Likelihood Magnitudes and Posterior Beliefs

Last registered on August 27, 2026
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Pre-Trial

Trial Information

General Information

Title
Likelihood Magnitudes and Posterior Beliefs
RCT ID
AEARCTR-0019513
Initial registration date
August 26, 2026

Initial registration date is when the trial was registered.

It corresponds to when the registration was submitted to the Registry to be reviewed for publication.

First published
August 27, 2026, 12:58 PM EDT

First published corresponds to when the trial was first made public on the Registry after being reviewed.

Locations

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Primary Investigator

Name
Tashfeen Saeed
Affiliation
Cornell University
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Other Primary Investigator(s)

Additional Trial Information

Status
In development
Start date
2026-08-31
End date
2026-09-20
Keywords
Behavior, Lab
Additional Keywords
Beliefs, Belief updating, Bayesian updating, Likelihood judgments, Posterior beliefs, Information processing, Probabilistic reasoning, Laboratory experiment
JEL code(s)
D83, C91
Secondary IDs
Prior work
This trial does not extend or rely on any prior RCTs.
Abstract
This study proposes an experiment that examines how the magnitude of underlying likelihoods influences likelihood judgments and posterior beliefs. The experiment constructs information environments that hold the likelihood ratio—and therefore the Bayesian posterior—fixed while varying the absolute magnitude of the underlying likelihoods. By eliciting both likelihood judgments and posterior beliefs, the study investigates whether likelihood-reporting distortions depend on likelihood magnitude, whether these distortions propagate to posterior beliefs, and whether pure and mixed samples with identical likelihood ratios generate different likelihood judgments or posterior beliefs.
External Link(s)

Registration Citation

Citation
Saeed, Tashfeen. 2026. "Likelihood Magnitudes and Posterior Beliefs." AEA RCT Registry. August 27. https://doi.org/10.1257/rct.19513-1.0
Sponsors & Partners
Experimental Details

Interventions

Intervention(s)
Intervention Start Date
2026-08-31
Intervention End Date
2026-09-18

Primary Outcomes

Primary Outcomes (end points)
The primary outcomes are participants’ reported posterior probabilities that a bag generated a given sample, and their reported likelihood probabilities of drawing the sample from each bag.
Primary Outcomes (explanation)

Secondary Outcomes

Secondary Outcomes (end points)
Secondary Outcomes (explanation)

Experimental Design

Experimental Design
The study uses a belief-updating task based on a standard bookbag-and-poker-chip paradigm. Participants complete multiple independent rounds in which there are two bags containing different proportions of colored balls. In each round, one bag is selected at random, a small sample of balls is drawn with replacement, and participants report probabilities based on the observed sample.

Participants are randomly assigned to one of two treatment conditions. In the Posterior (P) condition, participants report only the probability that each bag generated the observed sample. In the Likelihood/Posterior (L/P) condition, participants first report the probability of drawing the sample from each bag (likelihood judgments) and then report posterior beliefs.

Across rounds, the experimental environments vary the sample size, bag compositions, and observed samples. The primary environments are constructed to hold the likelihood ratio—and therefore the Bayesian posterior—fixed while varying the absolute magnitude of the underlying likelihoods. Additional benchmark environments compare pure and mixed samples that imply the same likelihood ratio and Bayesian posterior. All questions are framed hypothetically, with probabilities fully determined by the stated bag compositions and samples.

Additional details on the experimental procedures, analysis plan, and exclusion criteria are provided in the uploaded Pre-Analysis Plan.
Experimental Design Details
Not available
Randomization Method
Participants are randomly assigned to one of two treatment conditions using Qualtrics’ built-in randomization features.
Randomization Unit
Individual participants
Was the treatment clustered?
No

Experiment Characteristics

Sample size: planned number of clusters
200 participants
Sample size: planned number of observations
200 participants
Sample size (or number of clusters) by treatment arms
100 participants in each of the two treatment groups
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
Supporting Documents and Materials
IRB

Institutional Review Boards (IRBs)

IRB Name
Cornell University Office of Research Integrity and Assurance
IRB Approval Date
2026-07-24
IRB Approval Number
IRB0151094
Analysis Plan

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