Multiphase experiments in practice: A look back

Brien, Chris

doi:10.1111/anzs.12221

Cited by 5 publications

(25 citation statements)

References 64 publications

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“…When all the allocations are randomizations, it is equivalent to a randomization model. It is modified prior to performing an analysis (see Brien , Section 5) to produce the prior allocation model , a starting model for an analysis. The initial allocation model for the example is as follows:

Lines false| Blocks + \underset{̲}{Blocks \land Plots} + false| Runs + Spots + \underset{̲}{Runs \land Spots} .

Lines is the first‐phase allocated factor, the remaining terms in the first line derive from the first‐phase recipient factors and the terms in the second line derive from the second‐phase, recipient factors.…”

Section: A Nonorthogonal Two‐phase Examplementioning

confidence: 99%

“…The advantages of structure–balanced designs are discussed by Brien , Section 3). Briefly, sources from the same tier are not (partially) aliased and, as for some first‐order balanced designs, all elementary contrasts for treatment sources have equal variance.…”

Section: A Nonorthogonal Two‐phase Examplementioning

confidence: 99%

“…() that cover nonorthogonal multiphase experiments. Further, assessing unbalanced designs as described by Brien () has not been demonstrated.…”

Section: Introductionmentioning

confidence: 99%

“…Brien () reviewed multiphase experiments, giving an overview of their design and analysis as it is currently practised, via a literature survey. It illustrated the use of the anticipated model, factor–allocation diagrams, anatomies of designs, skeleton analysis‐of‐variance (ANOVA) tables and a series of allocation models in designing structure‐balanced experiments.…”

Section: Introductionmentioning

confidence: 99%

“…() and in this paper. Brien () explains some of the philosophy, notation and terminology used here. A glossary is available from the multitiered experiments web site (Brien et al .…”

Section: Introductionmentioning

confidence: 99%

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Multiphase experiments with at least one later laboratory phase. II. Nonorthogonal designs

Brien

2019

Aus NZ J of Statistics

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Principles and laws that apply to nonorthogonal multiphase experiments are developed and illustrated using examples that are nonorthogonal but structure-balanced, not structure, but first-order, balanced or unbalanced, thus exposing the differences between the different design types. The design of such experiments using standard designs, a catalogue of designs and computer searches is exemplified. Factor-allocation diagrams are employed to depict the allocations in the examples, and used in producing the anatomies of designs or, when possible, the related skeleton-analysis-of-variance tables, to assess the properties of designs. The formulation of mixed models based on them is also described. Tools used for structure-balanced experiments are also shown to be applicable to those experiments that are not. Example 1. A small wheat experiment with a Youden square design in the laboratory phase. A simpler example of a nonorthogonal multiphase experiment is used to establish concepts and introduce terminology associated with them.Design identification. A two-phase experiment begins with a field phase in which seven lines of wheat are compared, with each line replicated six times. Discussion with the researcher establishes that a soil fertility trend in one direction is likely, but not in the perpendicular direction. That is, the anticipated model is Lines | Blocks + Blocks∧Plots, where the term to the left of the vertical line (|) is assumed fixed and those to the right are assumed random. The underlined term is an identity term. A randomized complete-block design is A-optimal for this model.In the second phase, a single sample of grain is taken from each of the 42 plots and the produce from the 42 plots is allocated to 42 oven spots for determining the moisture content using the standard oven drying method. The oven can hold seven samples and so six drying runs are needed. It is believed that drying could vary between spots in the oven in a manner that is consistent from one run to the next. Extra variation is also likely between the runs. Main effects would capture these two behaviours and so the anticipated model for the second-phase units is the random model Runs + Spots + Runs∧Spots and a row-column design is required for the allocation of plots to spots. However, each first-phase unit factor cannot be allocated to a second-phase unit factor; in particular, it is impossible to allocate the 42 levels of Blocks∧Plots to the seven levels of Spots. So the allocation to Runs∧Spots needs to consider the allocation of Lines, to avoid an undesirable amount of Lines information being confounded with Spots. When the formulation of the allocation to second-phase units must account for the factors in both first-phase tiers and the allocations are randomizations, the randomizations are termed randomized-inclusive (Brien & Bailey 2006. For the example, both the lines and plots tiers must be accounted for in formulating the randomization to the spots tier. This is in contrast to composed randomizations, in which the firstphase a...

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Lines false| Blocks + \underset{̲}{Blocks \land Plots} + false| Runs + Spots + \underset{̲}{Runs \land Spots} .

Section: A Nonorthogonal Two‐phase Examplementioning

confidence: 99%

Section: A Nonorthogonal Two‐phase Examplementioning

confidence: 99%

“…() that cover nonorthogonal multiphase experiments. Further, assessing unbalanced designs as described by Brien () has not been demonstrated.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…() and in this paper. Brien () explains some of the philosophy, notation and terminology used here. A glossary is available from the multitiered experiments web site (Brien et al .…”

Section: Introductionmentioning

confidence: 99%

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Multiphase experiments with at least one later laboratory phase. II. Nonorthogonal designs

Brien

2019

Aus NZ J of Statistics

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Exposing the confounding in experimental designs to understand and evaluate them, and formulating linear mixed models for analyzing the data from a designed experiment

2023

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Comparative experiments involve the allocation of treatments to units, ideally by randomization. This necessarily confounds treatment information with unit information, which we distinguish from the other forms of information blending, in particular aliasing and marginality. We outline a factor‐allocation paradigm for describing experimental designs with the aim of (i) exhibiting the confounding in a design, using analysis‐of‐variance‐like tables, so as to understand and evaluate the design and (ii) formulating a linear mixed model based on the factor allocation that the design involves. The approach exhibits the dispersal of treatments information between units sources, allows designers a choice in the strategy that they adopt for including block‐treatment interactions, clarifies differences between experiments, accommodates systematic allocation of factors, and provides a consolidated analysis of nonorthogonal designs. It provides insights into the process of designing experiments and issues that commonly arise with designs. The paradigm has pedagogical advantages and is implemented using the R package dae.

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Bayesian A-optimal two-phase designs with a single blocking factor in each phase

Vo-Thanh

Piepho

2022

Stat Comput

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Two-phase experiments are widely used in many areas of science (e.g., agriculture, industrial engineering, food processing, etc.). For example, consider a two-phase experiment in plant breeding. Often, the first phase of this experiment is run in a field involving several blocks. The samples obtained from the first phase are then analyzed in several machines (or days, etc.) in a laboratory in the second phase. There might be field-block-to-field-block and machine-to-machine (or day-to-day, etc.) variation. Thus, it is practical to consider these sources of variation as blocking factors. Clearly, there are two possible strategies to analyze this kind of two-phase experiment, i.e., blocks are treated as fixed or random. While there are a few studies regarding fixed block effects, there are still a limited number of studies with random block effects and when information of block effects is uncertain. Hence, it is beneficial to consider a Bayesian approach to design for such an experiment, which is the main goal of this work. In this paper, we construct a design for a two-phase experiment that has a single treatment factor, a single blocking factor in each phase, and a response that can only be observed in the second phase.

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Multiphase experiments in practice: A look back

Cited by 5 publications

References 64 publications

Multiphase experiments with at least one later laboratory phase. II. Nonorthogonal designs

Multiphase experiments with at least one later laboratory phase. II. Nonorthogonal designs

Exposing the confounding in experimental designs to understand and evaluate them, and formulating linear mixed models for analyzing the data from a designed experiment

Bayesian A-optimal two-phase designs with a single blocking factor in each phase

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