Change-over designs

TR Number
Date
1970
Journal Title
Journal ISSN
Volume Title
Publisher
Virginia Polytechnic Institute and State University
Abstract

When it is necessary to apply several different treatments in succession to a given subject, the residual effect of one treatment on another must be taken into consideration. A number of various designs have been developed for this purpose. A number of them are presented in this paper and can be summarized as follows:

Type I: Balanced for first-order residual effects. For n, the number of treatments, even, any number of Latin squares can be used; for n odd, an even number of squares is necessary.

Type II: Formed by repeating the final period of Type I designs. Direct and residual effects are orthogonal.

Type III: Formed from p<n corresponding rows of n-1 orthogonal nxn Latin squares.

Type IV: Complete orthogonality except for subjects and residuals. Very efficient but large numbers of observations are necessary.

Type V: Designs balanced for first and second order effects. Also formed from orthogonal Latin squares.

Type VI: Designs orthogonal for direct, first and second order residuals. Designs presented for n=2, 3 and 5.

Type VII: Orthogonal for linear, quadratic, ...components of direct and linear component of residual effects. Analysis includes linear direct x linear residual interaction. Designs given for n = 4, 5.

Type VIII: Type II designs analyzed under model for Type VII designs. Less efficiency, but designs available for all n.

Type IX: Designs useful for testing more than one treatment and direct x residual interactions.

Analysis for most designs includes normal equations, analysis of variance, variances of estimates, expected mean squares, efficiencies and missing value formulas.

A list of designs is presented in an appendix.

Description
Keywords
Citation
Collections