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1.
H. M. Kashif Rasheed Mujahid Rasul Maria Batool M. H. Tahir Farrukh Shehzad 《统计学通讯:模拟与计算》2013,42(10):3022-3030
AbstractRepeated measurement designs are widely used in medicine, pharmacology, animal sciences and psychology. If there is a restriction on the total number of treatments, some experimental units can receive on the total length of time while some experimental units can remain in the trial, then repeated measurements designs with unequal period sizes should be used. In this article, some infinite series are developed to generate the minimal balanced repeated measurement designs in periods of three different sizes p1, p2 and p3, where 2?≤?p3?<?p2 ≤ 10 and p2?<?p1. 相似文献
2.
Repeated measurements designs are widely used in medicine, pharmacology, animal sciences, and psychology. In this article, some infinite series are developed to generate the balanced repeated measurements designs for p (periods) even. For p odd, construction procedures are also described. Catalogues of the proposed designs are also presented for p = 5, 7, 9, when v ≤ 100. 相似文献
3.
Rashid Ahmed Farrukh Shehzad Muhammad Rajab Muhammad Daniyal M. H. Tahir 《统计学通讯:理论与方法》2013,42(21):5223-5232
AbstractRepeated measurement designs (RMDs) are widely used in medicine, pharmacology, animal sciences and psychology. In these fields, there are several situations where these designs should be used in periods of different sizes. With the use of RMD, residual effects or carry over effects may arise and balanced RMDs are solution to this problem. In this article, therefore, some infinite series are developed through method of cyclic shifts to obtain circular balanced repeated measurements designs in periods of two different sizes. 相似文献
4.
Minimal circular strongly balanced repeated measurements designs in periods of three different sizes
Repeated measurements designs (RMD) are widely used in medicine, pharmacology, animal sciences, and psychology. If there is a restriction on the total number of treatments, some experimental units can receive on the total length of time while some experimental units can remain in the trial, then RMD in periods of unequal sizes should be used. In this article, some infinite series are developed to generate the minimal circular strongly balanced RMD in periods of three different sizes p1, p2, and p3, where 2 ≤ p3 < p2 ≤ 10. 相似文献
5.
AbstractBalanced repeated measurements designs (RMDs) balance out the residual effects. Williams Latin square designs work as minimal combinatorial balanced as well as variance balanced for RMDs for p (period sizes) = v (number of treatments). If minimal balanced RMDs cannot be constructed for the situations where p must be less than v then weakly balanced RMDs should be preferred. In this article, some generators are developed to generate circular weakly balanced RMDs in periods of two different sizes. To obtain the proposed designs, some construction procedures are also described for some of the cases where we could not develop generators. 相似文献
6.
AbstractRepeated Measurements Designs have been widely used in agriculture, animal husbandry, education, biology, botany and engineering. Balanced or strongly balanced repeated measurements designs are useful to balance out the residual effects. In this article, some new generators and construction procedures are proposed to obtain circular strongly balanced repeated measurements designs in periods of (a) equal sizes, (b) two different sizes, and (c) three different sizes. 相似文献
7.
Repeated measurement designs are widely used in medicine, pharmacology, animal sciences, and psychology. In this paper the works of Iqbal and Tahir (2009) and Iqbal, Tahir, and Ghazali (2010) are generalized for the construction of circular-balanced and circular strongly balanced repeated measurements designs through the method of cyclic shifts for three periods. 相似文献
8.
Sharma (1977) and Aggarwal et al. (2006) considered non circular construction of first- and second-order balanced repeated measurements designs. Sharma et al. (2002) constructed circular first- and second-order balanced repeated measurements designs only for a class with parameters (v, p = 3n, n = v 2) and also showed its universal optimality. In this article, we consider circular construction of first- and second-order balanced repeated measurements designs and strongly balanced repeated measurements designs by using the method of cyclic shifts. Some new circular designs with parameters (v, p, n) for cases p = v, p < v and p > v are given. 相似文献
9.
Deborah J. Street J.A. Eccleston William H. Wilson 《Australian & New Zealand Journal of Statistics》1990,32(3):345-359
This paper presents tables of the optimal repeated measurements designs for the estimation of direct effects and of residual effects for a model with independent errors, for up to n = 10 experimental units, for t= 2 treatments and p= 2, 3 or 4 periods, and for t= 3 treatments and p= 2 or 3 periods. 相似文献
10.
Neighbor-balanced designs are useful to remove the neighbor effects in experiments where the performance of a treatment is affected by the treatments applied to its adjacent neighbors. In this article, neighbor-balanced designs are constructed in linear blocks of (i) equal sizes and (ii) two different sizes k 1 and k 2. 相似文献
11.
Dibyen Majumdar 《统计学通讯:理论与方法》2013,42(11):3687-3703
A-optimal and mv optimal repeated measurments designs for comparing serveral test treatments with a control are considered. the models considered are basically of two types: without preperides and the cirular model. It is shown known that some known strongly balanced uniform repeated measurements designs can be modified to obtain optimal designs for this problem. Some other methods of finding optimal designs are also given. 相似文献
12.
Joachim Kunert 《统计学通讯:理论与方法》2013,42(21):2665-2671
Magda (1980) introduced a model for repeated measurements designs with a circular structure of the residual effects. He proved the universal optimality of circular balanced uniform designs over a subclass of the possible designs. We strengthen his result to optimality over the set of all designs with the same number of experimental units, periods and treatments. 相似文献
13.
In this article, the exchange and interchange algorithm of Zergaw (1989) and Martin and Eccleston (1992) have been modified and used for searching efficient block designs for making all possible pairwise treatment comparisons when observations are dependent. The lower bounds to the A- and D-efficiencies of the designs in a given class of the designs have been obtained for correlated observation structure and the procedure of computing lower bounds to A- and D-efficiencies has been incorporated in the algorithm. The algorithm has been translated into a computer program using Microsoft Visual C++. Using this program, a search for efficient designs for making all possible pairwise treatment comparisons has been made for v ≤ 10, b ≤ 33, k ≤ 10 such that bk ≤ 100 and v > k. The block designs considered are usual block designs (rectangular block designs) and circular block designs. Nearest neighbor (NN), autoregressive of order 1 (AR(1)) correlation structures are studied. The ranges of correlation coefficients for different correlation structures investigated are |ρ|≤0.50 for NN correlation structure in rectangular blocks, |ρ|≤0.45 for NN correlation structure in circular blocks, and |ρ|≤0.95 for AR(1) correlation structure. For these ranges, the matrix of correlation coefficients among observations within a block is positive definite. Robustness aspects of designs that are efficient for a given value of correlation have been investigated against other values of correlation coefficients. Robustness aspects of designs that are efficient for independent observations have also been studied for experimental situations with dependent observations. 相似文献
14.
D.K. ParkMausumi Bose W.I. NotzA.M. Dean 《Journal of statistical planning and inference》2011,141(2):846-860
Crossover designs, or repeated measurements designs, are used for experiments in which t treatments are applied to each of n experimental units successively over p time periods. Such experiments are widely used in areas such as clinical trials, experimental psychology and agricultural field trials. In addition to the direct effect on the response of the treatment in the period of application, there is also the possible presence of a residual, or carry-over, effect of a treatment from one or more previous periods. We use a model in which the residual effect from a treatment depends upon the treatment applied in the succeeding period; that is, a model which includes interactions between the treatment direct and residual effects. We assume that residual effects do not persist further than one succeeding period.A particular class of strongly balanced repeated measurements designs with n=t2 units and which are uniform on the periods is examined. A lower bound for the A-efficiency of the designs for estimating the direct effects is derived and it is shown that such designs are highly efficient for any number of periods p=2,…,2t. 相似文献
15.
ABSTRACTNeighbor designs are recommended for the cases where the performance of treatment is affected by the neighboring treatments as in biometrics and agriculture. In this paper we have constructed two new series of non binary partially neighbor balanced designs for v = 2n and v = 2n+1 number of treatments, respectively. The blocks in the design are non binary and circular but no treatment is ever a neighbor to itself. The designs proposed here are partially balanced in terms of nearest neighbors. No such series are known in the literature. 相似文献
16.
Neighbor designs are useful to remove the neighbor effects. In this article, an algorithm is developed and is coded in Visual C + +to generate the initial block for possible first, second,…, and all order neighbor designs. To get the required design, a block (0, 1, 2,…, k ? 1) is then augmented with (v ? 1) blocks obtained by developing the initial block cyclically mod (v ? 1). 相似文献
17.
Neighbor designs are useful to neutralize the neighbor effects. In literature, most of the constructed neighbor designs are in circular blocks but linear blocks have more practical application in field experiments. In this article, some infinite series of minimal neighbor designs are constructed in proper linear blocks. There are many situations where minimal neighbor designs cannot be constructed in proper linear blocks. To overcome this problem neighbor designs in improper linear blocks and GN2-designs in proper linear blocks are constructed. 相似文献
18.
Magda (1980) and Hedayat (1981) first considered the construction of circular strongly balanced repeated measurements designs. Sen and Mukerjee (1987) and Roy (1988) considered the optimality and existence of circular strongly balanced repeated measurements designs based on the method of differences and Hamiltonian decomposition of lexicographic product of two graphs. In this article, we consider the construction of circular strongly balanced repeated measurements designs using the newly proposed method called cyclic shifts, and propose some new designs for p < v. 相似文献
19.
Sheng-Li Zhao 《统计学通讯:理论与方法》2013,42(17):5028-5036
ABSTRACTIn this article, we consider the construction of minimum aberration 2n ? k: 2p designs with respect to some existing combined wordlength patterns, where a 2n ? k: 2p design is a blocked two-level design with n treatment factors, 2p blocks, and N = 2q runs with q = n ? k. Two methods are proposed for two situations: n ? 2q ? p ? 1 and n > N/2. These methods enable us to obtain some new minimum aberration 2n ? k: 2p designs from existing minimum aberration unblocked and blocked designs. Examples are included to illustrate the theory. 相似文献
20.
Neighbor balance designs were first introduced by Rees (1967) in circular blocks for the use in serological research. Subsequently several researchers have defined the neighbor designs in different ways. In this paper, neighbor balance circular designs for (k≤v) block size are constructed for even number of treatments i.e. v=2n. No such series of designs is known in literature. Two theorems are developed for circular designs. Theorem 1 gives the non-binary circular blocks, whereas Theorem 2 generates binary circular blocks when n≤4 and non-binary blocks for n>4. In suggested designs no treatment is ever a neighbor of itself. Blocks are constructed in such a way that each treatment is a right and left neighbor of every other treatment for a fixed number of times say λ. Sizes of initial circular blocks are not same. One main guiding principle for such designs is to ensure economy in material use. 相似文献