Journal ArticleDOI

Block Designs Robust Against the Presence of an Aberration in a Treatment-Control Setup

20 Jan 2012-Communications in Statistics-theory and Methods (Taylor & Francis Group)-Vol. 41, Iss: 5, pp 920-933

TL;DR: In this article, the authors considered the problem of finding designs insensitive to the presence of an outlier in a treatment-control block design setup for estimating the set of elementary contrasts between the effects of each test treatment and a control treatment.

AbstractThe author considers the problem of finding designs insensitive to the presence of an outlier in a treatment-control block design setup for estimating the set of elementary contrasts between the effects of each test treatment and a control treatment. The criterion of robustness suggested by Mandal (1989) in block design setup for estimating a full set of orthonormal treatment contrasts is adapted. A new class viz. partially balanced treatment incomplete block designs (PBTIBD) is introduced and it is shown that balanced treatment incomplete block designs (BTIBD) and PBTIB designs, under certain conditions, are robust in the previous sense. Such designs are important in the sense that the inference on the treatment contrasts under consideration remain unaffected by the presence of an outlier.

Citations
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Journal ArticleDOI

20 citations

Journal ArticleDOI
TL;DR: In this article, the robustness of incomplete block designs against non-normality in the observations has been investigated and a new measure of robustness is introduced for further study, which is called robustness measure.
Abstract: In this article, designs are found for which the F-test of analysis of variance is insensitive to violation of normality assumption. Atiqullah (1962) proved that the F-test for treatments adjusting for blocks in the intra-block analysis of a balanced incomplete block design is robust against non-normality in the observations. Here an attempt has been made to identify other designs robust in this sense. In particular, it is observed that for testing relevant hypothesis, a partially balanced incomplete block design in block design setup, under certain conditions, is robust. Robustness of a balanced treatment incomplete block design and a partially balanced treatment incomplete block design (Biswas, 2012), in treatment-control design setup, is also studied. Moreover, a new measure of robustness is introduced for further study. The performance of the F-test in presence of non-normality in the observations for a quadratically balanced design is also examined.

4 citations

Cites background or methods from "Block Designs Robust Against the Pr..."

• ...However, a separable S-type BTIB design (Biswas, 2012) for which t = 0 (t + 1 and t being the number of times the control treatment occurs in s and the remaining b − s blocks respectively) can be considered a nearly robust design among competing designs as it can be easily proved that for such a…...

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• ...Generalizing GDT designs, a new general class of partially balanced treatment incomplete block designs (PBTIB designs) was introduced in Biswas (2012)....

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• ...Robustness of a balanced treatment incomplete block design and a partially balanced treatment incomplete block design (Biswas, 2012), in treatment-control design setup, is also studied....

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• ...Further, examples of such designs are given in Biswas (2012)....

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• ...…obtained robust designs against the presence of an outlier in block design setup for estimating a full set of orthonormal treatment contrasts and Biswas (2012) extended it to the treatment-control setup for the estimation of a set of elementary contrasts between each test treatment and a…...

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Journal ArticleDOI
TL;DR: In this article, the authors find that complete and partial diallel cross designs are robust to the presence of an outlier in a block design setup for estimating a complete set of orthonormal contrasts among the effects of the general combining abilities of a set of parental lines.
Abstract: In this article, we find designs insensitive to the presence of an outlier in a diallel cross design setup for estimating a complete set of orthonormal contrasts among the effects of the general combining abilities of a set of parental lines. The criterion of robustness, suggested by Mandal (1989) in block design setup and used by Biswas (2012) in treatment-control setup, is adapted here. Complete diallel cross designs, suggested by Gupta and Kageyama (1994), and partial diallel cross designs, suggested by Gupta et al. (1995) and Mukerjee (1997), are found to be robust under certain conditions.

1 citations

Cites background or methods from "Block Designs Robust Against the Pr..."

• ...The criterion of robustness, suggested by Mandal (1989) in block design setup and used by Biswas (2012) in treatment-control setup, is adapted here. Complete diallel cross designs, suggested by Gupta and Kageyama (1994), and partial diallel cross designs, suggested by Gupta et al....

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• ...Without going into the details of the methods for deriving the criterion, given in Biswas (2012), only the definition is given below....

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• ...Box and Draper (1975) were the first to investigate, in this context, the problem of predicting the observed response vector in a response surface model....

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• ...The criterion of robustness, suggested by Mandal (1989) in block design setup and used by Biswas (2012) in treatment-control setup, is adapted here. Complete diallel cross designs, suggested by Gupta and Kageyama (1994), and partial diallel cross designs, suggested by Gupta et al. (1995) and Mukerjee (1997), are found to be robust under certain conditions....

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• ...Box and Draper (1975) were the first to investigate, in this context, the problem of predicting the observed response vector in a response surface model. Later, Gopalan and Dey (1976), Ghosh and Kipngeno (1985), Mandal (1989), Mandal and Shah (1993), Biswas (2012), and some others studied robustness of designs against the presence of outliers under different contexts....

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Journal ArticleDOI
Ganesh Dutta
TL;DR: In this paper, the authors show that the presence of one or more outliers in the observations affect inference procedure in statistical analysis and propose robust designs robust against presence of a single outlier.
Abstract: Presence of one or more outliers in the observations affect inference procedure in statistical analysis. Designs robust against presence of a single outlier can be found in the literature for both ...
Journal ArticleDOI
Ganesh Dutta
01 Dec 2020
TL;DR: In this article, an attempt has been made to find robust designs in a block design set-up with covariates, when there is one single wild observation in the study variable.
Abstract: Presence of one or more aberration in the observations affects inference procedure in statistical analysis. Block designs robust against presence of aberrations can be found in the literature for both regression and block design set-ups. In this paper, an attempt has been made to find robust designs in a block design set-up with covariates, when there is one single wild observation in the study variable. Specifically, effects on the estimation of a full set of orthonormal treatment contrasts and that on the estimation of covariate parameters have been considered.

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Book
01 Jan 1971

622 citations

"Block Designs Robust Against the Pr..." refers background or methods in this paper

• ...Examples of designs, with the parametric combinations given in the list of Raghavarao (1971) for which the value of t satisfying condition (3.9) comes out as zero, are given in Appendix 6.1....

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• ...…contains c test treatments from each group, where k∗1 = cm, c being any positive integer and m being the number of groups of test treatments (cf. Raghavarao, 1971). c) All triangular PBIB designs in the test treatments satisfying r + n− 4 1 − n− 3 2 = 0, there being v = n n− 1 /2 test…...

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• ...Here every block contains 2k∗1/n test treatments from each row (or column), 2k ∗ 1/n being an integer (cf. Raghavarao, 1971). d) All Latin-square type designs in the test treatments with two constraints L2 satisfying r + s − 2 1 − s − 1 2 = 0, there being v = s2 test treatments, where each block is…...

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• ...Here every block contains k∗1/s test treatments from each row (or column; cf. Raghavarao, 1971)....

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• ...The BTIB designs are taken from the list of designs in Raghavarao (1971)....

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Journal ArticleDOI
A. S. Hedayat
TL;DR: In this article, existing knowledge on optimal designs for comparing test treatments with controls under 0-, 1-, and 2-way elimination of heterogeneity models is presented. But the results are motivated through numerical examples.
Abstract: This article outlines existing knowledge on optimal designs for comparing test treatments with controls under 0-, 1- and 2-way elimination of heterogeneity models. The results are motivated through numerical examples.

98 citations

Journal ArticleDOI
TL;DR: In this article, a theory of optimal incomplete block designs for comparing several treatments with a control is developed, and a procedure for making exact joint confidence statements for this multiple comparisons problem is described.
Abstract: In this paper we develop a theory of optimal incomplete block designs for comparing several treatments with a control. This class of designs is appropriate for comparing simultaneously p ≥ 2 test treatments with a control treatment (the so-called multiple comparisons with a control (MCC) problem) when the observations are taken in incomplete blocks of common size k < p + 1. For this problem we propose a new general class of incomplete block designs that are balanced with respect to (wrt) test treatments. We shall use the abbreviation BTIB to refer to such designs. We study their structure and give some methods of construction. A procedure for making exact joint confidence statements for this multiple comparisons problem is described. By using a new concept of admissibility of designs, it is shown how “inferior” designs can be eliminated from consideration, and attention limited to a small class of BTIB designs that can be constructed from so-called generator designs in the minimal complete class of such d...

98 citations

"Block Designs Robust Against the Pr..." refers background or methods in this paper

• ...For a definition and other properties of such designs see Bechhofer and Tamhane (1981) and Hedayat et al. (1988)....

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• ...In the class of incomplete treatment-control block designs, Bechhofer and Tamhane (1981) introduced balanced treatment incomplete block designs (BTIBD)....

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Journal ArticleDOI
TL;DR: In this article, the problem of finding optimal incomplete blocks designs for comparing $p$ test treatments with a control is studied, and conditions for a design to be φ-optimal are found for a large class of functions.
Abstract: The problem of finding optimal incomplete blocks designs for comparing $p$ test treatments with a control is studied. B.I.B. designs are found to be $D$-optimal. $A$- and $E$-optimal designs are also obtained. For a large class of functions $\phi$, conditions for a design to be $\phi$-optimal are found. Most of the optimal designs are certain types of B.T.I.B. designs, introduced by Bechhofer and Tamhane (1981), which are binary in test treatments.

82 citations

"Block Designs Robust Against the Pr..." refers background in this paper

• ...Such designs are also optimal as can be seen in Majumdar and Notz (1983)....

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• ...Such designs are also optimal as can be seen in Majumdar and Notz (1983). In the class of PBTIB designs introduced by us, those designs are found to be robust for which the number of first associates of any test treatment in any block is a constant....

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Book
01 Jan 1986
TL;DR: Introduction Some Mathematical and Statistical Results General Properties of Block Designs Balanced Incomplete Block Designs - Properties and Analysis Construction and Existence of Balanced In complete Block Designs Partially Balanced In Complete Block Designs Additional Topics in Block Designs Index.
Abstract: Introduction Some Mathematical and Statistical Results General Properties of Block Designs Balanced Incomplete Block Designs - Properties and Analysis Construction and Existence of Balanced Incomplete Block Designs Partially Balanced Incomplete Block Designs Additional Topics in Block Designs Index.

78 citations