A comparison of three methods of fitting the normal ogive
- 59 Downloads
The Mueller-Urban method of fitting the normal ogive is derived, and the inadequacies of its inherent assumptions are discussed. This and the unweighted least squares method are compared to the maximum likelihood solution which is shown to be very close to the “ideal” least squares solution. As an empirical demonstration of the superiority of the maximum likelihood solution, random ogives are fitted by all three methods and they are compared on the basis of the expected values and the standard errors of the estimates. It is concluded that the maximum likelihood solution is uniformly superior to the others in all respects.
KeywordsStandard Error Public Policy Statistical Theory Empirical Demonstration Inherent Assumption
Unable to display preview. Download preview PDF.
- Berkson, J. Tables for use in estimating the normal distribution function by normit analysis.Biometrika, 1957,44, 411–435.Google Scholar
- Cramer, E. M. Fitting the normal ogive on the IBM 650.J. ed. Measmt, 1962,22, 177–181.Google Scholar
- Cramer, E. M. The long-term effects of experience on judgments of loudness.Percept. mot. Skills, 1962,14, 271–280.Google Scholar
- Cornfield, J. and Mantel, N. Some new aspects of the application of maximum likelihood to the calculation of the dosage response curve.J. Amer. statist. Ass., 1950,45, 181–210.Google Scholar
- Finney, D. J. The application of probit analysis to the results of mental tests.Psychometrika, 1944,9, 31–39.Google Scholar
- Finney, D. J.Probit analysis. Cambridge, Eng.: Univ. Press, 1952.Google Scholar
- Guilford, J. P.Psychometric methods (2nd ed.). New York: McGraw-Hill, 1954.Google Scholar