Figure 2 shows the average subjective discounted value for each delay period. A repeated measures ANOVA indicated a reliable main effect of delay (F4, 516 = 32.822, MSe = 1.592 p < .001, \({\eta }_{p}^{2}\) = .203), and a reliable linear effect of delay (F1, 129 = 67.756, MSe = 2.970 p < .001, \({\eta }_{p}^{2}\) = .344) indicating that the participants showed a robust discounting effect.
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INSERT FIGURE 2 ABOUT HERE
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The discount function (k) was derived from the subjective discounted value (v) defined as the preferred smaller sooner outcome (v) from the five intervals (D) using Mazur’s (1987) hyperbolic discount function (1). Table 1 shows the average discount rates (k), BPVS scores, AQ scores, and SWAN scores for males and females. There were reliable differences between males and females in AQ and SWAN Scores, but not in discount rates or BPVS.
Table 1 Average discount rates (k), BPVS scores, AQ scores, and SWAN scores for males and females.
|
Male
|
Female
|
|
|
|
Mean
|
n
|
sd
|
Mean
|
n
|
sd
|
t
|
p
|
Discount rate (k)
|
0.0038
|
83
|
0.0091
|
0.0025
|
67
|
0.0047
|
1.070
|
.286
|
|
|
|
|
|
|
|
|
|
BPVS-3
|
|
|
|
|
|
|
|
|
Raw score
|
115.875
|
84
|
26.473
|
118.132
|
68
|
22.777
|
0.560
|
.576
|
Standardised score
|
105.134
|
82
|
13.707
|
102.250
|
67
|
11.828
|
1.364
|
.175
|
Equivalent year
|
8.536
|
82
|
2.885
|
8.537
|
67
|
2.245
|
.002
|
.999
|
|
|
|
|
|
|
|
|
|
AQ-Child
|
64.090
|
82
|
18.226
|
50.620
|
66
|
14.932
|
4.828
|
<.001
|
|
|
|
|
|
|
|
|
|
SWAN
|
|
|
|
|
|
|
|
|
Inattention
|
-0.318
|
82
|
0.967
|
-0.829
|
66
|
0.808
|
3.436
|
<.001
|
Hyperactive/impulsive
|
-0.446
|
82
|
0.983
|
-0.819
|
66
|
0.973
|
2.310
|
<.022
|
Combined
|
-0.382
|
82
|
0.849
|
-0.825
|
66
|
0.785
|
3.261
|
<.001
|
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INSERT TABLE 1 ABOUT HERE
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The indices of multiple deprivation (IMD) were computed from the demographic information provided by parents using the publicly available resource provided by the Ministry of Housing, Communities and Local Government (http://imd-by-postcode.opendatacommunities.org/). This provides decile ranks from 1 = most deprived to 10 = least deprived. These were collapsed into quintiles (from 1 to 5). The average subjective discounted value for delay period for each IMD decile are shown in Table 2.
Table 2 Average subjective discounted value of £10 and discount rate (k) for each decile of multiple deprivation.
|
|
|
Delay
|
|
|
|
IMD
|
|
|
7-days
|
|
14-days
|
|
30-days
|
|
180-days
|
|
365-days
|
|
Discount rate (k)
|
Quintile
|
n
|
|
Mean
|
sd
|
|
Mean
|
sd
|
|
Mean
|
sd
|
|
Mean
|
sd
|
|
Mean
|
sd
|
|
Mean
|
sd
|
1
|
19
|
|
8.778
|
1.457
|
|
8.187
|
2.337
|
|
7.559
|
2.963
|
|
7.464
|
2.257
|
|
6.786
|
3.173
|
|
0.0086
|
0.0041
|
2
|
19
|
|
9.289
|
0.384
|
|
8.868
|
0.704
|
|
8.789
|
1.018
|
|
7.289
|
2.893
|
|
6.917
|
3.469
|
|
0.0036
|
0.0013
|
3
|
31
|
|
8.661
|
1.881
|
|
8.283
|
2.156
|
|
8.500
|
1.402
|
|
7.481
|
2.199
|
|
6.552
|
2.971
|
|
0.0040
|
0.0012
|
4
|
33
|
|
9.109
|
1.517
|
|
8.906
|
0.902
|
|
8.742
|
1.040
|
|
7.968
|
2.105
|
|
8.000
|
2.017
|
|
0.0020
|
0.0007
|
5
|
53
|
|
9.260
|
0.394
|
|
8.706
|
1.001
|
|
8.570
|
1.355
|
|
8.410
|
1.466
|
|
8.240
|
1.523
|
|
0.0014
|
0.0003
|
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INSERT Table 2 ABOUT HERE
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Figure 3 shows the implied discount curves for each IMD quintile. A one-way ANOVA on discount rates with IMD quintile as a between-subject factor was significant (F1, 149 = 3.639, MSe= < .001 p = .007, \({\eta }_{p}^{2}\) = .208) indicating that there are reliable differences in impulsive choice made by children from different economic and social backgrounds. Planned contrasts showed that participants from the most deprived postcodes (IMD 1) show steeper discounting than participants in the least deprived postcodes (IMD 5, p <.001), and the each of the other postcodes (IMD 4, p =.002; IMD 3, p =.33; IMD 2, p = .035).
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INSERT FIGURE 3 ABOUT HERE
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Finally, to test the hypothesis that relative deprivation is a casual factor in the development of impulsivity the IMD quintiles, age, gender, AQ score, SWANN score, and standardised BPVS-3 scores were entered into a linear regression as predictors of the discount function. The model was significant (F1, 35 = 2.834, MSe = < .001 p = .013). Table 3 shows the regression coefficients. The Index of Multiple Deprivation was the only reliable predictor of discount rates.
Table 3 Regression coefficients predictor variables onto discount rates.
|
Regression coefficients
|
|
b
|
t
|
p
|
Age
|
.083
|
0.972
|
.333
|
Sex
|
.008
|
0.083
|
.333
|
Standardised BPVS-3
|
.064
|
0.721
|
.472
|
AQ-Child
|
.139
|
1.488
|
.139
|
SWANN Combined
|
.120
|
1.353
|
.178
|
IMD Quintile
|
-.256
|
-2.986
|
.003
|
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INSERT Table 3 ABOUT HERE
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