Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-07T18:28:59.138Z Has data issue: false hasContentIssue false
  • English
  • Français

An Empirical Comparison of Several Interval Estimation Procedures for Coefficient Alpha

Published online by Cambridge University Press:  01 January 2025

Tej N. Pandey  and
Lawrence Hubert
Tej N. Pandey
Affiliation:
The University of Wisconsin
Lawrence Hubert
Affiliation:
The University of Wisconsin
Get access Rights & Permissions [Opens in a new window]

Abstract

Following a general introduction to Tukey’s Jackknife technique and the construction of approximate confidence intervals, ten variants of the procedure are defined for giving interval estimates for coefficient alpha. A data base of known population characteristics was generated and used to compare the robustness of the ten Jackknife alternatives with Feldt’s well-known sampling theory based upon the assumptions of normality. The empirical results indicate that out of the ten variants, defined by five transformations and two methods of data subdivision, only two are justifiable competitors to Feldt’s approach.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 2 , June 1975 , pp. 169 - 181
Copyright
Copyright © 1975 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

Presently at the Office of Program Evaluation and Research, California Department of Education, Sacramento, California.

References

Arvesen, J. N.. Jackknifing U-statistics. Annals of Mathematical Statistics, 1969, 40, 2076–2100.CrossRefGoogle Scholar
Arvesen, J. N. and Schmitz, T. H.. Robust procedures for variance component problems using the jackknife. Biometrics, 1970, 26, 677–686.CrossRefGoogle Scholar
Bay, K. S. An empirical investigation of the sampling distribution of the reliability coefficient estimates based on Alpha and KR20 via computer simulation under various models and assumptions. Unpublished Doctoral Dissertation, University of Alberta, 1971.Google Scholar
Collins, J. R.. Jackknifing generalizability, 1970, Boulder, Colorado: University of Colorado.Google Scholar
Cronbach, L. J., Gleser, G. C., Nanda, H., and Rajaratnam, N.. The dependability of behavioral measurements, 1972, New York: Wiley.Google Scholar
Donaldson, T. S.. Robustness of the F-test to errors of both kinds and the correlation between the numerator and denominator of the F-ratio. Journal of American Statistical Association, 1968, 63, 660–676.CrossRefGoogle Scholar
Ebel, H. W.. Estimation of reliability of ratings. Psychometrika, 1951, 16, 407–424.CrossRefGoogle Scholar
Feldt, L. S.. The approximate sampling distribution of Kuder-Richardson reliability coefficient twenty. Psychometrika, 1965, 30, 357–370.CrossRefGoogle ScholarPubMed
Jackson, R. W. and Ferguson, G. A.. Studies on the reliability of tests. Bulletin No. 12, 1941, Toronto: University of Toronto Press.Google Scholar
Kristof, W.. The statistical theory of stepped-up reliability coefficients when a test has been divided into several equivalent parts. Psychometrika, 1963, 28, 221–238.CrossRefGoogle Scholar
Kristof, W.. On the sampling theory of reliability estimation. Journal of Mathematical Psychology, 1970, 7, 371–377.CrossRefGoogle Scholar
Leone, F. C., Nelson, L. S.. Sampling distributions of variance components I. Empirical studies of balanced nested designs. Technometrics, 1966, 8, 457–468.CrossRefGoogle Scholar
Lord, F. M. and Novick, M. R.. Statistical theories of mental test scores, 1968, Reading, Mass.: Addison-Wesley.Google Scholar
Lord, F. M.. Variance stabilizing transformations of the stepped-up reliability coefficient. Journal of Educational Measurement, 1974, 11, 55–57.CrossRefGoogle Scholar
Miller, R. G. Jr.. A trustworthy jackknife. Annals of Mathematical Statistics, 1964, 35, 1594–1605.CrossRefGoogle Scholar
Miller, R. G. Jr.. Jackknifing variances. Annals of Mathematical Statistics, 1968, 39, 567–582.CrossRefGoogle Scholar
Mosteller, F. and Tukey, J. W.. Data analysis, including statistics. In Lindzey, G. and Aronson, E. (Eds.), Handbook of social psychology, 1968, Reading, Mass.: Addison-Wesley.Google Scholar
Nitko, A. J. The power functions of some proposed tests for the significance of coefficient alpha. Paper presented at the annual convention of the American Educational Research Association, Los Angeles, California, February, 1969.Google Scholar
Pandey, T. N.. The robustness of interval estimation of coefficient alpha using the jackknife procedure, 1973, Madison: University of Wisconsin.Google Scholar
Quenouille, M.. Approximate tests of correlation in time series. Journal of Royal Statistical Society, 1949, 11, 68–84.CrossRefGoogle Scholar
Quenouille, M.. Notes on bias in estimation. Biometrika, 1956, 43, 353–360.CrossRefGoogle Scholar
Rogers, W. T.. Jackknifing disattenuated correlations, 1971, Boulder, Colorado: University of Colorado.Google Scholar
Scheffé, H.. The analysis of variance, 1959, New York: Wiley.Google Scholar
Tukey, J. W.. Bias and confidence in not-quite large samples (abstract). Annals of Mathematical Statistics, 1958, 29, 614–614.Google Scholar