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A Special Latin Square for the Use of Each Subject “As His Own Control”

Published online by Cambridge University Press:  01 January 2025

Lorna S. Benjamin
Lorna S. Benjamin*
Affiliation:
University of Wisconsin
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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 a p ×p factorial design in blocks of size p. The two factors are treatments (T) and positions (P). Sequence is one component of the TP 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.

Type
Original Paper
Information
Psychometrika , Volume 30 , Issue 4 , December 1965 , pp. 499 - 513
Copyright
Copyright © 1965 Psychometric Society

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Footnotes

*

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.

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