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 onF tests. The results indicate that as the number of random effects included in the experiment increase, moreF tests are unbiased, and that some of these are validF tests. However, whenF test bias does occur it is almost always of a negative nature so that the conclusions stated are conservative ones. PositiveF test bias may occur when the triple interaction is extant and when zero or one random variate is included in the experiment.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson R. L. and Bancroft, T. A.Statistical theory in research. New York: McGraw-Hill, 1952.
Gourlay, N.F-test bias for experimental designs of the Latin square type.Psychometrika, 1955,20, 273–287.
Greenwood, J. A. Analysis of variance and components of variance factorial experiments. Unpublished paper, Bureau of Aeronautics, 1956 (revised).
Kempthorne, O.The design and analysis of experiments. New York: Wiley, 1952.
Lindquist, E. F.Design and analysis of experiments in psychology and education. New York: Houghton Mifflin, 1953.
McNemar, Q. On the use of Latin squares in psychology.Psychol. Bull., 1951,48, 398–401.
McNemar, Q.Psychological statistics. New York: Wiley, 1955.
Mood, A. M.Introduction to the theory of statistics. New York: McGraw-Hill, 1950.
Tukey, J. W. Interaction in a row by column design. Memorandum Report 18, Princeton Univ., 1949.
Wilk, M. B. and Kempthorne, O. Non-additivities in a Latin square design.J. Amer. statist. Ass., 1957,52, 218–236.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gaito, J. The single latin square design in psychological research. Psychometrika 23, 369–378 (1958). https://doi.org/10.1007/BF02289785
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02289785