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Abstract
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Before
This research follows up on a previous study of the effect of the gambler's fallacy on bidding for taxi bookings among Singapore taxi drivers.
In the previous study, subjects were randomly assigned to three conditions---a control group, treatment 1 (placebo), and treatment 2 (tutorial). Subjects in treatment 1 (placebo) and treatment 2 (tutorial) were asked to compare the probabilities of pairs of sequences of five random coin tosses. In addition, treatment 2 (tutorial) subjects were taught that the probabilities of the two sequences are equal. The control group was not asked the coin toss question.
Then, subjects in all three conditions were presented a scenario in which the previous job was a booking which was randomly posed as either completed or cancelled. Then they were presented a new booking 5 minutes away and asked to bid an estimated time of arrival (2, 4, 6, or 8 minutes) for the booking.
The previous study found that the debiasing tutorial mitigated the effect of previous cancellation on the ETA bid on the next booking. However, owing to small sample size based on a pilot with unusually large effect size, the estimated effect was not significant at conventional levels.
Also, the previous study did not register an examination of the effect of the extent of gambler's fallacy beliefs on bidding for bookings. Based on comments from the behavioral economics community, this is an issue of first-order importance.
Accordingly, in the present study, the main analysis will focus on subjects who believe in the gambler's fallacy (as revealed by their answers to revised questions on coin tosses). The analysis will test the effect of a previous cancellation on the ETA bid on the next booking.
The secondary analysis will examine the contingent effect of the debiasing tutorial on the effect of previous cancellation on the ETA bid on the next booking.
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After
This experiment aims to investigate sequence effects in the context of taxi driving. Specifically, it examines how the outcome of a previous booking (whether it was completed or canceled) influences taxi drivers’ beliefs about the likelihood of the next booking being canceled and their bidding on the next booking.
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Last Published
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Before
August 15, 2024 05:34 AM
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After
October 31, 2024 04:01 AM
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Primary Outcomes (End Points)
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Before
(1) All subjects: Proportion of subjects who believe in the gambler's fallacy.
(2) All subjects: Estimated time of arrival (2, 4, 6, or 8 minutes) for a new booking request 5 minutes drive away.
(3) Subjects in the control group: (i) If they were posed the previous job as a cancelled booking: The reason for their ETA bid---whether disappointment at cancellation or belief that the next booking is less likely to be cancelled. (ii) If they were posed the previous job as a completed booking: The reason for their ETA bid---whether gladness with success or belief that the next booking is more likely to be cancelled.
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After
(1) Belief that next booking would be cancelled.
Subjects will be asked to estimate the likelihood that the next booking will be cancelled, using a 5-point Likert scale ranging from "much less likely than usual" to "much more likely than usual."
(2) Bidding.
Subjects will be asked to bid on the next booking from multiple choices based on the options in the taxi company booking system: 2 minutes, 4 minutes, 6 minutes, 8 minutes, or "do not bid."
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Randomization Method
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Before
Randomization by online Qualtrics system: (i) Assignment to conditions---control and treatment (tutorial); (ii) Posing the previous booking as completed or cancelled.
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After
Randomization by online Qualtrics system.
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Planned Number of Clusters
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Before
Not clustered: Please refer to Planned Number of Observations below.
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Not clustered.
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Planned Number of Observations
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Before
Main analysis
The main analysis will be a Poisson regression in which the main coefficient of interest is an interaction. For Poisson regressions, GPower provides power analysis only for a single non-interacted variable. Accordingly, we calculated the required sample size as follows:
(a) OLS regression with three explanatory variables, focusing on the interaction, belief in the gambler's fallacy x previous booking cancelled: 658;
(b) OLS regression limited to believers in the gambler's fallacy with one explanatory variable, focusing on the previous booking cancelled: 102;
(c) Poisson regression limited to believers in the gambler's fallacy with one explanatory variable, focusing on the previous booking cancelled: 114.
Poisson inflation factor = (c)/(b) = 114/102. Poisson with interaction = OLS with interaction x Poisson inflation factor = (a) x (c)/(b) = 658 x 114/102 = 736.
Secondary analysis
The secondary analysis will be a Poisson regression in which the main coefficient of interest is an interaction. For Poisson regressions, GPower provides power analysis only for a single non-interacted variable. Accordingly, we calculated the required sample size as follows:
(a) OLS regression with three explanatory variables, focusing on the interaction, tutorial x previous booking cancelled: 69;
(b) OLS regression limited to previous booking cancelled with one explanatory variable, focusing on tutorial: 59;
(c) Poisson regression limited to previous booking cancelled with one explanatory variable, focusing on tutorial: 90.
Poisson inflation factor = (c)/(b) = 90/59. Poisson with interaction = OLS with interaction x Poisson inflation factor = (a) x (c)/(b) = 69 * 90/59 = 106.
Based on the previous study, 0.34 of subjects believe in the gambler's fallacy. Accordingly, the required sample for the secondary analysis is 106/0.34 = 312.
Considering both the main and secondary analyses, the required sample size is the larger of the required sample size for the two analyses, i.e., 736. In addition, we must allow for subjects not completing the survey . Based on the previous study, 0.2 of subjects did not complete the survey. Accordingly, the required sample (Planned Number of Observations) is 736/0.80 = 920.
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After
Target sample size: 2641 drivers. However, due to administrative constraints in scheduling surveyors and recruiting taxi drivers, we plan to stop at the collection of 500 responses or 15 December 2024, which ever is earlier.
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Sample size (or number of clusters) by treatment arms
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Before
Randomize into control and treatment (tutorial) in the ratio 1:1.
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Each subject will have an equal probability (25%) of being assigned to one of four conditions:
(a) Low fare, first booking cancelled.
(b) Low fare, first booking completed.
(c) High fare, first booking cancelled.
(d) High fare, first booking completed.
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Power calculation: Minimum Detectable Effect Size for Main Outcomes
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Before
Please refer to Planned Number of Observations above.
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We focus on Hypothesis 1 for our power calculation. Using G*Power, we conducted a power analysis for a Poisson regression of the stated belief on the cancellation condition posed to drivers, with fixed effects for survey administration (time of the day, surveyor). Assuming a conventional Type I error rate (α = 0.05) and a power of 0.80 (1 - β = 0.80), the analysis indicated that a sample size of 2641 participants is required.
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Intervention (Hidden)
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Before
Subjects will be randomly assigned in proportions 1:1 to two conditions---control group and treatment (tutorial) group. All subjects (both control and treatment groups) will be asked to perform (i) prediction tasks---predict the next outcome of a computer generated sequence of random coin tosses; and (ii) recognition tasks---say which outcome of a computer generated sequence of random coin tosses is more likely.
In addition, treatment (tutorial) subjects will be taught that the probabilities of all sequences of coin tosses are equal. The control group will not receive the tutorial.
Next, all subjects will be presented a scenario in which the previous job was a booking and the outcome is randomly posed as either completed or cancelled. Then they will be presented a request for a new booking 5 minutes away and must bid an estimated time of arrival (2, 4, 6, or 8 minutes) for the booking.
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After
The study involves two levels of randomization, and each subject will be assigned to one of four groups. Subjects will be presented with a scenario that involves bidding on booking requests.
Randomization 1. Subjects will be randomly assigned to a condition where the fares for bookings are either low or high.
Randomization 2. Subjects will be randomly assigned to a condition where the first booking is either cancelled or completed. After the first booking, subjects will be asked questions regarding a second booking before being informed that this second booking has been cancelled. Following the cancellation of the second booking, subjects will then be asked the same questions for a third booking.
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Building on Existing Work
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Yes
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No
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