Designs Robust Against the Presence of an Aberration in a Diallel Cross Design Setup

doi:10.1080/03610926.2011.620210

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Journal Article•DOI•

Nonexistence of robust designs against presence of more than one outlier in a restricted class

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Ganesh Dutta, Nripes Kumar Mandal¹, Premadhis Das²•Institutions (2)

University of Calcutta¹, Kalyani Government Engineering College²

17 Jun 2021-Communications in Statistics-theory and Methods

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.

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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 ...

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Journal Article•DOI•

Concept of general and specific combining ability in relation to diallel crossing systems

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B Griffing

01 Nov 1956-Australian Journal of Biological Sciences

TL;DR: In this paper, a detailed examination of combining ability in relation to diallel crossing systems is made, and eight different analyses are presented, with two alternative assumptions with regard to the sampling nature of the experimental material.

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Abstract: A detailed examination of the concept of combining ability in relation to diallel crossing systems is made. Eight different analyses aro presented. 'l'hese result from a consideration of four different diallel crossing systems together wit.h two alternative assumptions with regard to the sampling nature of tho experimental material. A numerical example is given.

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3,856 citations

"Designs Robust Against the Presence..." refers background in this paper

...Designs of experiments for diallel crosses have received considerable attention in the literature; see Griffing (1956), Received May 11, 2011; Accepted August 24, 2011 Address correspondence to Amrita Biswas, St. Xavier’s College, Kolkata, India; E-mail: amristat@gmail.com 2810 Gilbert (1958),…...
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Journal Article•DOI•

The Partial Diallel Cross

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Oscar Kempthorne, R. N. Curnow

01 Jun 1961-Biometrics

291 citations

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

...…August 24, 2011 Address correspondence to Amrita Biswas, St. Xavier’s College, Kolkata, India; E-mail: amristat@gmail.com 2810 Gilbert (1958), Kempthorne and Curnow (1961), Curnow and Draper (1963), Hinkelmann and Kempthorne (1963), Hinkelmann (1975), Arya (1983), Singh and Hinkelmann…...
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...For example, the designs of Kempthorne and Curnow (1961), Arya (1983), and Singh and Hinkelmann (1990) can be obtained using these plans....
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Journal Article•DOI•

Diallel cross in plant breeding

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N E G Gilbert

01 Nov 1958-Heredity

TL;DR: The utility of diallel crosses is considered, using data available in the literature together with some new figures from an i8x i8 cross in tomatoes, based on ideas introduced in the classical paper of Fisher (1918) and developed by Fisher, Immer and Tedin (1932) and Mather (i4g).

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Abstract: A DIALLEL cross consists of all possible crosses between a number of varieties. Reciprocal crosses, and the selfed parents, may or may not be omitted. Such a set of crosses is obviously of interest to the plant breeder, but the information obtained may not be worth the trouble of making the cross. In this paper the utility of such crosses is considered, using data available in the literature together with some new figures from an i8x i8 cross in tomatoes. The statistical analysis of a diallel cross has been described by Yates (1947). It consists of fitting additive main effects for parents, and their interactions in the individual crosses. Such a main effect is sometimes called\" general combining ability \"or\" additive genetical component\" while an interaction may be referred to as \"specific combining ability\" or \"non-additive genetical component \". The word interaction is used here in its purely statistical sense of a departure from additivity. It should not be confused with any form of genetical interaction between postulated \"genes \". The interactions are part of the statistical description of the data, being the ups and downs which remain when the main effects have been taken out. The analysis is similar to that of factorial experiments, and merely assumes that the contributions of male and female parents are equally important. The exact mode of inheritance is not specified, and the analysis would be as effective for, say, blending inheritance as for Mendelian. There is no need for the parents to be inbred (or to have a uniform coefficient of inbreeding). It may be objected that a plant breeder is interested in, say, the top 2 per cent. of each progeny, and so wishes to estimate not the mean a but j-+2a where a is the standard deviation. This, however, involves an adjustment in practice and not in principle. In many cases there will not be enough replication to give useful estimates of a for each particular cross and heterogeneity of variance will be undetectable. Main effects can, however, be fitted for log variance or standard deviation in the same way as for progeny means. This factorial method of analysis is to be judged by its success in describing the data. 1. THE POLYGENE\" ANALYSIS A second method of analysis, based on ideas introduced in the classical paper of Fisher (1918) and developed by Fisher, Immer and Tedin (1932) and Mather (i4g), has been put forward by Jinks and Hayman Jinks (i) and Hayman (i954b). It involves the assumption, inter alia, that the yield (or whatever character is being

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124 citations

"Designs Robust Against the Presence..." refers background in this paper

...…May 11, 2011; Accepted August 24, 2011 Address correspondence to Amrita Biswas, St. Xavier’s College, Kolkata, India; E-mail: amristat@gmail.com 2810 Gilbert (1958), Kempthorne and Curnow (1961), Curnow and Draper (1963), Hinkelmann and Kempthorne (1963), Hinkelmann (1975), Arya (1983), Singh and…...
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Journal Article•DOI•

On Robust Designs

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Nripes Kumar Mandal

01 Mar 1989-Calcutta Statistical Association Bulletin

TL;DR: In this paper, the robustness of block designs for the problem of estimation of any full set of orthonormal varietal contrasts is examined, and an attempt has been made to examine their robustness against the presence of wild observations.

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Abstract: Box and Draper (1975) proposed a criterion of robustness against the presence of wild observations for the problem of estimation of Xβ in the response surface model E(Y) = Xβ, D(Y) = σ2.I. Gopalau and Dey (1976) elttended this concept to block designs setting, for the problem of estimation of σ2. In the present note an attempt has been made to examine the robustness of block designs for the problem of estimation of any full set of orthonormal varietal contrasts.

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62 citations

"Designs Robust Against the Presence..." refers background in this paper

...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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Journal Article•DOI•

Optimal complete diallel crosses

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Sudhir Gupta¹, Sanpei Kageyama•Institutions (1)

Northern Illinois University¹

01 Jun 1994-Biometrika

TL;DR: In this paper, the optimality of complete diallel cross in incomplete blocks is investigated, and a table of optimal complete cross plans for up to 15 lines is provided, where the optimal complete crossing plan is derived using nested balanced incomplete block designs.

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Abstract: SUMMARY Optimality of complete diallel crosses in incomplete blocks is investigated. Optimal complete diallel crosses are characterized, and such binary plans are derived using nested balanced incomplete block designs. A table of optimal complete diallel crosses for up to 15 lines is also provided.

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58 citations

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

...CDC in a Nested BIB Design As pointed out earlier, for the purpose of restricting to one replication of each cross, let us follow the approach of Gupta and Kageyama (1994) for getting a CDC....
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...In subsequent discussions, Gupta and Kageyama (1994), Gupta et al. (1995), and Mukerjee (1997) will be referred frequently....
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...1, CDC designs, suggested by Gupta and Kageyama (1994), are proved to be robust....
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...CDC in a Nested BIB Design As pointed out earlier, for the purpose of restricting to one replication of each cross, let us follow the approach of Gupta and Kageyama (1994) for getting a CDC. Thus, considering the v parental lines as treatments in an incomplete block design D in b blocks and constant replication r for each parent and constant block size k′ = 2k, k pairs of parents are formed in each block which provides k crosses for each block. The pairing results in a complete diallel cross if an irreducible balanced incomplete block design, say Dn, with block size 2 is nested within D. Now, D is also taken to be a BIB design for the sake of robustness. Gupta and Kageyama (1994) constructed two series of such designs with n = 1....
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...The study has been done for single replicate designs and it is found that CDC designs, suggested by Gupta and Kageyama (1994), and PDC designs, suggested by GDK (1995) and Mukerjee (1997), are robust under certain conditions....
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Designs Robust Against the Presence of an Aberration in a Diallel Cross Design Setup

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

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"Designs Robust Against the Presence..." refers background in this paper

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

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