An Evaluation of Fixed and Randomized Price Sequence on the Alcohol Purchase Task

Abstract

Factors influencing drug consumption can be effectively evaluated in the context of behavioral economic demand. Specifically, hypothetical purchase tasks (HPT) allow for estimated drug consumption at a range of prices in which drug administration is not ethically or feasibly possible. With the marked increase of HPTs in behavioral research, understanding methodological influences on responding is paramount. One such methodological consideration is the price sequence, which can be presented in a fixed, ascending order or a randomized sequence. This study compared fixed and fully randomized sequence order with college student drinkers using a within-subjects design. Self-reported consumption revealed that despite some small differences between the fixed and random sequences, consumption preferences were highly similar regardless of presentation order. These results suggest participants are likely not anchoring their responses to the prior price on a fixed order sequence. Implications for HPTs and future research suggest fixed sequences do not lead to anchoring effects on prior prices and that the fixed sequence is a viable option for HPTs.

Public significance statement:

This empirical report compared fixed and randomized price sequence order to determine if consumption is anchored to the sequence. Results suggest self-reported consumption is not anchored to the order of price presentation on hypothetical purchase tasks.

Operant demand is a behavioral economic translation of the law of demand which dictates consumption of a commodity decreases as price increases (Hursh, 1980; 1984; Rachlin, 1980; Rachlin, Green, Kagel, & Battalio, 1976; Stigler, 1954). The resulting demand curves provide a quantitative model of the extent to which an organism defends its baseline consumption of a commodity amidst increasing constraints (e.g., work requirements, financial costs). This behavioral economic approach to reinforcer consumption has been successfully translated to behavioral pharmacology, given that demand provides an excellent proxy to how individuals make decisions to pursue drug consumption amidst budgetary constraint. The extent to which an individual defends consumption of a drug provides a unique lens by which to understand levels of dependence and the abuse liability of the drug itself (Jacobs & Bickel, 1999; Murphy & MacKillop, 2006).

Operant demand assessments have been used to model choice making under different constraints (Hursh, 1984, 2014; Hursh & Silberberg, 2008). Conventional operant demand has used work tasks during which organisms must meet work requirements (e.g., a lever press) to maintain consumption of a reinforcer (Hursh, 1978). Hypothetical purchase tasks (HPTs), extensions of the conventional demand tasks, typically involve a scenario or vignette with assumptions and limitations under which the participant is to imagine and verbally report upon the hypothetical scenario (Roma, Reed, DiGennaro Reed, & Hursh, 2017). Hypothetical purchase tasks have been used with human participants to produce similar outcomes without risk of harm when involving substances of potential risk of abuse (Jacobs & Bickel, 1999; MacKillop et al., 2008; Murphy, MacKillop, Skidmore, & Pederson, 2009).

Despite the low cost and ethical advantages of HPTs, conducting experiments that rely on verbal report has been a concern for some behavioral scientists (Roma et al., 2017). To address this possible concern, researchers have identified correlations between responses on purchase tasks and actual purchasing of alcohol in controlled settings (Amlung & MacKillop, 2015; Amlung, Acker, Stojek, Murphy, & Mackillop, 2012) and found predictive validity between alcohol purchase tasks and alcohol use (e.g., MacKillop & Murphy, 2007). Additional studies have assessed construct validity between HPTs and real-world cues (e.g., Becirevic et al., 2017; Mackillop et al., 2013; MacKillop et al., 2012), while a number of studies have compared demand metrics with previously validated clinical assessments (MacKillop et al., 2008; Murphy, MacKillop, Tidey, Brazil, & Colby, 2011; Reed, Kaplan, Becirevic, Roma, & Hursh, 2016). Meta-analyses of alcohol (Kiselica, Webber, & Bornovalova, 2016) as well as cigarette (González-Roz, Jackson, Murphy, Rohsenow, & MacKillop, 2019) and illicit substance use (Strickland, Campbell, Lile, & Stoops, 2019) have demonstrated this convergent validity of the HPT as well as its sensitivity to experimental manipulations relevant to reinforcer valuation (Acuff, Amlung, Dennhardt, MacKillop, & Murphy, 2019; see also the systematic review by Zvorsky et al. 2019). The validity and reliability of HPTs suggests these purchase tasks may offer additional avenues to study drug related behaviors (Kaplan et al., 2018).

With increasing reliance on HPTs to obtain consumer data and understand drug valuation, it is imperative for scientists to understand how methodological dimensions of the purchase task impact reporting. Prior research has suggested framing of the purchase task may impact responding (see Kaplan et al., 2018 for a review). Although these findings do suggest that participants are attentive and sensitivity to the instructional vignette, failure to consider these parametric manipulations may impact study results in unexpected or undesired ways. Different variations of the vignette, completion of the purchase task on one-page versus presentation of the stimuli on different pages, and the price sequence are all methodological components to be considered when using an HPT (Kaplan et al. 2018). Specifically, the typical escalating price sequence, which allows for an item-by-item anchor of reference, may influence responding on the current price. Having an escalating and orderly anchor point provided by the previous trial may artificially increase consistency of responding which would result in a greater than expected systematic decrease in responding as a function of increasing price of the commodity.

Randomization of price points may be a valid alternative because it does not provide an anchor point of reference to the previous price (Jacowitz & Kahneman, 1995). To date, the only empirical study assessing fixed compared to randomized price sequences on HPTs is Amlung and MacKillop (2012) using a state-based alcohol purchase task (APT) with a $30 bar tab. Participants were instructed to estimate how much of the tab they would spend on alcohol at randomized followed by fixed prices from “free” to $30. Consistent with previous research (e.g., Amlung & MacKillop, 2012), participants were instructed that each drink was approximately half the size of a standard drink, the maximum number of drinks available was eight, and the total volume would be sufficient to raise their blood alcohol level to 0.07%. Although absolute consistency was high across both sequences, the $30 bar tab may have artificially inflated the consistency at higher prices on the task ($16-$30) because only zero or one drink may be purchased at those prices.

Given that the study by Amlung and MacKillop (2012) is the only published manuscript comparing fixed and random price sequence to date, the purpose of the present study was to evaluate fixed and randomized price sequences on a standard, validated APT to determine how sequence order impacts responding. Through the use of a field standard APT (Kaplan et al., 2018), we aimed to determine if fixed pricing results in participants anchoring responses to the previous price on the sequence.

Method

Participants

Participants were recruited from introductory behavioral science courses from a midsized mid-western university. The initial sample consisted of 137 participants, with three incomplete demographic surveys. Of the complete demographic surveys, 119 were female participants (88.81%) with the median age of 19 (M = 20.84; SD = 5.58). A majority of the sample identified as white (85.07%) with seven people identifying as Asian (5.22%), four identifying as African American (2.98%), three as Hispanic (2.23%) and one each as Pacific Islander and Native American. Four preferred not to say or did not answer. Of the 134 participants who completed the Qualtrics® survey, 25 did not complete the PsyToolkit demand tasks, resulting in a remaining 109 participants. All procedures were approved by the University of Kansas Institutional Review Board (Consumer Valuation of Behaviors and Commodities; IRB #20635). These procedures stipulated that demographic and alcohol use data could not be linked with HPT data given the nature of the sample (i.e., undergraduate students potentially engaging in underage drinking).

Procedures

All study materials were accessed through the Qualtrics® platform (Qualtrics.com) from a shareable link. Participants were linked to PsyToolkit (Stoet, 2010; 2017; psytoolkit.org), a free, programmable website for research studies from the Qualtrics® page. The PsyToolkit link directed students to the demand tasks. All participants were shown two versions of the APT with attention checks embedded into the task verifying understanding of the task instructions. Questions asked participants to correctly identify relevant information in the vignette prior to moving to the demand task. A majority of the participants saw a randomized price sequence first, but a small sub-set were given the fixed price first (see Testing Order in Results). Participants viewed the randomized order first to avoid a potential bias from the sequential order of the fixed prices on subsequent assessments. The randomized price sequence presented a variable randomized task order to each participant, rather than a pre-set randomized order. Within the task, participants were shown the vignette followed by the price during that particular trial. Procedures were conducted in a within-subjects design with an N-back distractor task between the two demand tasks to mitigate sequence effects. The N-back is a task that asks participants to recall if a particular stimulus was presented N trials prior to the current trial (Owen, McMillan, Laird, & Bullmore, 2005). The task requires participants to engage in the response prior to moving to the next trial. Upon completion of the demand tasks, participants completed the Qualtrics® survey with demographics information and select clinical scales.

Alcohol Purchase Task and Clinical Scales

The presented APT included a previously validated and commonly used vignette followed by 17 prices listed one price per page (Kaplan et al. 2018). The novel application of PsyToolkit presented a page to include spherical buttons with a number of drinks from zero to 79 drinks available at a given price as the response option. These modifications were used to facilitate price randomization and precise control experimental timing allowed for in PsyToolKit. The vignette for the APT and an image of the task presentation can be found in Supplemental Materials.

Participants also answered questions regarding approximate self-reported alcohol consumption using the Daily Drinking Questionnaire (DDQ; Collins, Parks, & Marlatt, 1985). The DDQ is a measure of alcohol consumption over an average week in the 30 days immediately prior to task completion (Collins et al., 1985; Kivlahan, Marlatt, Fromme, Coppel, & Williams, 1990).

Data Analysis

Demand indices included demand intensity, demand elasticity, O_max, P_max, and breakpoint. Derived intensity and elasticity values were calculated using the exponentiated demand equation with k = 1.5, chosen a priori based on typical patterns of responding (Koffarnus, Franck, Stein, & Bickel, 2015). Other parameters were evaluated directly from the demand curve, including observed intensity (consumption at free price), O_max (maximum expenditure), and P_max (price at maximum expenditure), and breakpoint (as breakpoint 1 [BP1] or last price at which participants reported consumption).

Purchase task data were first evaluated for consistency and systematicity in accordance with prior research on randomization (Amlung & MacKillop, 2012) and current standard practice. Consistency was evaluated as percentage of positive reversals (increased consumption with increased price) to allow for comparisons to data previously reported on randomized task order (Amlung & MacKillop, 2012). Systematicity was evaluated using best practice standardized three-point algorithm (Stein, Koffarnus, Snider, Quisenberry, & Bickel, 2015). McNemar’s test for paired nominal data was used to compare systematicity between price sequence types. Data violating one or more systematicity criterion were removed for demand index analyses resulting in a sample size of 90 participants. Zero purchasing across all price points was considered non-systematic and subsequently removed (i.e., one participant reported all zeros in the fixed condition and one reported all zeros in the fixed and random condition). Prior to analysis, each demand index was evaluated for normality and transformed, when appropriate.¹ Sensitivity analyses were also conducted using 1) winsorized values transformed for values 1.5 times the IQR outside the upper or lower limit and 2) data removing individuals reflecting possible influential cases due to large consumption values (i.e., more than 50 drinks on initial price point) on the purchase task (see Supplemental Materials). Individual prices and demand indices were compared between fixed and randomized sequences using paired-samples t-test with effect sizes summarized using Cohen’s d_z. This approach was selected a priori to provide an overtly liberal approach to detecting possible differences (e.g., as opposed to conducting comparisons across price only after an omnibus ANOVA with corrections). Additional tests were conducted to determine if the effect of price sequence differed by alcohol consumption by evaluating 1) the upper 50% of participants based on demand intensity values and 2) evaluating a 2 × 3 ANOVA with Price Sequence as a within-subject factor and Demand Intensity group (0–4, 5–9, and 10+) as a between-subject factor. Testing order was then evaluated using general linear mixed effect models parameterizing the main effect and interaction of testing order (fixed first versus second) and pricing sequence (fixed versus randomized). All tests were conducted using R Statistical Language with two-tailed test and a type I error rate of .05.

Results

Alcohol Use

Reports from the DDQ indicate that the female participants reported an average of 6.02 drinks per week (SD = 6.23) and male participants an average of 4.47 drinks per week (SD = 5.74). Women averaged 2.60 (SD = 2.90) binge drinking episodes in the last 30 days, whereas men averaged 1.93 binge drinking episodes in the last month (SD = 1.94). A majority of the sample (81.51% of women; 80% of men) scored as either abstinent/infrequent drinkers (0–1 drinks) or moderate volume drinkers (less than 4 drinks).

Consistency, Systematic Data, and Price-Point Data

Consistency analyses indicated a greater percentage of positive reversals with the randomized sequence (mean[SD] = 12.5%[11.4]) than with the fixed sequence (mean[SD] = 2.7%[7.6]). Evaluation of reversals of only 2 or more drinks approximately halved these percentages for both price sequences (randomized = 5.9%[9.4]; fixed = 1.7%[4.9]). Evaluation of demand curves using a three-point algorithm indicated that 19 participants provided non-systematic data on one or more curves (1 on the fixed only, 11 on the randomized only, and 7 on both). This proportion of non-systematic data was higher in the randomized compared to fixed tests, p = .009. Demand curve model fits for systematic data were also higher for the fixed (R² Mean = .91, Median = .94) than randomized (R² Mean = .85, Median = .90) price sequence, p = .003, d_z = 0.32.

Table 1 contains demand across the 16 price points for systematic demand curves (N = 90). Small effect size differences across each price point (absolute d_z = 0.02–0.22). Significantly greater consumption was observed with randomized sequence at two prices, $0.25, p = .04, and $0.50, p = .04, per drink. Visuals of mean number of purchases at each price is presented in Figure 1.

Table 1.

Individual Price Consumption and Demand Indices

	Fixed Mean (SD)/Median	Randomized Mean (SD)/Median	Cohen’s dz
Individual Prices
$0.05	12.12 (16.78)/7	11.76 (15.55)/7	0.06
$0.10	10.78 (14.55)/6	11.23 (15.35)/6.5	−0.09
$0.25	9.49 (11.83)/6	10.92 (15.05)/6.5	−0.22*
$0.50	9.00 (11.11)/6	10.13 (12.92)/6	−0.22*
$1	7.62 (7.36)/6	8.39 (9.52)/6	−0.18
$1.50	6.94 (6.74)/5	7.36 (9.33)/5	−0.08
$2	5.87 (5.33)/5	6.63 (8.40)/5	−0.19
$3	4.97 (5.04)/4	6.17 (10.52)/4	−0.14
$4	3.91 (4.21)/3	3.97 (6.89)/3	−0.02
$5	3.21 (3.68)/3	4.03 (8.11)/3	−0.16
$6	2.72 (3.43)/2	2.96 (6.92)/2	−0.05
$8	1.8 (2.56)/1	2.64 (8.13)/2	−0.14
$10	1.18 (2.12)/1	1.80 (7.30)/1	−0.11
$15	0.60 (1.41)/0	1.50 (8.40)/0	−0.12
$20	0.28 (0.87)/0	0.99 (7.48)/0	−0.10
$30	0.12 (0.52)/0	0.79 (6.64)/0	−0.10
Demand Indices
Observed Intensity	12.84 (17.45)/7	13.61 (19.56)/8	−0.14
Derived Intensity (Q0)	13.59 (23.08)/6.87	12.45 (17.27)/7.11	0.07
Elasticity (α)	0.06 (0.37)/0.01	0.03 (0.14)/0.01	0.22*
Omax	22.26 (22.91)/16	48.57 (199.31)/20	−0.24*
Pmax	7.07 (6.10)/6	7.49 (5.51)/6	−0.11
Breakpoint	11.12 (6.87)/10	11.82 (7.16)/10	−0.13

Note. Differences in Cohen’s dz effect sizes reflect Fixed-Randomized order direction.

^*p < .05

Figure 1.

Mean number of hypothetical drinks purchased at each price for fixed and randomized purchase tasks.

Demand Indices

Table 1 also contains demand indices for fixed and randomized sequences and effect size comparisons. Significant effects of price sequence were observed for elasticity, p = .04, and O_max, p = .02, with more inelastic and higher O_max values observed with randomized sequences. In both cases, these effects were of a small effect size (d_z = 0.22–0.24). Differences in elasticity were partially related to influential cases given that removal of large consumption curves attenuated this difference (Supplemental Table 1). Other sensitivity comparisons were consistent with the primary findings. Correlations between demand indices across the two price sequences were also large and all statistically significant, p values < .001 (r values: Observed Intensity = .96, Q₀ = .95, α = .84, O_max = .69, P_max = .47, Breakpoint = .70).

Tests conducted in the upper 50% of participants based on demand intensity values revealed similar findings with a significant difference in O_max, p = .05, but not for other demand indices (see Supplemental Table 2). Consistent results were observed for the 2 × 3 ANOVAs which did not indicate a significant interaction between Price Sequence and Intensity grouping, p values > .10.

Testing Order

An alternative testing order was evaluated in a subset of participants (n = 18). These participants did not differ from other participants on demand indices overall (i.e., no main effect of testing order in mixed effect models, p values > .34) nor did they differ in the impact of testing order on demand indices (i.e., no interaction of testing order, p values > .58) (see also between-subject effect sizes in Supplemental Table 3).

Discussion

This study aimed to evaluate price sequence on the APT through use of the standard fixed-price sequence and a randomized order sequence. Results suggest that despite some small differences between the fixed and random sequences, overall consumption preferences were highly similar. These findings suggest that alcohol valuation rather than an anchoring effect related to price sequencing contributes to consumption patterns observed on typical “fixed price” alcohol purchase tasks. These findings collectively indicate that the fixed price sequence continues to be a viable option for delivery of HPTs.

The demand indices of P_max, intensity, and breakpoint were similar with less than small effect size differences between sequences. However, consistent with Amlung and MacKillop (2012), O_max was modestly higher in the randomized than the fixed price sequence. Additionally, demand elasticity was different between the two sequences, with more inelastic demand in the randomized sequences. Taken together, these data suggest that price sequence does not impact consumption at very low prices or at very high prices, intensity and breakpoint, respectively. Two prices, $0.25 and $0.50 resulted in significantly greater consumption estimates with the randomized price sequence as compared to the fixed price sequence when tested using a liberal threshold (i.e., no p value correction). These two data points are within the inelastic portion of the demand curve for both price sequences and may simply be a result of participants being unaware of the full range of drink prices.

Consistency outcomes were also comparable to Amlung and MacKillop (2012) in that randomization significantly reduced response consistency as compared to the fixed price sequence. Higher rates of non-systematic data were also observed with the randomized compared to fixed order task similar to the consistency findings. The slight reduction in consistency observed here compared to in the prior study by Amlung and Mackillop (2012) is likely attributable to the nature of purchasing in that study. Specifically, participants were provided a bar tab of $30 and were told they could purchase a maximum of 8 drinks. These two factors acted as a task-based ceiling constraint that could have limited the opportunities for positive reversals to occur thereby improving consistency scores.

A small subset of the participants saw the fixed order price sequence prior to the randomized price sequence. Although the small sample size did limit power to evaluate these differences, analyses indicated no significant differences between demand indices for the presentation of the random sequence first compared to presentation of the fixed sequence first. This outcome further supports the minimal impact that price sequence likely has on consumption values on the alcohol purchase task.

As noted above, a number of the results align with Amlung and MacKillop’s (2012) initial study on consistency of behavior across price sequences. The current study extends that research in a number of ways. First, with no limit on number of purchases or a bar tab, consumption values were not restricted to an arbitrary number or budget and, therefore, may more closely resemble real-world purchasing behaviors. Additionally, the current study explored counter-balancing the order of random and fixed price sequences. The lack of difference between the groups who saw the sequences in different order lends additional support for the noted consistency of fixed and randomized price structures. Lastly, a more standard APT was used for this task with respect to features like study vignette, study income, and price sequence, rather than one adapted for a task in which participants receive real alcoholic drinks. Given the number of studies utilizing hypothetical only trait-based tasks, it is advantageous to demonstrate that a similar consistency across fixed and randomized sequences is observed with the typical trait APT measure (Kaplan et al., 2018).

These results should be taken in light of a number of limitations. The sample consisted of mostly underage, white female college students with low levels of self-reported drinking. Although college samples are commonly used in alcohol research, extending the study to a broader range of college drinkers or a community sample may influence the results. Additionally, only a small sub-set of participants completed the fixed sequence condition first. Although we decided to present the randomized sequence first to reduce the possibility of carryover effects, future research could evaluate the extent to which carryover effects occur when the fixed sequence is presented before the randomized sequence. Despite no main effect with testing order in the current sample, statistical power is limited due to the sample size of the fixed first group. The time between the two tasks was also short (i.e., approximately 5 minutes). Given the difficulty of the N-back, we believe the distractor was sufficient to separate the two demand tasks. However, it is plausible that temporal proximity of the tasks influenced responding. Future studies may attempt to increase the temporal distance (e.g., hours or days) between the tasks as an alternative approach.

Overall, the data suggest using a fixed sequence is not leading to artifacts in the data as a results of anchoring effects. Amlung and MacKillop (2012) suggested randomized sequences may be an alternative approach to yield consistent data with the APT. We suggest that although randomized presentation may be an option, the fixed price sequence renders more consistent data patterns and does not appear to hinder results through artifacts or anchoring effects to the prior price on the sequence. Given fixed price sequencing is the standard approach at this time and there appears to be no detriment to its use, researchers should feel comfortable with using the fixed-price sequence on the APT. Therefore, continuation of fixed prices may be the appropriate option in behavioral economics research.