Table 1.

The Ratio of the Observed Type I Error Rate versus the Nominal Value for the Bonferroni Test, the Unconstrained Score Test, and the Constrained Score Tests

Proportional
n Cases/n Controls	p Value Level	Bonferroni	Unconstrained	One-Sided	Bidirectional	Standard	Corrected
Independent Exposures
500/500	0.05	0.99	1.01	1.1	1.02	1.17	0.88
	0.001	0.97	1.01	1.57	1.07	4.4	1.05
	0.0001	0.88	1.14	1.98	1.32	14.24	1.5
2,500/2,500	0.05	0.98	1.00	1.03	1	1.04	0.98
	0.001	0.94	1.05	1.25	1.07	1.5	1.04
	0.0001	0.98	1.04	1.34	1.10	2.68	1.40
5,000/5,000	0.05	0.98	0.99	1.02	0.99	1.01	0.99
	0.001	0.96	1	1.14	0.97	1.25	1
	0.0001	0.76	1.02	1.18	1.02	1.56	1
Correlated Exposures
500/500	0.05	0.94	0.99	1.09	0.99	1.10	0.91
	0.001	1.03	1.01	1.65	1.1	3.08	1.18
	0.0001	1.34	1.06	2.12	1.34	9.62	2.06
2,500/2,500	0.05	0.98	1.01	1.04	1.01	1.03	0.99
	0.001	1.04	0.99	1.38	1.06	1.48	1.1
	0.0001	0.92	0.80	1.54	0.90	1.92	0.98
5,000/5,000	0.05	0.97	0.99	1.01	0.99	1.01	0.99
	0.001	0.99	1.02	1.21	0.94	1.17	0.99
	0.0001	1.12	0.94	1.34	1.16	1.38	1.04