Abstract
When the purpose of the experiment is to compare treatments, the Sequences × Positions Latin Square has been employed to control unwanted effects attributable to individuals, position, and sequence. This particular Latin Square has been subjected to criticism on the grounds there is confounding due to structure, random variables, and subject interactions. Special Latin Square, a subclass of the Sequences × Positions Latin Square, is basically ap ×p factorial design in blocks of sizep. The two factors are treatments (T) and positions (P). Sequence is one component of theTP interaction, and square uniqueness is the sum of the remaining components. This completely replicated factorial design has no structural or random variable confounding; if subject interactions are present, square uniqueness may be used as the error term and the bias in the test of treatments will be conservative.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cochran, W. and Cox, G.Experimental designs (2nd ed.). New York: Wiley, 1957.
Edwards, A. L.Experimental design in psychological research. New York: Holt, Rinehart and Winston, 1960.
Federer, W. T.Experimental design. New York: Macmillan, 1955.
Fisher, R. A.The design of experiments (5th ed.). London: Oliver and Boyd, 1949.
Gaito, J. The single Latin Square in psychological research.Psychometrika, 1958,23, 369–378.
Grant, D. A. The Latin Square principle in the design and analysis of psychological experiments.”Psychol. Bull., 1948,45, 427–442.
Grant, D. A. The statistical analysis of a frequent experimental design.Amer. J. Psychol., 1949,62, 119–122.
Gourlay, N. F-test bias for experimental design of the Latin Square type.Psychometrika, 1955,20, 273–287.
Lindquist, E. G.Design and analysis of experiments in psychology and education. Boston: Houghton Mifflin, 1953.
McNemar, Q.Psychological statistics (2nd ed.). New York: Wiley, 1955.
Mood, A. M.Introduction to the theory of statistics. New York: McGraw-Hill, 1950.
Wilk, M. B. and Kempthorne, O. Non-additivities in a Latin Square Design.J. Amer. statist. Ass., 1957,52, 218–236.
Winer, B. J.Statistical principles in experimental design. New York: McGraw-Hill, 1962.
Author information
Authors and Affiliations
Additional information
D. T. Graham aroused the author's interest in writing this paper. Thanks are expressed to Professor Graham and to Professor David A. Grant for their very helpful readings of earlier versions of this manuscript.
Rights and permissions
About this article
Cite this article
Benjamin, L.S. A special latin square for the use of each subject “as his own control”. Psychometrika 30, 499–513 (1965). https://doi.org/10.1007/BF02289540
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02289540