Abstract/Details

Predictors of treatment means for a one factor completely randomized design


2009 2009

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Abstract (summary)

A one factor experimental design is developed based on the potential observable outcome framework, sampling from finite population of units and random allocation of treatments. No assumptions are made about the distribution of units and distribution of treatments. We introduce sampling and treatment assignment random variables to represent the joint permutation of the potentially observable population. The joint roles of sampling and treatment assignments are considered. The predictors for treatment means, presented by the observed values in the sample and unobserved values of the remainder, are obtained by Royall’s (1976) prediction theory. We take three cases into account: the latent values correspond to a no interaction model and there are no response errors; the latent values correspond to a model with interaction and there are no response errors; the latent values correspond to a model with interaction and response errors. The predictors with the property of being “shrunk” towards the overall mean are similar to realized random effects in the one way random effect model. If the treatment is not selected in the sample, the predictors correspond to the overall mean. The model is based solely on the population sampling and treatment assignments, and provides a design based framework for inference of linear combinations of the treatment means. The population of treatments can be of small size and up to all of the treatments can be assigned to the samples. This model extended the randomization model developed by Kempthorne (1952) via introducing random allocation of the treatments. Theoretically the predictors provide smaller MSEs than using the linear combination of sample means. When the variance components are unknown, the empirical predictors are considered. The confidence intervals for the empirical predictors are calculated using bootstrapping methods. Several bootstrap methods, such as bootstrapping with replacement (BWR) or bootstrapping without replacement (BWO) are introduced. Each bootstrap method is developed to account for the sampling from the finite population of units and random allocation of treatments. Comparisons of the different bootstrapping methods are made methodologically, and via simulation. We discuss these comparisons, and recommend an appropriate bootstrapping method for statistical inference in the one factor experimental design.

Indexing (details)


Subject
Biostatistics
Classification
0308: Biostatistics
Identifier / keyword
Biological sciences, Experimental design, Prediction, Random effects, Simple random sample, Treatment mean
Title
Predictors of treatment means for a one factor completely randomized design
Author
Xu, Bo
Number of pages
225
Publication year
2009
Degree date
2009
School code
0118
Source
DAI-B 70/09, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781109352269
Advisor
Stanek, Edward J.
Committee member
Buonaccorsi, John P.; Pekow, Penelope S.
University/institution
University of Massachusetts Amherst
Department
Public Health
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3372284
ProQuest document ID
304927233
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304927233
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