Theses and Dissertations

DOI

10.17077/etd.midgyxmw

Dissertation

Spring 2015

Degree Name

PhD (Doctor of Philosophy)

Statistics

Lang, Joseph B

Chan, Kung-Sik

Cowles, Kate

Jones, Michael P

Tan, Aixin

Abstract

Comparative experiments, in which subjects are randomized to one of two treatments, are performed often. There is no shortage of papers testing whether a treatment effect exists and providing confidence intervals for the magnitude of this effect. While it is well understood that the object and scope of inference for an experiment will depend on what assumptions are made, these entities are not always clearly presented.

We have proposed one possible method, which is based on the ideas of Jerzy Neyman, that can be used for constructing confidence intervals in a comparative experiment. The resulting intervals, referred to as Neyman-type confidence intervals, can be applied in a wide range of cases. Special care is taken to note which assumptions are made and what object and scope of inference are being investigated. We have presented a notation that highlights which parts of a problem are being treated as random. This helps ensure the focus on the appropriate scope of inference.

The Neyman-type confidence intervals are compared to possible alternatives in two different inference settings: one in which inference is made about the units in the sample and one in which inference is made about units in a fixed population. A third inference setting, one in which inference is made about a process distribution, is also discussed. It is stressed that certain assumptions underlying this third type of inference are unverifiable. When these assumptions are not met, the resulting confidence intervals may cover their intended target well below the desired rate.

Through simulation, we demonstrate that the Neyman-type intervals have good coverage properties when inference is being made about a sample or a population. In some cases the alternative intervals are much wider than necessary on average. Therefore, we recommend that researchers consider using our Neyman-type confidence intervals when carrying out inference about a sample or a population as it may provide them with more precise intervals that still cover at the desired rate.

Public Abstract

Comparative experiments, in which subjects are randomly assigned to one of two treatment groups, are performed often. There is no shortage of papers testing whether a treatment effect exists and providing an interval of plausible values for the magnitude of this effect. However, what is meant by a “treatment effect” is not always clearly presented. The scope and target of one’s inference will depend on what assumptions are made.

We have proposed one possible method, based on ideas of Jerzy Neyman, for constructing intervals of plausible values for a treatment effect. The resulting intervals, which we refer to as Neyman-type intervals, can be applied in a wide range of cases. Special care is taken to note what assumptions are made and what is meant by a treatment effect in a particular application.

Through computer simulation, we demonstrate that in many cases the Neymantype intervals will be narrower on average than other intervals while still containing the true treatment effect the desired proportion of the time.

Keywords

publicabstract, confidence interval, randomization-based confidence interval, randomized experiment, treatment effect

xi, 141 pages

Bibliography

Includes bibliographical references (pages 139-141).