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Subjective Probability and Prizes
Initial registration date
July 23, 2020
August 14, 2020 6:11 PM EDT
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Other Primary Investigator(s)
Queen Mary University of London
University of California at Los Angeles
Additional Trial Information
We collect experimental evidence to examine the descriptive validity of Anscombe & Aumann's (1963) definition of subjective probability. We document the proportion of subjects in our sample who give responses consistent with the definition and explore the responses of those who violate it. We also report at how violations co-vary with measures including competency in dealing with probabilities and demographic information.
Subjects choose between various risky choices in a way designed to test whether they behave consistently with Anscombe & Aumann's (1963) definition of subjective probability. A within-subject treatment will provide data for us to examine how the prize level of the risky choices affects responses.
Intervention Start Date
Intervention End Date
Primary Outcomes (end points)
The proportion of subjects who have the same switch point between choosing an ambiguous (for which the probability of winning a prize is unknown) vs. an uncertain (for which the probability of winning a prize is known) option, across scenarios that differ by payoff level.
Primary Outcomes (explanation)
Our primary outcome is a function of the point at which subjects switch from choosing the ambiguous option to choosing the uncertain option. This measure is a natural number (including zero), where the highest value possible is defined by the number of choices a subject makes per prize level. We want to know whether each subject has the same switch point across different prize levels.
Secondary Outcomes (end points)
Probability competency questions formed of the first five items of the "Expanded numeracy scale" of Lipkus et al. (2001).
Demographics: Age, gender, race, mother tongue, income, education, and political affiliation.
Reference: Lipkus, I. M., Samsa, G., & Rimer, B. K. (2001). General performance on a numeracy scale among highly educated samples. Medical decision making, 21(1), 37-44.
Secondary Outcomes (explanation)
We will investigate associations between these secondary measures and our primary measure.
Subjects make multiple choices between an ambiguous option (for which the probability of winning a prize is unknown) and an uncertain option (for which the probability of winning a prize is known). For each subject and prize level we vary the attractiveness of the uncertain option while keeping the ambiguous option fixed.
We will run two robustness checks of the main design. One will have exactly the same design but will use a pool of workers with Amazon's "Masters" qualification. The other will present the same choices as the main design, but in a different layout/format.
Experimental Design Details
Within-subject randomization (of the order in which each subject sees the different prize levels) is conducted by the software Qualtrics.
Randomization is within-subject.
Was the treatment clustered?
Sample size: planned number of clusters
Sample size: planned number of observations
1200 for the main wave
100-125 per robustness wave
Sample size (or number of clusters) by treatment arms
Randomization is within-subject.
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
We aim for a 95% confidence interval on our primary outcome measure (a proportion) with +/- 3 percentage points. Assuming a proportion of 0.5 (which generates the widest possible confidence interval), n=1200 provides a 95CI = [0.472,0.528].
INSTITUTIONAL REVIEW BOARDS (IRBs)
University of Oxford Economics Departmental Research Ethics Committee
IRB Approval Date
IRB Approval Number