Skip to main content Accessibility help
×
Hostname: page-component-7c8c6479df-p566r Total loading time: 0 Render date: 2024-03-18T16:49:57.582Z Has data issue: false hasContentIssue false

6 - Neyman's Repeated Sampling Approach to Completely Randomized Experiments

from PART II - CLASSICAL RANDOMIZED EXPERIMENTS

Published online by Cambridge University Press:  05 May 2015

Guido W. Imbens
Affiliation:
Stanford University, California
Donald B. Rubin
Affiliation:
Harvard University, Massachusetts
Get access

Summary

INTRODUCTION

In the last chapter we introduced the Fisher Exact P-value (FEP) approach for assessing sharp null hypotheses. As we saw, a sharp null hypothesis allowed us to fill in the values for all missing potential outcomes in the experiment. This was the basis for deriving the randomization distributions of various statistics, that is, the distributions induced by the random assignment of the treatments given fixed potential outcomes under that sharp null hypothesis. During the same period in which Fisher was developing this method, Neyman (1923, 1990) was focused on methods for the estimation of, and inference for, average treatment effects, also using the distribution induced by randomization, sometimes in combination with repeated sampling of the units in the experiment from a larger population of units. At a general level, he was interested in the long-run operating characteristics of statistical procedures under both repeated sampling from the population and randomized assignment of treatments to the units in the sample. Specifically, he attempted to find point estimators that were unbiased, and also interval estimators that had the specified nominal coverage in large samples. As noted before, his focus on average effects was different from the focus of Fisher; the average effect across a population may be equal to zero even when some, or even all, unit-level treatment effects differ from zero.

Neyman's basic questions were the following. What would the average outcome be if all units were exposed to the active treatment, ȳ(1) in our notation? How did that compare to the average outcome if all units were exposed to the control treatment, ȳ(0) in our notation? Most importantly, what is the difference between these averages, the average treatment effect (Here we use the subscript fs to be explicit about the fact that the estimand is the finite-sample average treatment effect. Later we use the notation τsp to denote the super-population average treatment effect.) Neyman's approach was to develop an estimator of the average treatment effect and derive its mean and variance under repeated sampling.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2015

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×