Skip to main content Accessibility help
×
Hostname: page-component-7c8c6479df-995ml Total loading time: 0 Render date: 2024-03-17T19:45:02.937Z Has data issue: false hasContentIssue false

4 - A Taxonomy of Classical 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 this chapter we introduce four specific examples of classical randomized assignment mechanisms, and we relate these examples to the general taxonomy of assignment mechanisms described in the previous chapter. The four examples, Bernoulli trials, completely randomized experiments, stratified randomized experiments (randomized blocks), and paired randomized experiments, all satisfy the four criteria necessary for assignment mechanisms to be classified as classical randomized experiments. These criteria, as discussed in more detail in Chapter 3, require that the assignment mechanism (i) is individualistic, with the dependence on values of covariates and potential outcomes for other units limited; (ii) is probabilistic – each experimental unit has a positive probability of being assigned to the active treatment and a positive probability of being assigned to the control treatment; (iii) is unconfounded – that is, given covariates, does not depend on potential outcomes; and (iv) has a known functional form that is controlled by the researcher.

The key difference between the four types of classical randomized experiments we consider in this chapter is in the set of assignment vectors W (the N-dimensional vector with elements Wi ∈ {0, 1}) with positive probability. Let the set of all possible values be denoted by W = {0, 1}N, with cardinality 2N, and let the subset of values for W with positive probability be denoted by W+. In the first example of randomized experiments, Bernoulli trials, each of the 2N possible vectors W defining the treatment assignments of the full population of size N has positive probability. However, such trials put positive probability on assignments in which all units receive the same treatment, thereby compromising our ability to draw credible and precise inferences regarding the causal effect of one treatment versus another from the resulting data. The remaining three types of classical randomized experiments impose increasingly restrictive sets of conditions on the set W+ of values of W with positive probability.

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
×