Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-08T16:53:29.175Z Has data issue: false hasContentIssue false
  • English
  • Français

F-Test Bias for Experimental Designs in Educational Research

Published online by Cambridge University Press:  01 January 2025

Neil Gourlay
Neil Gourlay*
Affiliation:
University of Birmingham
Get access Rights & Permissions [Opens in a new window]

Abstract

Reference is made to Neyman's study of F-test bias for the randomized blocks and Latin square designs employed in agriculture, and some account is given of later statistical developments which sprang from his work—in particular, the classification of model-types and the technique of variance component analysis. It is claimed that there is a need to carry out an examination of F-test bias for experimental designs in education and psychology which will utilize the method and, where appropriate, the known' results of this new branch of variance analysis. In the present paper, such an investigation is carried out for designs which may be regarded as derivatives of the agricultural randomized blocks design. In a paper to follow, a similar investigation will be carried out for experimental designs of the Latin square type.

Type
Original Paper
Information
Psychometrika , Volume 20 , Issue 3 , September 1955 , pp. 227 - 248
Copyright
Copyright © 1955 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.)

References

Alexander, H. W.. The estimation of reliability when several trials are available. Psychometrika, 1947, 12, 79–99CrossRefGoogle ScholarPubMed
Cochran, W. G.. Some consequences when the assumptions for the analysis of variance are not satisfied. Biometrics, 1947, 3, 22–38CrossRefGoogle Scholar
Cochran, W. G.. Testing a linear relation among variances. Biometrics, 1951, 7, 17–32CrossRefGoogle ScholarPubMed
Cochran, W. G., Cox, G. M.. Experimental designs, New York: Wiley, 1950Google Scholar
Crump, S. L.. The present status of variance component analysis. Biometrics, 1951, 7, 1–16CrossRefGoogle ScholarPubMed
Diamond, S.. Comment on “A qualification in the use of analysis of variance. Psychol. Bull., 1952, 49, 151–154CrossRefGoogle ScholarPubMed
Edwards, A. L.. Experimental design in psychological research, New York: Rinehart, 1950Google Scholar
Eisenhart, C.. The assumptions underlying analysis of variance. Biometrics, 1947, 3, 1–21CrossRefGoogle ScholarPubMed
Johnson, N. L.. Alternative systems in the analysis of variance. Biometrika, 1948, 36, 80–87CrossRefGoogle Scholar
Kendall, M. G.. The advanced theory of statistics, II, London: Griffin, 1946Google Scholar
Lindquist, E. F.. Goodness of fit of trend curves and significance of trend differences. Psychometrika, 1947, 12, 65–78CrossRefGoogle ScholarPubMed
Lindquist, E. F.. Statistical analysis in educational research, New York: Houghton Mifflin, 1940Google Scholar
McNemar, Q.. On the use of Latin squares in psychology. Psychol. Bull., 1951, 48, 398–401CrossRefGoogle ScholarPubMed
Neyman, J.. Statistical problems in agricultural experimentation. Suppl. J. roy. statist. Soc., 1935, 2, 107–154CrossRefGoogle Scholar
Smith, H. F.. Analysis of variance with unequal but proportionate numbers of observations in the subclasses of a two-way classification. Biometrics, 1951, 7, 70–74CrossRefGoogle ScholarPubMed
Snedecor, G. W.. The method of expected numbers for tables of multiple classification with disproportionate subclass numbers. J. Amer. statist. Assoc., 1934, 29, 389–393CrossRefGoogle Scholar
Snedecor, G. W.. Statistical methods, Ames, Iowa: Iowa State College Press, 1946Google ScholarPubMed
Tsao, F.. General solution of the analysis of variance and covariance in the case of unequal or disproportionate numbers of observations in the subclasses. Psychometrika, 1946, 11, 107–128CrossRefGoogle Scholar
Webb, W. B., Lemmon, V. W.. A qualification in the use of analysis of variance. Psychol. Bull., 1950, 47, 130–136CrossRefGoogle Scholar
Welch, B. L.. On the z-test in randomized blocks and Latin squares. Biometrika, 1937, 29, 21–52CrossRefGoogle Scholar