The use of weights also permits adjustments for variations in the reliability of estimates obtained from the data. The computational steps involved in the solution are enumerated, the amount of labor required comparing favorably with other procedures. A quick, yet accurate, graphical approximation suggested by the least squares derivation is also described.

References

Bishop, Ruth Points of neutrality in social attitudes of delinquents and non-delinquents. Psychometrika, 1940, 5, 35–45CrossRef Google Scholar

Edwards, A. L. The scaling of stimuli by the method of successive intervals. J. appl. Psychol., 1952, 36, 118–122CrossRef Google Scholar

Finney, D. J. Probit analysis, New York: Cambridge Univer. Press, 1952Google Scholar

Fisher, R. A. Theory of statistical estimation. Proc. Cam. Phil. Soc., 1925, 22, 700–725CrossRef Google Scholar

Garner, W. R. and Hake, H. W. The amount of information in absolute judgments. Psychol. Rev., 1951, 58, 446–459CrossRef Google Scholar

Green, B. F. Attitude measurement. In Lindzey, G. (Eds.), Handbook of social psychology, Cambridge, Mass.: Addison-Wesley, 1954Google Scholar

Guilford, J. P. Psychometric methods, New York: McGraw-Hill, 1936Google Scholar

Guilford, J. P. The computation of psychological values from judgments in absolute categories. J. exp. Psychol., 1938, 22, 32–42CrossRef Google Scholar

Gulliksen, H. A least squares solution for successive intervals assuming unequal standard deviations. Psychometrika, 1954, 19, 117–139CrossRef Google Scholar

Kendall, M. G. The advanced theory of statistics. II, London: Griffin, 1948Google Scholar

Messick, S., Tucker, L., and Garrison, H. A punched card procedure for the method of successive intervals. Princeton: Educational Testing Service, Research Bulletin 55-25.Google Scholar

Mosier, C. I. A modification of the method of successive intervals. Psychometrika, 1940, 5, 101–107CrossRef Google Scholar

Rimoldi, H. J. A. and Hormaeche, Marceva. The law of comparative judgment in the successive intervals and graphic rating scale methods. Princeton: Educational Testing Service, Research Bulletin 54-5.Google Scholar

Saffir, M. A comparative study of scales constructed by three psychophysical methods. Psychometrika, 1937, 2, 179–198CrossRef Google Scholar

Thurstone, L. L. A method of scaling psychological and educational tests. J. educ. Psychol., 1925, 16, 433–451CrossRef Google Scholar

Thurstone, L. L. The unit of measurement in educational scales. J. educ. Psychol., 1927, 18, 505–524CrossRef Google Scholar

Thurstone, L. L. and Chave, E. J. The measurement of attitude, Chicago: Univer. Chicago Press, 1929Google Scholar

Torgerson, W. S. A law of categorical judgment. In Clark, L. S. (Eds.), Consumer behavior, New York: New York Univer. Press, 1954Google Scholar

Torgerson, W. S. Theory and method of scaling. Social Science Research Council (to be published).Google Scholar

Tucker, L. R. A level of proficiency scale for a unidimensional skill. Amer. Psychologist, 1952, 7, 408–408. (Abstract)Google Scholar