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# Field Experiments : Design, Analysis, and Interpretation

**by**GERBER,ALAN

00

### 9780393979954

0393979954

Textbook Paperback

5/17/2012

W W NORTON

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## Summary

Written by two leading experts on experimental methods, this concise text covers the major aspects of experiment design, analysis, and interpretation in clear language. Students learn how to design randomized experiments, analyze the data, and interpret the findings. Beyond the authoritative coverage of the basic methodology, the authors include numerous features to help students achieve a deeper understanding of field experimentation, including rich examples from the social science literature, problem sets and discussions, data sets, and further readings.

## Author Biography

Alan S. Gerber is Professor of Political Science and Director of the Center for the Study of American Politics at Yale University, where he teaches courses on experimental methods, statistics, and American politics. His experimental research has appeared in numerous academic journals, including the leading journals in political science. Donald P. Green is Professor of Political Science at Columbia University and the former director of Yale University's Institution for Social and Policy Studies. He is the author of numerous articles and several scholarly books on voter turnout, party identification, and experimental methods, including Get Out the Vote! How to Increase Voter Turnout (with Alan S. Gerber).

## Table of Contents

Preface | p. xv |

Introduction | p. 1 |

Drawing Inferences from Intuitions, Anecdotes, and Correlations | p. 2 |

Experiments as a Solution to the Problem of Unobserved Confounders | p. 5 |

Experiments as Fair Tests | p. 7 |

Field Experiments | p. 8 |

Advantages and Disadvantages of Experimenting in Real-World Settings | p. 13 |

Naturally Occurring Experiments and Quasi-Experiments | p. 15 |

Plan of the Book | p. 17 |

Suggested Readings | p. 18 |

Exercises | p. 18 |

Causal Inference and Experimentation | p. 21 |

Potential Outcomes | p. 21 |

Average Treatment Effects | p. 23 |

Random Sampling and Expectations | p. 26 |

Random Assignment and Unbiased Inference | p. 30 |

The Mechanics of Random Assignment | p. 36 |

The Threat of Selection Bias When Random Assignment Is Not Used | p. 37 |

Two Core Assumptions about Potential Outcomes | p. 39 |

Excludability | p. 39 |

Non-interference | p. 43 |

Summary | p. 44 |

Suggested Readings | p. 46 |

Exercises | p. 46 |

Sampling Distributions, Statistical Inference, and Hypothesis Testing | p. 51 |

Sampling Distributions | p. 52 |

The Standard Error as a Measure of Uncertainty | p. 54 |

Estimating Sampling Variability 59 3.4- Hypothesis Testing | p. 61 |

Confidence Intervals | p. 66 |

Sampling Distributions for Experiments That Use Block or Cluster Random Assignment | p. 71 |

Block Random Assignment | p. 71 |

Matched Pair Design | p. 77 |

Summary of the Advantages and Disadvantages of Blocking | p. 79 |

Cluster Random Assignment | p. 80 |

Summary | p. 85 |

Suggested Readings | p. 86 |

Exercises | p. 86 |

Power | p. 93 |

Using Covariates in Experimental Design and Analysis | p. 95 |

Using Covariates to Rescale Outcomes | p. 96 |

Adjusting for Covariates Using Regression | p. 102 |

Covariate Imbalance and the Detection of Administrative Errors | p. 105 |

Blocked Randomization and Covariate Adjustment | p. 109 |

Analysis of Block Randomized Experiments with Treatment Probabilities That Vary by Block | p. 116 |

Summary | p. 121 |

Suggested Readings | p. 123 |

Exercises | p. 123 |

One-Sided Noncompliance | p. 131 |

New Definitions and Assumptions | p. 134 |

Denning Causal Effects for the Case of One-Sided Noncompliance 13 | p. 137 |

The Non-interference Assumption for Experiments That Encounter Noncompliance | p. 138 |

The Excludability Assumption for One-Sided Noncompliance | p. 140 |

Average Treatment Effects, Intent-to-Treat Effects, and Complier Average Causal Effects | p. 141 |

Identification of the CACE | p. 143 |

Estimation | p. 149 |

Avoiding Common Mistakes | p. 152 |

Evaluating the Assumptions Required to Identify the CACE 15 | p. 155 |

Non-interference Assumption | p. 155 |

Exclusion Restriction | p. 156 |

Statistical Inference | p. 157 |

Designing Experiments in Anticipation of Noncompliance | p. 161 |

Estimating Treatment Effects When Some Subjects Receive "Partial Treatment" | p. 164 |

Summary | p. 165 |

Suggested Readings | p. 167 |

Exercises | p. 168 |

Two-Sided Noncompliance | p. 173 |

Two-Sided Noncompliance: New Definitions and Assumptions | p. 175 |

ITT, ITT_{D}, and CACE under Two-Sided Noncompliance | p. 179 |

A Numerical Illustration of the Role of Monotonicity | p. 181 |

Estimation of the CACE: An Example | p. 185 |

Discussion of Assumptions | p. 189 |

Monotonicity | p. 190 |

Exclusion Restriction | p. 191 |

Random Assignment | p. 192 |

Design Suggestions | p. 192 |

Downstream Experimentation | p. 193 |

Summary | p. 204 |

Suggested Readings | p. 206 |

Exercises | p. 206 |

Attrition | p. 211 |

Conditions Under Which Attrition Leads to Bias | p. 215 |

Special Forms of Attrition | p. 219 |

Redefining the Estimand When Attrition Is Not a Function of Treatment Assignment | p. 224 |

Placing Bounds on the Average Treatment Effect | p. 226 |

Addressing Attrition: An Empirical Example | p. 230 |

Addressing Attrition with Additional Data Collection | p. 236 |

Two Frequently Asked Questions | p. 241 |

Summary | p. 243 |

Suggested Readings | p. 244 |

Exercises | p. 244 |

Optimal Sample Allocation for Second-Round Sampling | p. 248 |

Interference between Experimental Units | p. 253 |

Identifying Causal Effects in the Presence of Localized Spillover | p. 256 |

Spatial Spillover | p. 260 |

Using Nonexperimental Units to Investigate Spillovers | p. 264 |

An Example of Spatial Spillovers in Two Dimensions | p. 264 |

Within-Subjects Design and Time-Series Experiments | p. 273 |

Waitlist Designs (Also Known as Stepped-Wedge Designs) | p. 276 |

Summary | p. 281 |

Suggested Readings | p. 283 |

Exercises | p. 283 |

Heterogeneous Treatment Effects | p. 289 |

Limits to What Experimental Data Tell Us about Treatment Effect Heterogeneity | p. 291 |

Bounding Var (¿) and Testing for Heterogeneity | p. 292 |

Two Approaches to the Exploration of Heterogeneity: Covariates and Design | p. 296 |

Assessmg Treatment-by-Covariate Interactions | p. 296 |

Caution Is Required When Interpreting Treatment-by-Covariate Interactions | p. 299 |

Assessing Treatment-by-Treatment Interactions | p. 303 |

Using Regression to Model Treatment Effect Heterogeneity | p. 305 |

Automating the Search for Interactions | p. 310 |

Summary | p. 310 |

Suggested Readings | p. 312 |

Exercises | p. 313 |

Mediation | p. 319 |

Regression-Based Approaches to Mediation | p. 322 |

Mediation Analysis from a Potential Outcomes Perspective | p. 325 |

Why Experimental Analysis of Mediators Is Challenging | p. 328 |

Ruling Out Mediators? | p. 330 |

What about Experiments That Manipulate the Mediator? | p. 331 |

Implicit Mediation Analysis | p. 333 |

Summary | p. 336 |

Suggested Readings | p. 338 |

Exercises | p. 338 |

Treatment Postcards Mailed to Michigan Households | p. 343 |

Integration of Research Findings | p. 347 |

Estimation of Population Average Treatment Effects | p. 350 |

A Bayesian Framework for Interpreting Research Findings | p. 353 |

Replication and Integration of Experimental Findings: An Example | p. 358 |

Treatments That Vary in Intensity: Extrapolation and Statistical Modeling | p. 366 |

Summary | p. 377 |

Suggested Readings | p. 378 |

Exercises | p. 379 |

Instructive Examples of Experimental Design | p. 383 |

Using Experimental Design to Distinguish between Competing Theories | p. 384 |

Oversampling Subjects Based on Their Anticipated Response to Treatment | p. 387 |

Comprehensive Measurement of Outcomes | p. 393 |

Factorial Design and Special Cases of Non-interference | p. 395 |

Design and Analysis of Experiments In Which Treatments Vary with Subjects' Characteristics | p. 400 |

Design and Analysis of Experiments In Which Failure to Receive Treatment Has a Causal Effect | p. 406 |

Addressing Complications Posed by Missing Data | p. 410 |

Summary | p. 414 |

Suggested Readings | p. 415 |

Exercises | p. 416 |

Writing a Proposal, Research Report, and Journal Article | p. 425 |

Writing the Proposal | p. 426 |

Writing the Research Report | p. 435 |

Writing the Journal Article | p. 440 |

Archiving Data | p. 442 |

Summary | p. 444 |

Suggested Readings | p. 445 |

Exercises | p. 445 |

Protection of Human Subjects | p. 447 |

Regulatory Guidelines | p. 447 |

Guidelines for Keeping Field Experiments within Regulatory Boundaries | p. 449 |

Suggested Field Experiments for Class Projects | p. 453 |

Crafting Your Own Experiment | p. 453 |

Suggested Experimental Topics for Practicum Exercises | p. 455 |

References | p. 461 |

Index | p. 479 |

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