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1
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Check plots in field breeding experiments

100%
Mejza S., Mejza I.
Biometrical Letters
|
2013
|
tom 50
|
nr 2
137-149
EN
This paper deals with the problems of selection in the early stages of a breeding program. During the improvement process, it is not possible to use an experimental design that satisfies the requirement of replicating all the treatments, because of the large number of genotypes involved, the small amount of seed and the low availability of resources. Hence unreplicated designs are used. To control the real or potential heterogeneity of experimental units, control (check) plots are arranged in the trial. There are many methods of using the information resulting from check plots. All of the usually applied adjusting methods for unreplicated experiments are appropriate for some specific structure of soil fertility. Their disadvantage is the fact that, before and also after the experiment, we usually do not know what a kind of soil structure is present in the experiment. Hence we cannot say which of the existing methods is appropriate for a given experimental situation. The method of inference presented below avoids this disadvantage. It is always appropriate, because of the fact that a trend of soil variability is identified and estimated. In the paper the main tool used to explore this information will be based on a response surface methodology. To begin with we will try to identify a response surface characterizing the experimental environments. We assume that observed yield (or another trait) results directly from two components, one of them due to soil fertility and the other due to the genotype effect. This means that difference between observed yield and forecast can be treated as the estimate of a genotype effect. The obtained response surface will then be used to adjust the observations for genotypes. Finally, the data so adjusted are used for inferences concerning the next stage of the breeding program. The theoretical considerations are illustrated with an example involving yields of spring barley.
2
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Use ofα-resolvable designs in the construction of two-factor experiments of split-plot type

81%
Ozawa K., Kuriki S., Mejza S.
Biometrical Letters
|
2016
|
tom 53
|
nr 2
105-118
EN
We consider an incomplete split-plot design (ISPD) with two factors generated by the semi-Kronecker product of two α-resolvable designs. We use an α-resolvable design for the whole plot treatments and an affine α-resolvable design for the subplot treatments. We characterize the ISPDs with respect to the general balance property, and we give the stratum efficiency factors for the ISPDs.
3
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Incomplete split-block designs constructed by affine α-resolvable designs

81%
Ozawa K., Kuriki S., Mejza S.
Biometrical Letters
|
2017
|
tom 54
|
nr 2
123-135
EN
We construct an incomplete split-block design (ISBD) by the semi- Kronecker product of two affine α-resolvable designs for row and column treatments. We characterize such ISBDs with respect to the general balance property and we give the stratum efficiency factors for the ISBDs.
4
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Control treatments in designs with split units generated by Latin squares

81%
Kuriki S., Mejza I., Ozawa K., Mejza S.
Biometrical Letters
|
2014
|
tom 51
|
nr 2
125-142
EN
This paper deals with two-factor experiments with split units. The whole plot treatments occur in a repeated Latin square, modified Latin square or Youden square, while subplot treatments occur in a block design within the whole plots. The statistical properties of the considered designs are examined. Special attention is paid to the case where one of the treatments is an individual control or an individual standard treatment. In addition, we give a brief overview of work on the design of experiments using the considered designs, as well as possible arrangements of controls in the experiments.
5
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Orthogonality, efficiency and balance of a block design

81%
Caliński T., Ceranka B., Mejza S.
Mathematica Applicanda
|
1982
|
tom 10
|
nr 20
PL
W planowaniu i analizowaniu eksperymentów badawczych spotykamy się często z pojęciami ortogonalności, efektywności i zrównoważenia. Pojęcia te są ściśle z sobą powiązane, choć zdarza się, że rozpatruje się je bez wzajemnego związku. Celem niniejszej pracy jest pokazanie podstawowych związków łączących te pojęcia.
EN
The authors discuss the interconnections between the concepts of orthogonality, efficiency, and balance of block designs. No new theorems are obtained. Illustrative examples are presented. MR0707816
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