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. Author manuscript; available in PMC: 2019 Oct 1.
Published in final edited form as: Decision (Wash D C ). 2017 May 29;5(4):205–252. doi: 10.1037/dec0000083

Table 4.

170 Experimental Replications of Decisions Under Risk and Our Model’s Predictions

Reference Model Inputs
1st Choice
2nd Choice
x→
a^−i
b^−i
 nrisky
nsafe
χ2 nrisky
nsafe
χ2
Actl. Pred. Actl. Pred. Actl. Pred. Actl. Pred.
Asian Disease Problem, North American, Japanese, and European Undergraduate Students
Tversky & Kahneman, 1981 [±1,0,0] 0.82 0.08 43 49.01 109 102.99 1.09 121 110.37 34 44.63 3.55
Fagley & Miller, 1990, #1 [±1,0,0] 0.48 0.07 48 37.64 46 56.36 4.75* 67 60.86 29 35.14 1.69
Fagley & Miller, 1990, #2 [±1,0,0] 0.46 0.08 21 21.97 33 32.03 0.07 40 34.78 15 20.22 2.13
Miller & Fagley, 1991 [±1,0,0] 0.86 0.08 19 11.31 17 24.69 7.63* 29 25.85 7 10.15 1.36
Reyna & Brainerd, 1991, standard [±1,0,0] 1.72 0.09 9 5.72 26 29.28 2.24 30 31.77 7 5.23 0.69
Reyna & Brainerd, 1991, ZCT [0,0,0] 0.00 0.09 18 18.25 17 16.75 0.01 21 18.77 15 17.23 0.55
Reyna & Brainerd, 1991, NCT [±1, ±1,0] 0.47 0.09 10 9.31 13 13.69 0.08 15 14.62 8 8.38 0.03
Tindale, Sheffey & Scott, 1993 [±1,0,0] 0.86 0.06 60 44.80 84 99.20 7.48* 113 102.96 31 41.04 3.43
Takemura, 1994 [±1,0,0] 0.70 0.09 9 15.92 36 29.08 4.66* 31 30.96 14 14.04 0.00
Kühberger, 1995, #1 [±1,0,0] 0.00 0.08 16 13.55 10 12.45 0.93 13 11.98 10 11.02 0.18
Kühberger, 1995, #2 [±1,0,0] 0.37 0.08 12 10.73 13 14.27 0.26 18 14.04 5 8.96 2.87
Kühberger, 1995, COD, #1 [0,0,0] −0.39 0.09 15 15.45 10 9.55 0.03 10 9.75 13 13.25 0.01
Kühberger, 1995, COD; problem, #2 [0,0,0] 0.00 0.09 9 11.50 13 10.50 1.14 7 9.93 12 9.07 1.82
Kühberger, 1995, 4NSCODT, #1 [∓1,0,0] 0.41 0.09 9 6.73 7 9.27 1.32 8 8.69 6 5.31 0.14
Kühberger, 1995, 4NSCODT, #2 [∓1,0,0] −0.40 0.09 8 9.90 8 6.10 0.96 7 8.06 12 10.94 0.24
Wang & Johnston, 1995 [±1,0,0] 0.86 0.09 20 15.74 30 34.26 1.68 34 36.04 16 13.96 0.41
Highhouse & Yüce, 1996 [±1,0,0] 0.84 0.09 35 39.04 87 82.96 0.61 90 87.50 32 34.50 0.25
Jou, Shanteau, & Harris, 1996 [±1,0,0] 0.44 0.08 28 32.90 52 47.10 1.24 64 50.04 16 29.96 10.41*
Wang, 1996 [±1,0,0] 0.86 0.08 13 9.79 18 21.21 1.54 26 24.44 8 9.56 0.36
Stanovich & West, 1998 (between subjects) [±1,0,0] 0.87 0.10 48 46.63 100 101.37 0.06 94 104.36 50 39.64 3.74
Stanovich & West, 1998 (within subjects) [±1,0,0] 0.49 0.10 118 117.50 173 174.50 0.01 174 188.06 118 103.94 2.96
Druckman, 2001a [±1,0,0] 0.85 0.08 22 21.93 47 47.07 0 60 56.67 19 22.33 0.69
Druckman, 2001b [±1,0,0] 0.85 0.08 16 15.88 34 34.12 0 42 39.48 13 15.52 0.57
Mayhorn, Fisk, & Whittle, young adults, 2002 [±1,0,0] 0.84 0.08 7 9.26 22 19.74 0.81 25 20.76 4 8.24 3.05
LeBoeuf & Shafir, 2003, #1, no justification [±1,0,0] 0.86 0.09 13 15.26 35 32.74 0.49 34 39.68 21 15.32 2.92
LeBoeuf & Shafir, 2003, #2 (between subjects) [±1,0,0] 0.52 0.13 106 115.79 184 171.21 1.78 146 188.86 141 98.14 28.45*
LeBoeuf & Shafir, 2003, #2 (within subjects) [±1,0,0] 0.87 0.12 36 47.14 111 99.86 3.88* 83 106.44 63 39.56 19.05*
Rönnlund, Karlsson, Laggnäs, & Lindström, 2005 [±1,0,0] 0.47 0.09 13 12.98 19 19.02 0 22 20.32 10 11.68 0.38
Druckman & McDermott, 2008 [±1,0,0] 0.72 0.09 6 5.90 11 11.10 0 13 11.74 4 5.26 0.44
Fischer, Jonas, Frey, & Kastenmüller, 2008 [±1,0,0] 0.35 0.08 45 43.64 56 57.36 0.07 76 68.53 37 44.47 2.07
Okder, 2012 [±1,0,0] 0.71 0.08 19 18.07 33 33.93 0.07 40 36.51 13 16.49 1.07
Stein, 2012 [±1,0,0] 0.86 0.08 19 14.79 28 32.21 1.75 39 41.08 18 15.92 0.38
Kühberger & Gradl, 2013, #1 [±1,0,0] 0.72 0.09 20 21.92 43 41.08 0.26 43 43.56 20 19.44 0.02
Kühberger & Gradi, 2013, #2 [±1,0,0] 0.73 0.08 8 4.82 6 9.18 3.21 11 10.39 4 4.61 0.12
TOTAL of 68 predicted 60 (88%)
Asian Disease Problem, North American and European Adults
Mayhorn, Fisk, & Whittle, 2002 [±1,0,0] 0.85 −0.34 6 6.75 23 22.25 0.11 20 18.09 9 10.91 0.54
Rönnlund, Karlsson, Laggnäs, Larsson, & Lindström, 2005 [±1,0,0] 0.47 −0.27 9 10.34 23 21.66 0.26 18 17.55 14 14.45 0.03
TOTAL of 4 predicted 4 (100%)
Asian Disease Problem, Chinese Undergraduate Students
Zhang & Miao, 2008, #1 [±1,0,0] 0.73 1.36 43 42.34 22 22.66 0.03 59 60.53 9 7.47 0.35
Zhang & Miao, 2008, #2 [±1,0,0] 0.73 1.33 30 29.06 15 15.94 0.09 42 42.56 6 5.44 0.07
Zhang, Xiao, Ma, & Miao, 2008, civilians [±1,0,0] 0.72 1.29 39 38.35 21 21.65 0.03 52 51.18 6 6.82 0.11
TOTAL of 6 predicted 6 (100%)
Allais Paradox Problems, North American and European Undergraduate Students
Conlisk, 1989 [−1,0,1] & [1,1,0] 1.68 0.14 121 109.63 115 126.37 0.49 34 32.79 202 203.21 0.05
Carlin, 1990 [−1,0,1] & [1,1,0] 1.71 0.11 39 30.72 26 34.28 4.23* 14 9.09 51 55.91 3.08
Huck & Müller, 2012 [−1,0,1] & [1,1,0] 1.46 −0.13 24 37.23 46 32.77 10.04* 9 14.58 61 55.42 2.69
TOTAL of 6 predicted 4 (67%)
Average of 30 assorted framing problems, North American Undergraduate Students
Reyna et al., 2014 [±1,0,0] 0.47 −0.29 21.80 20.03 41.20 42.97 0.23 34.84 34.36 28.16 28.64 0.01
Reyna et al., 2014, ZCT [±1,0,0] 0.00 −0.32 27.03 26.58 35.97 36.42 0.01 30.87 26.58 32.13 36.42 1.20
Reyna et al., 2014, NCT [±1,0,0] 0.95 −0.19 14.30 15.32 48.70 47.68 0.09 37.55 42.93 25.45 20.07 2.12
TOTAL of 6 predicted 6 (100%)
Average of 30 assorted framing problems, North American Undergraduate Students
Reyna et al., 2014 [±1,0,0] 0.47 0.10 21.71 22.03 32.29 31.97 0.01 32.35 34.55 21.65 19.45 0.39
Reyna et al., 2014, experts [±1,0,0] 0.46 0.06 13.61 14.45 22.39 21.55 0.08 25.38 22.66 10.62 13.34 0.88
Reyna et al., 2014, ZCT [±1,0,0] 0.00 0.07 27.32 27.98 26.68 26.02 0.03 29.81 27.98 24.19 26.02 0.25
Reyna et al., 2014, experts, ZCT [±1,0,0] 0.00 0.05 18.54 18.47 17.46 17.53 0 22.18 18.47 13.82 17.53 1.52
Reyna et al., 2014, NCT [±1,0,0] 0.94 0.11 14.04 16.39 39.96 37.61 0.49 39.47 39.95 14.53 14.05 0.02
Reyna et al., 2014, experts, NCT [±1,0,0] 0.93 0.09 7.09 10.89 28.91 25.11 1.90 29.05 26.45 6.95 9.55 0.96
TOTAL of 12 predicted 12 (100%)
Refugee Problem, North American and European Undergraduate Students
Mandel, 2001, COD [0,0,0] 0.00 0.35 12 13.50 11 9.50 0.40 11 12.92 11 9.08 0.69
Mandel, 2001, #1, 4NS6NST [0,0,0] 0.00 0.33 13 13.38 10 9.62 0.03 14 13.96 10 10.04 0.00
Mandel, 2001, #2, 4NS6NST [0,0,0] 0.00 0.30 23 20.72 13 15.28 0.59 22 21.30 15 15.70 0.05
Mandel, 2014, #2 [±1,0,0] 0.72 0.32 16 15.24 22 22.76 0.06 28 28.13 10 9.87 0.00
Mandel, 2014, #3 [±1,0,0] 0.71 0.33 8 10.15 17 14.85 0.77 20 18.46 5 6.54 0.49
Mandel, 2014, COD, #3 [0,0,0] 0.00 0.37 9 13.03 13 8.97 3.05 12 14.21 12 9.79 0.84
Mandel, 2014, COD ZCT #3 [∓1,0,0] −0.73 0.38 15 19.56 11 6.44 4.29* 8 10.35 17 14.65 0.91
TOTAL of 20 predicted 19 (95%)
Plant Problem, European Undergraduate Students
Kühberger, 1995, #1 [±1,0,0] 0.36 −0.15 13 9.39 12 15.61 2.22 19 12.74 4 10.26 6.89*
Kühberger, 1995, #2 [±1,0,0] 0.35 0.10 3 7.01 13 8.99 4.09* 12 10.39 5 6.61 0.64
Kühberger, 1995, COD, #1 [0,0,0] 0.00 0.07 12 13.44 14 12.56 0.32 12 11.89 11 11.11 0.00
Kühberger, 1995, COD, #2 [0,0,0] 0.00 0.16 4 7.01 9 5.99 2.81 7 10.25 12 8.75 2.24
Kühberger, 1995, 4NSCODT, #1 [+1,0,0] −0.44 0.05 12 16.76 15 10.24 3.57 13 9.32 10 13.68 2.44
Kühberger, 1995, 4NSCODT, #2 [+1,0,0] −0.40 0.03 8 8.49 6 5.51 0.07 7 5.74 7 8.26 0.47
TOTAL of 12 predicted 10 (83%)
Cancer Problem, European Undergraduate Students
Kühberger, 1995, #1 [±1,0,0] 0.40 0.20 9 10.82 15 13.18 0.56 12 16.18 13 8.82 3.06
Kühberger, 1995, #2 [±1,0,0] 0.41 0 11 6.39 5 9.61 5.54* 9 8.43 5 5.57 0.10
Kühberger, 1995, COD, #1 [0,0,0] 0.00 0.20 12 13.22 12 10.78 0.25 8 12.67 15 10.33 3.83
Kühberger, 1995, COD, #2 [0,0,0] 0.00 0.04 5 3.56 2 3.44 1.18 8 6.62 5 6.38 0.59
Kühberger, 1995, 4NSCODT, #1 [+1,0,0] −0.37 0.01 18 14.23 6 9.77 2.45 10 9.46 13 13.54 0.05
Kühberger, 1995, 4NSCODT, #2 [+1,0,0] −0.40 0.13 7 8.81 7 5.19 1.01 7 6.92 9 9.08 0
TOTAL of 12 predicted 11 (92%)
Drinking Water Contamination Problem, Mixed North American and European Sample
Kühberger & Tanner, 2010 [±1,0,0] 0.63 0.34 31 39.78 62 53.22 3.38 68 67.51 25 25.49 0.01
Kühberger & Tanner, 2010, ZCT [0,0,0] 0.00 0.23 50 51.85 43 41.15 0.15 60 51.85 33 41.15 2.89
Kühberger & Tanner, 2010, NCT [±1, ±1,0] 1.30 0.26 23 24.28 70 68.72 0.09 79 76.96 14 16.04 0.31
TOTAL of 6 predicted 6 (100%)
Genetically Engineered Crops Problem, Mixed North American and European Sample
Kühberger & Tanner, 2010 [±1,0,0] 0.68 0.07 31 32.74 62 60.26 0.14 55 63.07 38 29.93 3.21
Kühberger & Tanner, 2010, ZCT [0,0,0] 0.00 0.02 50 46.95 43 46.05 0.40 40 46.95 53 46.05 2.08
Kühberger & Tanner, 2010, NCT [±1, ±1,0] 1.35 −0.11 27 17.46 66 75.54 6.41* 73 72.09 20 20.91 0.05
TOTAL of 6 predicted 5 (83%)
Fish Kidney Disease Problem, Mixed North American and European Sample
Kühberger & Tanner, 2010 [±1,0,0] 0.66 0.14 26 34.61 67 58.39 3.41 55 64.09 38 28.91 4.15*
Kühberger & Tanner, 2010, ZCT [0,0,0] 0.00 −0.08 59 44.75 34 48.25 8.74* 40 44.75 53 48.25 0.97
Kühberger & Tanner, 2010, NCT [±1, ±1,0] 1.30 −0.08 20 18.70 73 74.30 0.11 77 71.90 16 21.10 1.60
TOTAL of 6 predicted 4 (67%)
Endangered Forest Problem, Mixed North American and European Sample
Kühberger & Tanner, 2010 [±1,0,0] −0.46 0.66 22 23 71 70 0.06 51 51.11 42 41.89 0.00
Kühberger & Tanner, 2010, ZCT [0,0,0] −0.53 0 37 34.51 56 58.49 0.29 40 34.51 53 58.49 1.39
Kuhberger & Tanner, 2010, NCT [±1, ±1,0] −0.42 1.34 14 13.66 79 79.34 0.01 60 66.55 33 26.45 2.27
TOTAL of 6 predicted 6 (100%)
TOTAL of 170 predicted 153 (90%)

Note.

*

= p < 0.05, Actl. = Actual, Pred. = Predicted, a^−i is the JLOO estimate of the a parameter and b^−i is the JLOO estimate of the b parameter. 1st (2nd) Choice is the certain (risky gamble) option in framing problems and the first (second) gamble in the Allais gambles. ZCT = zero complement truncated; NCT = nonzero complement truncated; COD = certain-option disambiguated; 4NSCODT = “400 not saved” certain-option disambiguated and truncated; 4NS6NST = “400 not saved vs. 2/3 chance that 600 not saved” truncation problem; The model in Table 2 differed significantly from the data for references in italics. Per Table 3, Japanese, European, and North American samples did not differ from one another and were therefore combined.