The robustness of chain block designs and coat-of-mail designs
01 Jan 1978-Communications in Statistics-theory and Methods (Marcel Dekker, Inc.)-Vol. 7, Iss: 5, pp 479-485
TL;DR: In this article, the authors compared the robustness of chain block designs and coat-of-mail designs and found that the latter is more robust to missing values or outliers than the former.
Abstract: Chain block designs are relatively vulnerable to loss of information when missing values or outliers may occur An alternative class of designs, coat-of-mail designs, are proposed and the relative robustness of the two types of design are compared
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TL;DR: This work presents a relatively simple alternative method for assessing the accuracy of the first-order Bonferroni upper bound that can be applied to any linear model and is suitable for routine use.
Abstract: At present, the first-order Bonferroni upper bound is the only practically useful tool for determining approximate critical values or p values for the maximum absolute studentized residual as a criterion for detecting a single outlier in a linear model. Available methods for assessing the accuracy of this bound require numerical integration and are difficult to apply routinely. We present a relatively simple alternative method that can be applied to any linear model and is suitable for routine use. The application to analyses of 2 m factorial experiments and regression models is illustrated with several examples.
39 citations
TL;DR: In this article, the information contained in each observation in a given design is compared with respect to the estlmability of parameters and against the unavailability of observations, and the observations in various 1-, 2-and 3-dimensional designs are compared on the basis of their informations.
Abstract: We consider the Information contained 1n each observation in a given design robust with respect to the estlmability of parameters and against the unavailability of observations. We compare the observations in various 1-, 2- and 3- dimensional designs on the basis of their informations.
24 citations
TL;DR: The effects of missing observations in a designed experiment are reviewed in this paper, where conditions are determined for a design to retain equal information, i.e. the same generalized variance of unknown parameters, when either any single or any pair of observations is lost.
Abstract: The effects of missing observations in a designed experiment are reviewed. Conditions are determined for a design to retain equal information, i.e. the same generalized variance of unknown parameters, when either any single or any pair of observations is lost. Some examples of designs with this property are given. Although there are many designs which retain equal information for the loss of exactly t observations, where t = 1,2,3,…, it is shown that it is not possible to obtain any design which retains equal information when any one and any two and also any three observations are missing.
Nous rappelons les effets que peuvent causer les observations manquantes dans le cadre d'une experience planifiee. Sous certaines conditions, nous demontrons que l'information contenue dans le plan d'experience est constante, en ce sens que la variance generalisee des parametres inconnus demeure la měme quelle que soit l'observation ou la paire d'observations manquantes. Nous donnons quelques exemples de plans d'experience dotes de cette propriete. De facon generale, il existe aussi des plans a information constante dans les situations ou exactement t = 1,2,3,…, observations sont declaree manquantes. Toutefois, nous demontrons qu'il n'existe aucun plan d'experience qui renferme la měme information pour toute observation, paire d'observations et triplet d'observations manquantes.
10 citations
TL;DR: In this paper, the authors investigate the problem of finding a BBD which is most robust against the lack of balance induced by the loss of a single observation, and give guidelines for finding the most robust design.
6 citations
TL;DR: The present paper surveys various results on robustness of block designs in three different directions, when some observations are missing.
3 citations
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TL;DR: In this paper, a two-factor design is shown to be optimal jointly for both the factors with respect to each of $A$-, $D$-, and $E$-optimalities.
Abstract: In a two-factor design, a design which is optimal for one factor is shown to be optimal jointly for both the factors with respect to each of $A$-, $D$-, and $E$-optimalities. As an interesting consequence we have that a linked block design is optimal for the estimation of treatment differences. Similar results are also obtained for a class of three factor designs.
24 citations
01 Oct 1958
TL;DR: In this article, the authors show how the intra-blockT analysis of a Linked Block (LB) design can be neatly carried out and give an exhaustive list of all LB designs with ten or less plots per block and involving 10 or less replications.
Abstract: In comparative experiments involving a fairly large number of varieties, when for lack of homogeneous experimental units, complete block designs are not available. Balanced Incomplete Block (BIB) designs prove very convenient in two respects. Firstly, the analysis is very simple and secondly, comparison between any two varieties has the same precision. On the other hand, a BIB design requires a large number of experimental units, because balancing is not possible unless the number of blocks is atleast as large as the number of varieties. To obviate this dif ficulty, different types of incomplete block designs have been introduced, of which the most notable is the Partially Balanced Incomplete Block (PBIB) design introduced by Bose and Nair (1939). Another class of incomplete block designs, called Linked Block (LB) designs was introduced by Youden (1951) which he obtained by dualising several BIB designs, that is by taking the varieties and blocks of the BIB design respectively as blocks and varieties in the LB design. The LB designs so constructed by Youden happen to be all PBIB designs, but this is not necessarily true. A great advantage of LB designs is that the analysis can be easily worked out. In this paper, we show how the intra-blockTanalysis of a LB design can be neatly carried out. The efficiency factor of a LB design is obtained. The methods are illustrated with a numerical example. An exhaustive list of all LB designs with ten or less plots per block and involving ten or less replications is given. These designs fall into three groups: (1) symmetrical BIB designs, (2) PBIB designs and (3) Irregular designs For plans of LB designs belonging to group (2) reference is made to the serial number of the two-associate class PBIB designs enumerated by Bose, Clatworthy and Shrikhande (1954). Plans for other designs belonging to groups (2) and (3) are given in detail. Certain theorems are derived which are useful in determining from the parameters of a given two-associate class PBIB design whether the design is of the LB type or not.
17 citations