Table 11 - uploaded by David James Fletcher
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Efficiencies for the bricks given in Table I. For designs without factorial balance the minimum and maximum efficiencies are given
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Context 1
... this case, all pairs of initial sequences were searched, giving rise to bricks comprising two initial sequences. The results of this search are given in Table I, with the corresponding efficiencies for the main effects A and B, and their interaction AB, in Table 11. ...
Context 2
... some contrasts within these effects will be estimated with higher efficiency and some with lower efficiency. The lowest and highest efficiencies that apply to a contrast within a particular effect are given by the minimum and maximum eigenvalues, and these are given in Table 11. When constructing a design including one of these bricks, it would be prudent to run a 'dummy' analysis to ensure that no practically important contrast is poorly estimated. ...
Context 3
... two drugs were given at two levels, the lower being a placebo in each case; the treatment periods lasted three weeks, with no intervening washout periods. There was a run-in period of three weeks on Table 111. Data from the anti-hypertension study, with treatment means. ...
Context 4
... Table IV there is little evidence that there are any carryover effects but, as Abeyasekera and Curnow' point out, simply omitting such terms because they are not significant can lead to bias in the direct estimates. As there is no evidence of an interaction between A and B, the treatment effects are summarized in Table 111, where adjusted and raw means are given for the direct effects of A and B. ...
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Citations
... Y is a vector of responses listed across subjects one period at a time and E is the corresponding error vector which is assumed to have mean 0 and variance 2 I vs , where I vs is a vs vs identity matrix. Fletcher and John (1985), Fletcher (1987), and Lewis, Fletcher and Matthews (1988) each considered the problem of estimating factorial treatment e ects in the presence of residual e ects under model (1), and based their designs on the class of generalized cyclic designs. In most of their designs, each treatment combination is replicated the same number of times per period. ...
... The second class that we consider for a factorial experiment with two factors is based on the class of generalized cyclic designs with 2{digit labels. This class was used by Fletcher and John (1985), Fletcher (1987), and Lewis, Fletcher and Matthews (1988) for experiments with v subjects and s < v periods. Addition of two treatment labels in this class of designs is de ned as addition modulo m i of the ith digits of the labels, where m i is the number of levels of the ith factor, (i = 1; 2). ...
The construction of cross-over designs, with a small number of subjects, efficient for estimating factorial effects in the presence of residual effects is considered. Two methods of constructing efficient designs are investigated, one based on latin squares balanced for carryover effects and the other on generalized cyclic designs. Tables of efficient designs are given for two-factor experiments. Key Words and Phrases: balance for carryover, cross-over design, factorial experiment, generalized cyclic designs, Williams latin squares, residual effects. 1 1
... Some interest has been centred on cases with a single unstructured set of treatments and pairwise comparison of these treatments, see Kunert (1984Kunert ( , 1985 and Matthews (1987). Attention has also been given to the estimation of factorial contrasts in cross-over designs with a factorial treatment structure, see Fletcher & John (1985) and Lewis, Fletcher & Matthews (1988). ...
... In defence of the model, work on designing factorial carryover trials has, to date, focused on the simple case where direct treatment x subject and direct treatment x carryover interactions are assumed negligible, see Fletcher & John (1985). Designs efficient for estimating the direct main effects of each factor, carryover main effects of each factor and interactions between direct treatment effects have been found for the simple case, see Lewis, Fletcher & Matthews (1988) and Fletcher, Lewis Sz Matthews (1990). However, similiar work seeking efficient designs capable of estimating further interactions is possible. ...
p>The study concerns the design of experiments whose purpose is to compare the joint effects of two drugs A and B, at n and m levels respectively, with the effect of each individual drug. The treatment containing both drugs at the zero level is excluded from the experiment on ethical grounds. The aim of this investigation is to identify efficient row-column and cross-over designs for estimating the dual versus single treatment contrasts, in the sense of having small total variance for the contrast estimators.
Initially, attention is restricted to row-column designs, that is designs for two orthogonal blocking factors. The criterion used for design selection is the A-criterion. Lower bounds on the total variance of the estimators of the contrasts of interest are developed and used to assess the performance of row-column designs obtained by amalgamating two single blocking factor designs which are part-balanced for the dual versus single contrasts. A subclass of part-balanced row-column designs, with the property that treatments are orthogonal to row blocks, is identified. A method of finding efficient designs for estimating any specific given set of treatment contrasts is also described.
In the latter part of this thesis, designs are identified for cross-over experiments where each subject is given a sequence of two or more distinct treatments. For such studies, it is necessary to consider the possibility that the effect of a particular treatment may persist beyond the period of application. Designs are considered for the cases where treatment effects persist for one and for two periods and simple additive models including first- and second-order carryover effects are assumed.(DX178951)</p
Serially Balanced Factorial Sequences (SBFSs) are defined as a new class of Serially Balanced Sequences. They also are an adaptation of Orthogonal Arrays to repeated-measurements designs. Methods of construction are given for some series of SBFSs with factors at two or three levels. These SBFSs are shown to be universally optimal for the estimation of direct factorial effects up to a given order and main carryover effects, if assumptions are made on the other effects.
When measuring the joint effect of two factors it is advantageous to use a factorial design. If the application is suitable, efficiency may be further improved by using a crossover design. This paper presents a flexible method for amalgamating these two devices. Designs are constructed from smaller designs, known as bricks, generated cyclically from tabulated initial sequences. The bricks have known efficiencies for estimation of direct treatment main effects and interactions; the efficiencies can be simply combined to approximate the efficiencies of the whole design. This allows the user to build a design that is tailored to the particular objectives of the experiment. Three and four periods, and two factors with up to four levels are considered.
