Expertise and gambling: Using Type 2 signal detection theory to investigate differences between regular gamblers and nongamblers

Abstract

This paper presents an experimental investigation into how individuals make decisions under uncertainty when faced with different payout structures in the context of gambling. Type 2 signal detection theory was utilized to compare sensitivity to bias manipulations between regular nonproblem gamblers and nongamblers in a novel probability-based gambling task. The results indicated that both regular gamblers and nongamblers responded to the changes of rewards for correct responses (Experiment 1) and penalties for errors (Experiment 2) in setting their gambling criteria, but that regular gamblers were more sensitive to these manipulations of bias. Regular gamblers also set gambling criteria that were more optimal. The results are discussed in terms of an expertise-transference hypothesis.

Keywords:

• Gambling
• Type 2 signal detection theory
• Expertise
• Optimal criterion
• Decision making

Acknowledgments

Preparation of this article was supported by PhD funding from the Responsible Gambling Fund, London.

Notes

¹ Type 1 SDT may have some application to gambling in that some games such as poker involve the detection of deception in other players. However, in many other games, the decision to gamble or pass involves assessing whether a candidate response is correct (which will be rewarded if gambled) or incorrect (which will be penalized if gambled). It is this latter type of discrimination that is the focus of this paper.

² Higham's (2007) method for estimating optimal criterion setting was designed for formula-scored tests that are written by students in educational settings. There are no doubt some important differences between performance on formula-scored tests and performance on a dice game. However, in terms of the soundness of the methodology, the similarities are more important than the differences. For example, formula-scored tests incorporate a point system just like the current gambling task; points are added if an answer is correct but taken away if the answer is incorrect, but these points only apply if an answer is offered (gambled). No points are won or lost if an answer is withheld (guessed). Thus, just as with the dice game, it is possible to calculate overall accuracy, resolution (Type 2 discrimination), and bias. We refer interested readers to Higham (2007) and Higham and Arnold (2007a, 2007b) for details regarding the logic, assumptions, and computations that are necessary to generate these estimates.

³ The number of points won or lost for a gamble decision varied between conditions as explained in detail below.

⁴ Before the χ² tests were conducted, some cells were collapsed for ethnicity and educational attainment analyses as more than 25% of cells had an expected frequency of less than 5. Chi-squared tests were conducted on Group (RGs, NGs) × Ethnicity (Caucasian, Chinese, Asian, Mixed, and Other) and Group (RGs, NGs) × Education (undergraduate, school, college, postgraduate).

⁵ Due to the uneven number of males and females in each group, all measures in the paper (total score, accuracy, gambling likelihood) were analysed both with and without gender as a between-subjects variable. Gender did not produce any main effects or interactions, largest F(1, 53) = 3.00, p = .09, and all important effects were significant with and without gender included as a factor in the analysis. Given these results, we report the analyses without gender to simplify the analyses and conclusions.

⁶ Gambling likelihood was chosen as a measure of bias because of its intuitiveness; a person who gambles a lot versus a little is likely to have a liberal versus a conservative gambling criterion, respectively. However, gambling likelihood can also be affected by variation in other performance parameters such as accuracy, so it is not a pure measure of bias. To ensure that the observed effects on gambling likelihood were indeed attributable to differences in criterion setting, we ran analogous analyses on the FARs. With such an analysis, liberal criterion setting is associated with a greater FAR than conservative criterion setting, and high sensitivity to our bias manipulations would be indicated by large changes in the FARs. Importantly, the 2 (group: RG, NG) × 2 (condition: liberal, conservative) × 2 (Experiment: 1, 2) mixed-model ANOVA on FARs yielded a significant Group × Condition interaction, F(1, 112) = 5.54, MSE = .05, η_p ²  =  .05, p = .02, supporting the groups' differential sensitivity to bias manipulations demonstrated by the gambling likelihood analysis. The difference between the FARs in the liberal (high-reward and low-penalty) versus conservative (low-reward and high-penalty) conditions was much greater for the RGs (liberal M = .64, SEM = .04; conservative M = .43, SEM = .04) than for the NGs (liberal M = .65, SEM = .04; conservative: M = .58, SEM = .04). The analysis further yielded a main effect of condition, F(1, 112) = 22.77, MSE = .05, η_p ²  =  .17, p < .001. No other effects or interactions were significant, although the Condition × Experiment interaction was approaching significance, largest F(1, 112) = 3.59, MSE = .19, η_p ²  =  .03, p = .06. Thus, the bias effects we observed on gambling likelihood are most likely attributable to movement of the Type 2 gambling criterion and not due to differences in other parameters such as accuracy.