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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.
Abstract: The 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

22 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
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
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.
References
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Journal ArticleDOI
TL;DR: In this paper, the sensitivity of the optimum balanced resolution V plans for 2m factorials, to outliers, using the measure suggested by Box and Drapper (1975), was studied.

9 citations

Journal ArticleDOI
TL;DR: Substantial conditions are obtained for a design to be robust against aberrations in the sense of Box and Draper.
Abstract: In this paper, we obtain sufficient conditions for a design to be robust against aberrations in the sense of Box and Draper. Block designs, row-column designs and fractional designs are considered here. An alternative formulation of robustness is also presented.AMS Subject Classification: Primary 62K99; Secondary 62K05.

5 citations


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

  • ...Later, Gopalan and Dey (1976), Mandal (1989), Mandal and Shah (1993), and some others studied robustness of designs under different contexts....

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Journal ArticleDOI
TL;DR: In this paper, it was shown that A - and E -optimum designs minimize the effect of d in the mean square error (m.s.s) of estimable linear functions of parameters under the ordinary linear model.

4 citations


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

  • ...Ghosh and Roy (1982) showed that A- and E-optimum designs minimize the effect of damaged observations in the mean square error of estimable functions of parameters under the ordinary linear model....

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