Table 3.

Estimated probability of response and standard errors

	Group 1	Group 2	Group 3	Group 4
Null
Truth	0.05	0.05	0.1	0.2
Simon	0.05 (0.05)	0.05 (0.05)	0.09 (0.06)	0.18 (0.08)
Independent Bayes	0.04 (0.04)	0.04 (0.04)	0.08 (0.06)	0.16 (0.09)
Hierarchical Bayes	0.05 (0.02)	0.05 (0.02)	0.09 (0.04)	0.14 (0.06)
Alternative
Truth	0.2	0.2	0.3	0.4
Simon	0.18 (0.08)	0.18 (0.08)	0.28 (0.09)	0.39 (0.09)
Independent Bayes	0.19 (0.08)	0.19 (0.08)	0.29 (0.10)	0.39 (0.10)
Hierarchical Bayes	0.20 (0.04)	0.20 (0.04)	0.30 (0.05)	0.40 (0.05)
One in the Middle
Truth	0.2	0.2	0.2	0.5
Simon	0.18 (0.08)	0.18 (0.08)	0.18 (0.08)	0.50 (0.09)
Independent Bayes	0.19 (0.08)	0.19 (0.08)	0.18 (0.09)	0.50 (0.09)
Hierarchical Bayes	0.20 (0.04)	0.20 (0.04)	0.26 (0.06)	0.44 (0.07)
All in the Middle
Truth	0.15	0.15	0.2	0.3
Simon	0.13 (0.07)	0.13 (0.07)	0.18 (0.08)	0.28 (0.09)
Independent Bayes	0.13 (0.08)	0.13 (0.08)	0.18 (0.09)	0.28 (0.11)
Hierarchical Bayes	0.14 (0.04)	0.14 (0.04)	0.21 (0.05)	0.29 (0.07)
One Nugget
Truth	0.05	0.05	0.1	0.4
Simon	0.05 (0.05)	0.05 (0.05)	0.09 (0.06)	0.39 (0.09)
Independent Bayes	0.04 (0.04)	0.04 (0.04)	0.08 (0.06)	0.39 (0.10)
Hierarchical Bayes	0.06 (0.03)	0.06 (0.03)	0.11 (0.05)	0.32 (0.12)
2 Null, 2 Alternative
Truth	0.05	0.05	0.3	0.4
Simon	0.05 (0.05)	0.05 (0.05)	0.28 (0.09)	0.39 (0.09)
Independent Bayes	0.04 (0.04)	0.04 (0.04)	0.29 (0.09)	0.39 (0.10)
Hierarchical Bayes	0.08 (0.04)	0.08 (0.04)	0.26 (0.08)	0.35 (0.09)