Delay discounting, probability discounting, and interdental cleaning frequency

Subjects were workers recruited from Amazon Mechanical Turk (MTurk). MTurk is a crowdsourcing marketplace that allows for the electronic recruitment of convenience samples for academic research [18]. In both experiments, potential subjects were required to (1) have at least 100 approved human interface tasks (HITs), (2) have at least a 95% HIT approval rate, (3) be located the in US, and (4) not have already completed either experiment previously. This last requirement ensured that the experiments consisted of wholly unique samples. Based on Rzeszutek et al. [19] subjects were required to complete a short set of percentage comprehension questions as a screener in advance of taking the surveys. An incorrect answer on any screener question resulted in exclusion from both studies. The first page of the survey was a consent document that described the study and specified that continuation of participation served as demonstration of consent. In Experiment 1, compensation was $0.25 for completion of the screener and $3.00 for completion of the experimental survey. In Experiment 2, no compensation was provided for the screener, and $3.50 was paid for completion of the experimental survey. Sample size for the larger experiments from which these data were collected was determined based on an detecting a small to medium effect size (r = 0.2) for other covariates.

Surveys were hosted by the online platform Qualtrics. In both experiments, demographic information and flossing were assessed in identical fashion prior to the discounting survey. All surveys used in the study are available as supplementary files. Flossing was assessed with a single multiple-choice question in which subjects selected how often they flossed. There were six options for flossing frequency: At least once a day, at least once a week, at least once a month, at least once in 6 months, at least once a year, and less than once a year. Subjects responded to the monetary discounting questions by moving sliders (i.e., dragging a button on a line to indicate a percentage or preference towards one of two outcomes). For each question, a smaller monetary amount (i.e., $500) was shown on the left and a larger monetary amount (i.e., $1000) was shown on the right. Probabilities were always expressed as percentages to subjects.

Figure 1 shows how the questions were presented, and complete instructions and experimental arrangements are provided separately (Additional files 1, 2). In Experiment 1, the smaller outcome was always set at the smallest delay (i.e., 1 day) and largest probability (i.e., 0.99). The larger outcome varied across questions in terms of probability and delay. Sets of five questions were presented in order of descending probability (0.99, 0.8, 0.5, 0.2, and 0.0). Within the set, delay to the larger outcome was held constant. Across sets, delay to the larger outcome was varied (1 day, 1 month, 6 months, 2 years, and 5 years). This resulted in 25 combinations of delays and probabilities of the larger outcome. Experiment 2 had similar questions, but instead of questions consisting of both delay and probability, outcomes were only delayed or probabilistic. The delays used were the same as in Experiment 1, except that 2 years was used as the largest delay instead of 5 years. Probabilities were the same as Experiment 1. Experiment 2 replicated Experiment 1, but differed in how probability and delay were manipulated. Experiment 2 also included an additional dichotomous independent variable; the framing of the values in terms of gain or loss. That is, some questions consisted of choices between smaller sooner/certain gains and larger later/uncertain gains, while others featured smaller sooner/certain losses and larger later/uncertain losses. This resulted in four different conditions, delayed gains, delayed losses, probabilistic gains, and probabilistic losses. Each condition was presented in a single block of five questions, with either ascending delays or descending probabilities, for a total of 20 questions.

Discounting was measured using area under the curve with ordinal scaling (AUC_ord; [20]). This was calculated with the formula AUC_ord = ∑_i(1/n_x)[(y₁ + y₂)/2], where n_x is the number of total intervals between data points, or the number of questions in a condition minus 1, and where y₁ and y₂ are the normalized responses of the two points that indicate an interval. Because subject responses were already in percentages, where 0% was sliding all the way the left, and 100% was all the way to the right, normalization was simply the response divided by 100 to produce a proportion. The area of the polygon is calculated for each interval and then summed up to create a total value between 0 and 1. Because each interval is equally spaced, area differences between contiguous data points in delays or probabilities are carry equal weight for purposes of analysis. Higher values indicate lower or shallower discounting, whereas lower values indicate higher or steeper discounting. That is, higher values indicate little decrease in subjective value between the outcomes over the independent variable, whereas lower values indicate a large decrease in subjective value between the two outcomes over the independent variable. Because the smaller option always remained on the left for the slider questions, questions from Experiment 2 that involved losses were converted by subtracting the response from 100. This is account for the decrease in subjective value of the loss so that area differences between gains and losses could be directly compared.

To determine the relationship between flossing and discounting, statistical analyses were conducted using R 4.03 [21]. Because flossing questions were asked in a categorical manner rather than in a continuous one (i.e., how often you floss from these seven options rather than indicate how many days a year you floss), flossing frequency was treated as levels of a factor and a linear regression was conducted to determine how discounting changes as frequency of flossing decreases. That is, each group mean was compared to each other’s to determine differences between them.¹ Daily flossing was used as the reference in the linear regression as it was expected that those who flossed daily would have the highest AUC_ord for delay discounting and lowest for probability discounting (i.e., least impulsivity/risk propensity), and thus would serve as a logical group to base comparisons from.

Post-hoc comparisons between all groups were also conducted using the emmeans package [22] with Holm-Bonferroni corrections to account for multiple comparisons. To analyze data from Experiment 1, AUC_ord was only calculated for the delays at 0.99 probability and probability at a delay of 1 day. This was to isolate the effects of delay relatively independent of probability and vice versa. To help ensure data quality, a slider question meant to determine attention of “Would you rather have $1000 immediately or $1 in a year?” was included in the survey. Values greater than 5% were excluded for purposes of analysis.

Demographic information is shown in Table 1. The sample (n = 584) was predominantly male (61.13%) and Caucasian (77.57%). The most commonly selected flossing frequency was flossing at least once a day (37.16%).

Discounting for delayed gains was related to self-reported flossing, F(5) = 7.502, p < 0.001. Regression outputs for both delay and probability discounting can be found in Table 2. Results of the regression of discounting of delayed gains indicated that there was a decrease in AUC_ord (i.e., higher preference for the smaller, sooner monetary gain) between daily flossing and less frequent flossing. That is, AUC_ord for delayed gains was higher for daily flossing relative to monthly, biannual, and yearly flossing. However, there was no significant difference between those who reported flossing daily, weekly, or less than once a year. By contrast, there was no relationship between flossing and probability discounting, F(5) = 0.891, p = 0.487. As shown in Table 1, group n tended to decrease as flossing frequency decreased. Figure 2 shows boxplots of delay and probability discounting as a function of self-reported flossing frequency. Post-hoc comparisons between all groups can be found in Table 3. Post-hoc comparisons generally agreed with the differences from daily flossing and other groups, although after corrections for multiple comparisons the difference between daily flossing and monthly flossing was no longer significant, t(578) = 2.46, p = 0.114.

Demographic information is shown in Table 4. As in Experiment 1, the sample (n = 321) was predominantly male (61.06%) and Caucasian (76.95%), and the most commonly selected flossing frequency was flossing at least once a day (33.96%). The proportions of subjects falling into each flossing frequency category were similar to those observed in Experiment 1.

Table 5 shows regression outputs of delay and probability discounting of gains and losses. Similar to Experiment 1, discounting of delayed gains was significant between self-reported flossing frequency, F(5) = 5.650, p < 0.001, but not for discounting of probabilistic gains, F(5) = 1.413, p = 0.219. For delay discounting, significant differences were observed for the same comparisons as in Experiment 1. Also similar to Experiment 1, probability discounting did not appear to be related to reported flossing frequency. Post-hoc comparisons were congruent with the regression analysis between daily flossing and other flossing frequencies. All post-hoc comparisons between flossing frequencies and discounting type can be found in Table 6.

There was a significant relationship for discounting of delayed, F(5) = 3.561, p = 0.004, and probabilistic, F(5) = 2.580, p = 0.026, losses by flossing frequency. Nevertheless, there were no significant differences related to daily flossing and other flossing frequencies based on AUC_ord of probabilistic losses determined by the regression output, nor were there any significant post-hoc differences between flossing frequency and discounting of probabilistic losses after correction for multiple comparisons. Discounting of delayed losses was similar to delayed gains, with the exception that of annual flossing was not significantly different from daily flossing. Boxplots of delay and probability discounting for gains and losses by flossing frequency can be found in Fig. 3. Reported flossing also followed the same pattern as Experiment 1, with the sizes of groups decreasing as frequency of flossing decreased.