Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-15T12:26:00.797Z Has data issue: false hasContentIssue false
  • English
  • Français

The Single Latin Square Design in Psychological Research

Published online by Cambridge University Press:  01 January 2025

John Gaito
John Gaito*
Affiliation:
Air Crew Equipment Laboratory, Philadelphia†
Get accessRights & Permissions [Opens in a new window]

Abstract

The expected value of mean square concept is used to determine the effects of the presence of interactions in the single Latin square design on F tests. The results indicate that as the number of random effects included in the experiment increase, more F tests are unbiased, and that some of these are valid F tests. However, when F test bias does occur it is almost always of a negative nature so that the conclusions stated are conservative ones. Positive F test bias may occur when the triple interaction is extant and when zero or one random variate is included in the experiment.

Information

Type
Original Paper
Information
Psychometrika , Volume 23 , Issue 4 , December 1958, pp. 369 - 378
Copyright
Copyright © 1958 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.)

Article purchase

Temporarily unavailable

Footnotes

†

Now at Wilkes College, Wilkes Barre, Pa.

References

Anderson, R. L. and Bancroft, T. A. Statistical theory in research, New York: McGraw-Hill, 1952.Google Scholar
Gourlay, N. F-test bias for experimental designs of the Latin square type. Psychometrika, 1955, 20, 273–287.10.1007/BF02289034CrossRefGoogle Scholar
Greenwood, J. A. Analysis of variance and components of variance factorial experiments. Unpublished paper, Bureau of Aeronautics, 1956 (revised).Google Scholar
Kempthorne, O. The design and analysis of experiments, New York: Wiley, 1952.10.1097/00010694-195205000-00012CrossRefGoogle Scholar
Lindquist, E. F. Design and analysis of experiments in psychology and education, New York: Houghton Mifflin, 1953.Google Scholar
McNemar, Q. On the use of Latin squares in psychology. Psychol. Bull., 1951, 48, 398–401.10.1037/h0060348CrossRefGoogle ScholarPubMed
McNemar, Q. Psychological statistics, New York: Wiley, 1955.Google Scholar
Mood, A. M. Introduction to the theory of statistics, New York: McGraw-Hill, 1950.Google Scholar
Tukey, J. W. Interaction in a row by column design. Memorandum Report 18, Princeton Univ., 1949.Google Scholar
Wilk, M. B. and Kempthorne, O. Non-additivities in a Latin square design. J. Amer. statist. Ass., 1957, 52, 218–236.Google Scholar