Testing for bias in forecasts for independent binary outcomes

Figures & data

Table 1. Realizations and forecasts concerning surviving the first round of the 2018 World Cup in Russia. Data source is Exhibit 2 of the 11 June 2018 Global Macro Research report of the Goldman Sachs Group, Inc

Brazil	1	0.875
France	1	0.814
Germany	0	0.805
Portugal	1	0.752
Belgium	1	0.785
England	1	0.723
Argentina	1	0.731
Spain	1	0.797
Colombia	1	0.749
Uruguay	1	0.744
Poland	0	0.685
Mexico	1	0.478
Denmark	1	0.520
Sweden	1	0.459
Iran	0	0.354
Peru	0	0.373
Russia	1	0.335
Switzerland	1	0.479
Australia	0	0.498
Croatia	1	0.428
Iceland	0	0.452
Costa Rica	0	0.368
Tunisia	0	0.329
Saudi Arabia	0	0.365
Serbia	0	0.434
Japan	1	0.352
Egypt	0	0.344
Morocco	0	0.216
Nigeria	0	0.171
Senegal	0	0.252
Korea Republic	0	0.201
Panama	0	0.132

Table 2. Size-corrected power. The 5% critical value is set at 10.71

	N
Replacement	50	100	500	1000
5%	0.241	0.240	0.558	0.847
10%	0.373	0.508	0.973	1.000
15%	0.543	0.733	1.000	1.000
20%	0.701	0.896	1.000	1.000
25%	0.803	0.970	1.000	1.000
30%	0.894	0.995	1.000	1.000
35%	0.944	0.999	1.000	1.000
40%	0.966	1.000	1.000	1.000
45%	0.981	1.000	1.000	1.000
50%	0.996	1.000	1.000	1.000
55%	1.000	1.000	1.000	1.000
60%	1.000	1.000	1.000	1.000
65%	1.000	1.000	1.000	1.000
70%	1.000	1.000	1.000	1.000
75%	1.000	1.000	1.000	1.000
80%	1.000	1.000	1.000	1.000
85%	1.000	1.000	1.000	1.000
90%	1.000	1.000	1.000	1.000