Method

 

Participants and Sample Selection

A total of one hundred and fifty Amazon Mechanical Turk (MTurk) workers in the United States were recruited online to participate in this study. The inclusion criteria include 1) native English Speaker; 2) have a HIT approval rate of 95% or higher. Fifteen who returned for session 2 but failed the attention check question were excluded from analyses. The attention check questions are designed to assess whether workers are actively engaging in the task instead of entering random answers. Of the 135 included MTurk workers between 19 and 68 years of age (M=32.61; SD=10.37), 67 were female. 68.89% was identified as White/Caucasian and 20% was identified as Asian. Yearly income was used as an index of objective SES. It was coded into 8 categories ranging from 1 (below 2,000,000 dollors) to 8 (above 14,000,000 dollors) in increments of 1,000,000 dollars. All participants completed MCQ at session 1, with 84 participants returned and completed the session 2 (Table 1). Participants received $0.50 after completing session1, and $1.50 after completing session 2, total $2.00 as compensation. The study was conducted in compliance with the Institutional Review Board of the University of Maryland, College Park.

Material and Procedure

Demographic Measures

Standard demographic measures were collected including gender, race, age, years of education, marital status, and annual income.

27 item Monetary Choice Questionnaire (MCQ)

The Monetary Choice Questionnaire (MCQ; \cite{Kirby_1996,Kirby_1999a} was used to assess DD. During the task, participants were presented a fixed set of 27 binary choice items, each between a smaller sooner (SS) amount of money and a large later (LL) amount of money. For example, on the first trial, participants were asked to choose between $54 today and $55 in 117 days. Participants were instructed to imagine the outcomes are real even they are hypothetical. The metric of delay discounting (k-value) is derived from hyperbolic equation (Mazur, 1987)
Vd = A / 1+(k*D)
where Vd is the discounted value at delay in days, A is the undiscounted amount, and k is the estimated discounting parameter.  As shown in Figure X,  the hyperbolic form allows the discounting curves of two delayed rewards to cross, where the intersection indicate participant is indifferent in chooseing between the two rewards. High values of k indicate greater discount of rewards. The delayed rewards were further grouped as small ($25-$35), medium ($50-$60), and large ($75-$85) magnitude groups.  Indifference points were calculated for each magnitude at each delay and fit to the hyperbolic model of the delay discounting rate (k). The geometric mean is used to calculate the overall k values to avoid underweighting the smaller value. Following the conventional analysis method, we used the natural logarithm transformed value of k in our analyses to reduce the positive skewness of the distribution(). 
[EXPLANE LOG TRANSFORMATION AND SKEWNESS OF THE DATA ]
Procedure
Participants completed brief demographic questions and MCQ in session 1. After one week, an email invitation was send to all participants who have completed session 1 prior to the session 2.

Statistical Analysis

Statistical analyses were performed using Stata version 15.0 for macOS (Stata Corp, College Station, Texas, USA). Bivariate analysis was performed using chi-square for categorical variables and Student’s t-test for continuous variable to assess mean effect between groups. Within-subject Analysis of Variance (ANOVA) was conducted to examine response consistency.
To assess the magnitude effect on DD rates as reported in previous studies (Yi et al., 2016), we adopt the method detailed in (Kirby & MarakoviĆ, 1996) and conduct within-subject Analysis of Variance (ANOVA).
To examine the relation between demographic characteristics and DD rates in each magnitude, we conducted Pearson Correlations for continuous variables and one-way Analysis of Variance (ANOVA) for categorical variables.
Logistic regression was conducted to examine whether DD rate in session 1 would predict return in the subsequent session.
A conventional α level of .05 were adopted for statistical significance in all analyses.
 

Result

All 135 participant (Female=67) completed the demographic measures and MCQ at session 1. No outliers were observed using 1.5 Interquartile Range (IQR) criteria. Means and standard deviations for demographic variables, DD rates in all magnitudes and between groups statistics are summarized in Table 1. Those who didn’t return for session 2 and session 2 completers did not differ in age, gender, marital status (all p>.47). Education was the only demographic characters that show significant mean difference (p<.05) and will be included in the subsequent analyses. We observed a significant difference in the overall lnk (t (133) = 2.395, p=.018) and lnk in medium (t (133)= 2.794, p =.006) and large magnitude (t (133)=2.605, p =.010) between groups, which indicate participants who dropped-out after session 1 have significantly greater DD rates compare to those who returned and complete session 2.
 

Response Consistency and Magnitude effect

Participants were highly consistent across all three reward magnitudes on the MCQ (lnk-small = 99.10%, SE = 0.28%; lnk-medium M = 96.61%, SE = 0.39%; lnk-large = 98.45%, SE = 0.46%). Consistency on the MCQ did not significantly differ between magnitudes (F(2,133) = 0.1.32, p = 0.269). A within-subject ANOVA was conducted to examine the magnitude effect of MCQ.  A significant main effect of magnitude was observed ( F(2, 133) = 56.47, p < .001 ) as shown in Table 2. The result indicate participants were most impulsive for small rewards, followed by medium and then la rewards, with all three magnitudes differing significantly (p < .001). Correlations among the three magnitudes of discounting on the MCQ were high (rs > .87).

Relations between Delayed Discounting and Demographic Variables

We conducted Pearson-wise correlations (for continuous variables) and between-subject one-way ANOVA (for categorical variables) to assess the relationship between the demographic characteristics and the overall normalized DD rates and at each magnitude in 135 MTurk workers who completed MCQ at session 1. Age and gender were not significantly correlated to the DD rates in any magnitude (.092 < r’s < .159, all p’s >.066). No significant correlation between education and DD in all magnitude were observed either (all p >.05), and we won’t further consider including the education * DD rate interaction terms in our logistic regression model. (Table 3)

Delay Discounting Rate Predict Drop-out in Session 2

[logistic model comparison]