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

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.

...read more

##### Citations

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…...

[...]

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

[...]

...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....

[...]

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

[...]

...…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…...

[...]

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....

[...]

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

[...]

...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....

[...]

...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....

[...]

...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....

[...]

##### References

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....

[...]

...…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…...

[...]

...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…...

[...]

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

[...]

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

[...]

98 citations

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)....

[...]

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

[...]

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)....

[...]

...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....

[...]

78 citations