Optimal alpha reduces error rates in gene expression studies: a meta-analysis approach

BMC Bioinformatics

Table 1 Type I and II error rates: Median, 1st and 3rd quartiles, minimum and maximum α, β, average of α and β, and implied costs of Type I/II errors, evaluated for the standard α = 0.05 and for the optimal α approach, at 3 critical effect sizes (1, 2, and 4 SD), for 203 fish microarray papers with tests that have at least 3 replicates, published between 2002 and 2011 (assuming two-tailed, two-sample t-tests)

Critical effect size	Decision threshold	Statistical parameter	Minimum	1st quartile	Median	3rd quartile	Maximum
1 standard deviation	standard α	α	0.05	0.05	0.05	0.05	0.05
		β	0.088	0.71	0.78	0.84	0.84
		(α + β)/2	0.069	0.38	0.41	0.45	0.45
		Implied Type I/II error cost ratio	1.5	2.6	3.1	3.4	3.9
	optimal α	α	0.064	0.26	0.29	0.32	0.32
		β	0.070	0.34	0.38	0.42	0.42
		(α + β)/2	0.067	0.30	0.33	0.37	0.37
		Implied Type I/II error cost ratio	1	1	1	1	1
2 standard deviations	standard α	α	0.05	0.05	0.05	0.05	0.05
		β	0.0000015	0.21	0.34	0.54	0.54
		(α + β)/2	0.025	0.13	0.20	0.29	0.29
		Implied Type I/II error cost ratio	0.00011	3.4	4.5	5.1	5.1
	optimal α	α	0.0011	0.11	0.15	0.21	0.21
		β	0.00094	0.10	0.13	0.18	0.18
		(α + β)/2	0.0010	0.10	0.14	0.19	0.19
		Implied Type I/II error cost ratio	1	1	1	1	1
4 standard deviations	standard α	α	0.05	0.05	0.05	0.05	0.05
		β	0	0.00023	0.0038	0.052	0.052
		(α + β)/2	0.025	0.025	0.027	0.051	0.051
		Implied Type I/II error cost ratio	0.00011	0.014	0.19	1.9	1.9
	optimal α	α	0.000000031	0.013	0.028	0.065	0.065
		β	0.000000017	0.0065	0.014	0.031	0.031
		(α + β)/2	0.000000024	0.0096	0.021	0.048	0.048
		Implied Type I/II error cost ratio	1	1	1	1	1

ISSN: 1471-2105