Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- PART I INTRODUCTION
- PART II CLASSICAL RANDOMIZED EXPERIMENTS
- 4 A Taxonomy of Classical Randomized Experiments
- 5 Fisher's Exact P-Values for Completely Randomized Experiments
- 6 Neyman's Repeated Sampling Approach to Completely Randomized Experiments
- 7 Regression Methods for Completely Randomized Experiments
- 8 Model-Based Inference for Completely Randomized Experiments
- 9 Stratified Randomized Experiments
- 10 Pairwise Randomized Experiments
- 11 Case Study: An Experimental Evaluation of a Labor Market Program
- PART III REGULAR ASSIGNMENT MECHANISMS: DESIGN
- PART IV REGULAR ASSIGNMENT MECHANISMS: ANALYSIS
- PART V PRGULAR ASSIGNMENT MECHANISMS:SUPPLEMENTARY ANALYSES
- PART VI REGULAR ASSIGNMENT MECHANISMS WITH NONCOMPLIANCE: ANALYSIS
- PART VII CONCLUSION
- References
- Author Index
- Subject Index
4 - A Taxonomy of Classical Randomized Experiments
from PART II - CLASSICAL RANDOMIZED EXPERIMENTS
Published online by Cambridge University Press: 05 May 2015
- Frontmatter
- Dedication
- Contents
- Preface
- PART I INTRODUCTION
- PART II CLASSICAL RANDOMIZED EXPERIMENTS
- 4 A Taxonomy of Classical Randomized Experiments
- 5 Fisher's Exact P-Values for Completely Randomized Experiments
- 6 Neyman's Repeated Sampling Approach to Completely Randomized Experiments
- 7 Regression Methods for Completely Randomized Experiments
- 8 Model-Based Inference for Completely Randomized Experiments
- 9 Stratified Randomized Experiments
- 10 Pairwise Randomized Experiments
- 11 Case Study: An Experimental Evaluation of a Labor Market Program
- PART III REGULAR ASSIGNMENT MECHANISMS: DESIGN
- PART IV REGULAR ASSIGNMENT MECHANISMS: ANALYSIS
- PART V PRGULAR ASSIGNMENT MECHANISMS:SUPPLEMENTARY ANALYSES
- PART VI REGULAR ASSIGNMENT MECHANISMS WITH NONCOMPLIANCE: ANALYSIS
- PART VII CONCLUSION
- References
- Author Index
- Subject Index
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.
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- Causal Inference for Statistics, Social, and Biomedical SciencesAn Introduction, pp. 47 - 56Publisher: Cambridge University PressPrint publication year: 2015