How does the phrasing of house edge information affect gamblers’ perceptions and level of understanding? A Registered Report

Figures & data

Table 1. The PCI RR study design template.

Question	Hypothesis	Sampling plan	Analysis plan	Rationale for deciding the sensitivity of the test	Interpretation given different outcomes
How does the phrasing of house edge information affect gamblers’ perceptions and level of understanding	There will be a difference in gamblers’ mean perceived chances of winning between the original and alternative format conditions	Collection of 2000 UK-based online gamblers via Prolific	Ordinary least squares regression. Perceived chances of winning DV (7 = ‘very high chance of coming out ahead’). Dummy variable (1 for alternative condition) as single IV. Interpretation based on p < .05. Sensitivity analysis planned if p ≥ .05.	In order to detect a change on this outcome from 4.1 in the original condition to 3.8 or 4.4 in the alternative condition (SD = 1.6), with 95% power and an alpha of 0.05, we would require 741 participants in each condition.	A lower mean level in either condition would support usage of that format. Equivalence testing used to reject effect sizes beneath the SESOI.
	There will be a difference in gamblers’ level of correct understanding of the information given between the original and alternative format conditions		Logistic regression. DV = 1 if correct response selected (‘For every £100 bet on this game about £90 is paid out in prizes’), otherwise 0. Dummy variable (1 for alternative condition) as single IV. Interpretation based on p < .05. Sensitivity analysis planned if p ≥ .05.	Sample size of 1000 per-condition chosen in order to detect a change in accuracy of 6% (accuracy moving from 50% to 44% or 56%, OR = 1.27), with an alpha of 0.05 and 95% power, which would require 771 participants per-condition	A higher mean rate of understanding in either condition would support usage of that format. Equivalence testing used to reject effect sizes beneath the SESOI.
How does house edge information compare to equivalent return-to-player information	Gamblers will have a lower perceived chances of winning when given house edge information than return-to-player information	Collection of 3000 (full sample) UK-based online gamblers via Prolific	Ordinary least squares regression. Perceived chances of winning DV (7 = ‘very high chance of coming out ahead’). Dummy variable (1 for alternative condition) as single IV. Interpretation based on p < .05	Power calculation not performed here; should be adequate given that previous literature has used sample sizes as small as 250 per-cell	A lower perceived chance of winning in the house edge conditions would further support the use of the house edge. Equivalence testing used to reject effect sizes beneath the SESOI.
	A higher proportion of gamblers will provide the correct response to the item of correct understanding in the house edge conditions compared to the return-to-player condition		Logistic regression. DV = 1 if correct response selected (‘For every £100 bet on this game about £90 is paid out in prizes’), otherwise 0. Dummy variable (1 for alternative condition) as single IV. Interpretation based on p < .05		A higher mean rate of understanding in the house edge conditions would further support the use of the house edge. Equivalence testing used to reject effect sizes beneath the SESOI.

Table 2. Descriptive statistics of participants’ gambling behavior.

Activity	Percent endorsing type of gambling
Baccarat	2.2
Bingo	50.2
Blackjack	34.7
Craps	2.0
Lottery	74.1
Roulette	37.8
Slots	44.9
Video poker	10.7
Video sports betting	25.2
Sports betting	29.1
Pachinko	2.2
Poker	31.5

Table 3. Responses to outcome measure of correct understanding.

Response	Original house edge (N = 1118)	Alternative house edge (N = 1116)	Return-to-player (N = 1099)
90% of people who play this game will win something	10.4%	4.5%	31.9%
This game will give out a prize 9 times in 10	8.4%	5.8%	20.9%
If you bet £1 on this game you are guaranteed to win 90p	2.5%	4.4%	2.2%
For every £100 bet on this game about £90 is paid out in prizes	57.7%	39.0%	37.5%
For every £100 bet you will lose no more than £10	10.2%	31.8%	3.2%
Don’t know	10.8%	14.5%	4.4%

Correct answer displayed in bold.

Figure 1. Plot of the difference between the original and alternative house edge conditions on their perceived chances of winning. The dashed lines are the smallest effect sizes of interest for the equivalence test. Negative values suggest lower perceived chances of winning in the alternative phrasing condition.

Figure 2. Plot of the difference between the house edge conditions in their correct understanding of the information given to them. The dashed lines are the smallest effect sizes of interest for the equivalence test. Negative values suggest lower rates of accurate understanding in the alternative phrasing condition.

Table 4. Regression model results comparing the two house-edge conditions, while adding a main effect of PGSI and an interaction term.

	Co-efficient [and 95% confidence interval]	t-statistic (p-value in parentheses)
Perceived chances of winning
Alternative house edge	−0.79 [−0.94, −0.64]	−10.1 (< .001)
PGSI	−0.00 [−0.03, 0.02]	−0.1 (.900)
Interaction	0.03 [–0.00, 0.07]	1.76 (.078)
Correct understanding
Alternative house edge	−0.17 [−0.22, −0.13]	−7.0 (< .001)
PGSI	0.00 [−0.01, 0.01]	0.3 (.766)
Interaction	−0.01 [−0.02, 0.01]	−0.9 (.347)