Changeover designs balanced for the linear component of first residual effects

Abstract

SUMMARY A method of constructing changeover designs for testing a treatment factor at equally spaced levels is given. The designs are such that the degree of freedom for the linear component of first residual effects and the degree of freedom for the linear direct by linear residual interaction are both orthogonal to the degrees of freedom for linear, quadratic, etc., components of the direct effects. We consider the construction of changeover designs for v quantitative treatments applied at equally spaced levels of a single factor in which allowance is made for the presence of first residual effects. It was shown (Berenblut, 1964) that the well-known extra period designs due to Lucas, although allowing full information to be extracted concerning contrasts between residual effects, failed to orthogonalize direct and subject effects. We have described a system of designs enabling full information to be obtained on contrasts between direct effects; 2v periods and v2 subjects are required for testing v treatments. The designs also ensure that the degrees of freedom of direct x residual interaction are orthogonal to those of direct and residual main effects. Thus estimates of contrasts between direct effects having minimum variance may be calculated simply as if no residual effects were present. The new designs presented here achieve the same object when certain plausible restrictions are placed on the nature of the residual effects. The efficiency of estimating residual effects is considered to be a subsidiary consideration when planning these experiments; though, of course, designs which also have high efficiency for residual effects are preferred.