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Analyzing Within-Subject Experiments: Identification, Testing, and Sensitivity

Shiyao Liu, Junni L. Zhang

arXiv 27 Aug 2026 · Statistics — Methodology

arXiv:2608.26606 · PDF · Extracted main text

Abstract

Recent work encourages political scientists to move from post-only toward within-subject designs for improved precision from repeated measurements. We formalize a potential-outcomes framework for two-period within-subject designs that allows for unequal allocation and heterogeneous treatment and carryover effects. We characterize the pooled estimator and evaluate the carryover test used to justify pooling. We find: first, pooling identifies the average treatment effect only when the gap in the average carryover effects is zero across the two treatment sequences. The unit-clustered standard error for the pooled estimator is identical to its design-based counterpart. Second, under mild conditions, the carryover test has strictly less power than the average-treatment-effect test with post-only data. The resulting two-step procedure, which pools only after a nonrejected test, produces confidence intervals that typically undercover. When the gap is zero, undercoverage occurs if and only if pooling is more efficient than post-only analysis, precisely when the within-subject design is worthwhile. When the gap is nonzero, undercoverage is typical unless the gap or sample size is large. Third, we derive a sensitivity analysis and find published conclusions robust to plausible carryover gaps. We therefore endorse within-subject designs but recommend justifying a zero carryover gap substantively and reporting sensitivity to departures.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Clifford, Scott, Sheagley, Geoffrey, Piston, Spencer (2021) Increasing precision without altering treatment effects: Repeated measures designs in survey experiments1.000277100%
2Jordan, Diana, Ollerenshaw, Trent, Trexler, Andrew (2026) New Evidence and Design Considerations for Repeated Measure Experiments in Survey Research1.000165100%
3Freeman, PR (1989) The performance of the two-stage analysis of two-treatment, two-period crossover trials1.00074100%
4Carnahan, Dustin, Bergan, Daniel E (2022) Correcting the misinformed: the effectiveness of fact-checking messages in changing false beliefs0.64422100%
5Clifford, Scott, Sheagley, Geoffrey, Piston, Spencer (2021) Replication Data for: Increasing Precision without Altering Treatment Effects: Repeated Measures Designs in Survey Experiments0.64422100%
6Halling, Aske (2024) Frontline employees' responses to citizens' communication of administrative burdens0.64422100%
7Jordan, Diana, Ollerenshaw, Trent, Trexler, Andrew (2026) Replication Data for: New Evidence and Design Considerations for Repeated Measure Experiments in Survey Research0.64422100%
8Ozer, Adam L., Wright, Jamie M (2022) Partisan news versus party cues: The effect of cross-cutting party and partisan network cues on polarization and persuasion0.64422100%
9Tappin, Ben M (2023) Estimating the between-issue variation in party elite cue effects0.64422100%
10Van Trappen, Sigrid (2023) Biased expectations? An experimental test of which party selectors are more likely to stereotype ethnic minority aspirants as le…0.64422100%

Showing the top 10 of 44 scored citations.