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How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It
Open accessAbstract
In principle, experiments offer a straightforward method for social scientists to accurately estimate causal effects. However, scholars often unwittingly distort treatment effect estimates by conditioning on variables that could be affected by their experimental manipulation. Typical examples include controlling for posttreatment variables in statistical models, eliminating observations based on posttreatment criteria, or subsetting the data based on posttreatment variables. Though these modeling choices are intended to address common problems encountered when conducting experiments, they can bias estimates of causal effects. Moreover, problems associated with conditioning on posttreatment variables remain largely unrecognized in the field, which we show frequently publishes experimental studies using these practices in our discipline's most prestigious journals. We demonstrate the severity of experimental posttreatment bias analytically and document the magnitude of the potential distortions it induces using visualizations and reanalyses of real‐world data. We conclude by providing applied researchers with recommendations for best practice.
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“almost 1 in 10 engaged in both (10.7%, eight studies)”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Don't We Already Know This?
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“which we show frequently publishes experimental studies using these practices in our discipline's most prestigious journals”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Abstract
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“14.7% of studies subsetted the data based on potential posttreatment criteria (11 of 75 studies reviewed)”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Don't We Already Know This?
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“problems associated with conditioning on posttreatment variables remain largely unrecognized in the field”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Abstract
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“21.3%(16 of 75) controlled for a posttreatment covariate in a statistical model”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Don't We Already Know This?
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“Among the studies that controlled for a posttreatment variable, six used a mediation technique (8%).”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Don't We Already Know This?
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In the paper
“Most strikingly, 12% of studies conditioned on a variable shown to be affected by the experimental treatment in analyses contained within the article itself (9 of 75).”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Don't We Already Know This?
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“few acknowledge potential concerns regarding the bias that posttreatment conditioning can introduce”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Don't We Already Know This?
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In the paper
“the magnitude of the negative coefficient approximately doubles relative to the unconditional estimate among respondents who perceive themselves as further from Eid (-.460; 95% CI: -0.567, -0.353).”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Analysis: An Original Study of Judge Perceptions
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In the paper
“Trump's endorsement reduced the likelihood of supporting Eid's retention by -0.214 (p < .01,95% CI: -0.301, -0.127) on the four-point scale.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Analysis: An Original Study of Judge Perceptions
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“while some studies lost cases due to posttreatment attrition (8.0%)”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Don't We Already Know This?
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“About 1 in 4 drop cases or subset the data based on posttreatment criteria, and nearly a third include posttreatment variables as covariates.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Don't We Already Know This?
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In the paper
“These effects are opposite in sign and in both cases highly significant (p < .01 in both directions).”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Analysis: An Original Study of Judge Perceptions
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“The sign of the estimated treatment effect reverses in the subsample of respondents who perceive themselves as being close to Eid, becoming positive (.257, 95% CI: 0.132, 0.382)”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Analysis: An Original Study of Judge Perceptions
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“Most notably, the appropriations treatment effect estimate in the limited information condition more than doubles in magnitude and becomes nearly statistically significant in the fourth column (p < .11).”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Reanalysis: Dickson, Gordon, and Huber (2015)
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“By contrast, the effect of appropriations among groups with limited information and the effect of limited information in either compensation group are not distinguishable from zero.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Reanalysis: Dickson, Gordon, and Huber (2015)
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“These practices are typically employed in an effort to address practical problems like noncompliance or to try to answer difficult inferential questions such as identifying causal mechanisms.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Conclusion
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“Reviewers often ask authors to try to rule out alternative explanations in this way.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Conclusion
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“| Insufficient information to code | 1.3% |”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Conclusion
Strength:plain· not yet calibratedn = 75Tests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
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“Assumption (1) implies that individuals in the treatment and control conditions will be similar in expectation with respect to unobserved confounders such as SES.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Why Experiments Generate Unbiased Estimates of Treatment Effects
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- The authors state this as an assumption: Treatment assignment is independent of potential outcomes conditional on covariates.
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In the paper
“As long as we do not condition on a posttreatment variable, randomization guarantees that Assumption (1) is satisfied and both quantities go to zero.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Why Experiments Generate Unbiased Estimates of Treatment Effects
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- The authors state this as an assumption: Treatment assignment is independent of potential outcomes conditional on covariates.
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In the paper
“Further, Assumption (1) requires that x is not causally related to T”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Why Experiments Generate Unbiased Estimates of Treatment Effects
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- The authors state this as an assumption: Treatment assignment is independent of potential outcomes conditional on covariates.
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In the paper
“Although it is possible to construct examples where this bias is zero, it will not be zero in general.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Dropping or Selecting Observations Based on Criteria Influenced by the Treatment.
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In the paper
“dropping cases or subsetting based on posttreatment criteria will unbalance the treatment and control conditions with respect to unmeasured confounders and bias our treatment effect estimates.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Dropping or Selecting Observations Based on Criteria Influenced by the Treatment.
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In the paper
“the dangers of posttreatment bias have long been recognized in the fields of statistics, econometrics, and political methodology”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Abstract
What the sources say
- Not checked yetcites Acharya, Blackwell, and Sen 2016
- Not checked yetcites Elwert and Winship 2014
- Not checked yetcites King and Zeng 2006
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In the paper
“Instead, it is a biased estimate of the direct effect of the Trump endorsement, and the bias can be in any direction at all.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Analysis: An Original Study of Judge Perceptions
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In the paper
“As a result, control group participants who think Eid is centrist on average and perceive themselves to be relatively close to her are being compared to treatment group participants who think she is close to them after finding out she was endorsed by President Trump.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Analysis: An Original Study of Judge Perceptions
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In the paper
“More recent work has amplified these points in the context of observational research”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Don't We Already Know This?
What the sources say
- Not checked yetcites Acharya, Blackwell, and Sen 2016
- Not checked yetcites Blackwell 2013
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
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In the paper
“By conditioning on a posttreatment variable, we have unbalanced the treatment and control groups in terms of ideology and unmeasured confounders and thus biased the treatment effect estimate.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Analysis: An Original Study of Judge Perceptions
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In the paper
“In this scenario, dropping respondents based on posttreatment attention checks is the equivalent of selecting on a posttreatment covariate and would again risk bias.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Use Pretreatment Moderators, Control Variables, and Attention Checks
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In the paper
“As a result, both approaches provide biased treatment effect estimates that do not correspond to meaningful causal estimands.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Reanalysis: Dickson, Gordon, and Huber (2015)
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In the paper
“Though it is not necessary to do so (randomization eliminates omitted variable bias in expectation), regression adjustment for covariates has been shown to induce only minor bias and to potentially increase efficiency under realistic conditions (e.g., Lin 2013).”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Use Pretreatment Moderators, Control Variables, and Attention Checks
What the sources say
- Not checked yetcites Lin 2013
Strength:plain· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“Dickson, Gordon, and Huber (2015) note that both models are sensitive to model specification; our analysis suggests that these results may be attributable to posttreatment bias.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Reanalysis: Dickson, Gordon, and Huber (2015)
What the sources say
- Not checked yetcites Dickson, Gordon, and Huber (2015)
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In the paper
“We replicate the appropriations treatment effect for full information groups, but our analysis raises concerns about posttreatment bias for both the limited information effect in the salary condition and the appropriation effect in the limited information condition.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Reanalysis: Dickson, Gordon, and Huber (2015)
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In the paper
“Under more realistic assumptions, however, the choices are more limited: Gerber and Green (2012) recommend extreme value bounds (Manski 1989), where analysts estimate the largest and smallest ATEs possible if missing information were filled in with extreme outcomes.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Use Double Sampling, Extreme Value Bounds, or Instruments to Account for Attrition
What the sources say
- Not checked yetcites Gerber and Green (2012)
- Not checked yetcites Manski 1989
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In the paper
“If we are willing to assume that missingness is not a function of unmeasured confounders, we can use familiar methods such as imputation or marginal structural models.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Use Double Sampling, Extreme Value Bounds, or Instruments to Account for Attrition
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- The authors state this as an assumption: Missingness is not a function of unmeasured confounders.
In the paper
“Finally, Huber (2012) seeks to reduce bias from attrition using inverse probability weighting and instrumental variables for missingness.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Use Double Sampling, Extreme Value Bounds, or Instruments to Account for Attrition
What the sources say
- Not checked yetcites Huber (2012)
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
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In the paper
“There is no reason to believe that these assumptions are correct in real-world data.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > The Inadequacy of Empirical Tests for Posttreatment Bias
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- The authors state this as an assumption: Critical parameters including the treatment effect, the effect of the treatment on the covariate, and the effects of the confounders on outcomes and covariates were constant for each individual.
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In the paper
“This approach is not only very difficult to execute (it requires a treatment that affects the mediator but not the outcome) but also subject to criticism for implausible assumptions.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Understand the Costs of Mediation Analysis
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In the paper
“First, even in the simplified examples presented above, posttreatment bias will not be eliminated unless the effect of the treatment on the covariate (␥ ) is precisely zero-something that cannot be established using traditional hypothesis testing.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > The Inadequacy of Empirical Tests for Posttreatment Bias
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In the paper
“Though these intentions are laudable, we demonstrate that posttreatment conditioning undermines the value of randomization and biases treatment effect estimates using analytical results as well as a reanalysis of real-world data from two studies.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Conclusion
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In the paper
“Finally, it is important to note that posttreatment bias cannot be easily diagnosed or remedied empirically.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > The Inadequacy of Empirical Tests for Posttreatment Bias
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In the paper
“Imai, Tingley, and Yamamoto (2013) outline several designs that allow researchers to estimate mediation effects, but these too come with additional assumptions (e.g., a consistency assumption) or require use of less intuitive estimands (e.g., average complier indirect effects).”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Understand the Costs of Mediation Analysis
What the sources say
- Not checked yetcites Imai, Tingley, and Yamamoto (2013)
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In the paper
“However, we also show that scholars can address the concerns that motivate the use of these practices using existing analytical approaches.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Conclusion
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Many of the practices described above appear to be driven by authors' efforts to show that their proposed mechanism is responsible for the treatment effect.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Conclusion
Strength:hedged· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✗ Checkable: fails✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Similarly, mediation analyses require strong assumptions that may be inconsistent with the goals of experimental research.”
§ How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It > Conclusion
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The authors state this as an assumption.
Treatment assignment is independent of potential outcomes conditional on covariates.
“Assumption (1) : (y [T =1] , y [T =0] ) ⊥ ⊥ T |X, which states that treatment assignment is independent of potential outcomes conditional on covariates.”
The authors state this as an assumption.
All variables are observed without error.
“For the sake of expositional clarity, and without loss of generality, we assume that all variables are observed without error.”
The authors state this as an assumption.
The main parameters in Model 4 do not vary as a function of T or x.
“Note that Model 4 also assumes that the main parameters in the model ( , ␣ Y , , , and Y ) do not vary as a function of T or x, which is why we can move these parameters outside of the expectations.”
The authors state this as an assumption.
The influence of unmeasured confounders along the various causal paths will not somehow cancel out.
“For instance, we assume that the influence of unmeasured confounders along the various causal paths will not somehow cancel out.”
The authors state this as an assumption.
x has no direct effect on y in the true model.
“If we instead allow x to have a direct effect on y in the true model, the biases we describe below still hold, but the calculations involved are more complex.We make this simplifying assumption so that we can focus our exposition on the posttreatment bias that arises from unblocking the path from u to y.”
The authors state this as an assumption.
β = 0.
“To simplify exposition, we focus here only on the bias resulting from the imbalance in u induced by controlling for the posttreatment variable x by assuming that  = 0.”
The authors state this as an assumption.
Critical parameters including the treatment effect, the effect of the treatment on the covariate, and the effects of the confounders on outcomes and covariates were constant for each individual.
“Second, we made the simplifying assumption in our examples above that critical parameters including the treatment effect ( ), the effect of the treatment on the covariate (␥ ), and the effects of the confounders on outcomes and covariates ( Y , X ) were constant for each individual.”
The authors state this as an assumption.
Missingness is not a function of unmeasured confounders.
“If we are willing to assume that missingness is not a function of unmeasured confounders, we can use familiar methods such as imputation or marginal structural models.”
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In the citing paper
“An important caveat for these analyses is that attention was measured post-treatment, which has the potential to undermine inferences drawn from these data43”
From Accuracy prompts are a replicable and generalizable approach for reducing the spread of misinformation (2022) · cites this paper as [43]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Year of the Broockman and Butler reanalysis differs
MinorThe discussion identifies the reanalyzed study as Broockman and Butler (2017), while the supporting-information list calls it Broockman and Butler (2015).
“• Reanalysis of Broockman and Butler (2015)”
“an additional demonstration of posttreatment bias using data fromBroockman and Butler (2017).”
Citations
Cites
Baron, R. M., & Kenny, D. A. (1986) · Journal of Personality and Social Psychology · doi:10.1037/0022-3514.51.6.1173 · Cited by 91,532
Data Analysis Using Regression and Multilevel/Hierarchical Models
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Metadata
- Authors
- Montgomery, J. M., Nyhan, B., & Torres, M.
- Affiliations
- Washington University in St. Louis (US)
- Dartmouth College (US)
- Venue
- American Journal of Political Science
- Publisher
- Wiley
- Published
- 2018-03-30
- Volume
- 62
- Issue
- 3
- Pages
- 760-775
- ISSN
- 0092-5853 (ISSN-L)
- 1540-5907
- OpenAlex
- W2794592087
- Cited by
- 800
- References
- 49
- Citations by year
- 2026: 68 · 2025: 128 · 2024: 120 · 2023: 114 · 2022: 105 · 2021: 89 · 2020: 95 · 2019: 48 · 2018: 27
- FWCI
- 53.73
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- American Journal of Political Science (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Social Sciences › Public Administration › Evaluation and Performance Assessment
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- causal effect estimation, experimental design, confounding, bias in treatment effect estimates
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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