Global tests of P-values for multifactor dimensionality reduction models in selection of optimal number of target genes

Dai, Hongying; Bhandary, Madhusudan; Becker, Mara; Leeder, J Steven; Gaedigk, Roger; Motsinger-Reif, Alison A

doi:10.1186/1756-0381-5-3

BioData Mining

Table 4 Type I error of six global tests of p-values when p-values are moderately correlated (The nominal Type I error rate is 0.05 and the severe inflation of Type I error with simulated error rate > 0.1 is written in bold italic)

From: Global tests of P-values for multifactor dimensionality reduction models in selection of optimal number of target genes

Correlated Uniform (0,1) ± 0.1Beta (5,1), $ρ = 0.2$
n	KS	Inverse chi	Inverse norm	Tippett	Wilcoxon	Logit
20	0.018	0.031	0.022	0.048	0.021	0.026
50	0.014	0.019	0.008	0.046	0.01	0.013
100	0.014	0.014	0.013	0.05	0.014	0.014
200	0.003	0.01	0.006	0.044	0.004	0.007
300	0.002	0.005	0.002	0.05	0.001	0.002
400	0.001	0.003	0	0.045	0	0
500	0.002	0.002	0.003	0.042	0.001	0.003
Correlated 0.5 Uniform (0,1) ± 0.5Beta (5,1), $ρ = 0.2$
n	KS	Inverse chi	Inverse norm	Tippett	Wilcoxon	Logit
20	0	0	0	0.023	0	0
50	0	0	0	0.023	0	0
100	0	0	0	0.029	0	0
200	0	0	0	0.025	0	0
300	0	0	0	0.024	0	0
400	0	0	0	0.021	0	0
500	0	0	0	0.024	0	0
Correlated 0.9 Uniform (0,1) ± 0.1Beta (6,3), $ρ = 0.2$
n	KS	Inverse chi	Inverse norm	Tippett	Wilcoxon	Logit
20	0.041	0.051	0.047	0.047	0.042	0.049
50	0.032	0.049	0.043	0.042	0.034	0.048
100	0.033	0.032	0.035	0.043	0.035	0.036
200	0.017	0.009	0.023	0.052	0.017	0.024
300	0.017	0.016	0.015	0.039	0.011	0.016
400	0.028	0.006	0.014	0.044	0.01	0.017
500	0.021	0.007	0.013	0.048	0.009	0.015
Correlated 0.5 Uniform (0,1) ± 0.5Beta (6,3), $ρ = 0.2$
n	KS	Inverse chi	Inverse norm	Tippett	Wilcoxon	Logit
20	0.008	0.004	0.003	0.025	0.001	0.003
50	0.021	0.002	0.001	0.024	0.001	0.002
100	0.046	0.001	0.001	0.028	0	0.001
200	*0.165*	0	0	0.023	0	0
300	*0.337*	0	0	0.025	0	0
400	*0.558*	0	0	0.017	0	0
500	*0.66*	0	0	0.018	0	0
Correlated Uniform (0,1) ± 0.1Beta (5,1), $ρ = Beta (2, 5)$
n	KS	Inverse chi	Inverse norm	Tippett	Wilcoxon	Logit
20	0.034	0.043	0.036	0.047	0.034	0.04
50	0.019	0.022	0.02	0.05	0.018	0.021
100	0.012	0.018	0.011	0.038	0.008	0.012
200	0.002	0.008	0.006	0.045	0.006	0.006
300	0.005	0.009	0.005	0.037	0.004	0.007
400	0.004	0.005	0.002	0.038	0.002	0.002
500	0	0.003	0.001	0.05	0	0.002
Correlated 0.5 Uniform (0,1) ± 0.5Beta (5,1), $ρ = Beta (2, 5)$
n	KS	Inverse chi	Inverse norm	Tippett	Wilcoxon	Logit
20	0.001	0.002	0.001	0.021	0	0.001
50	0	0	0	0.026	0	0
100	0	0	0	0.016	0	0
200	0	0	0	0.02	0	0
300	0	0	0	0.031	0	0
400	0.002	0	0	0.02	0	0
500	0.001	0	0	0.028	0	0
Correlated 0.9 Uniform (0,1) ± 0.1Beta (6,3), $ρ = Beta (2, 5)$
n	KS	Inverse chi	Inverse norm	Tippett	Wilcoxon	Logit
20	0.049	0.046	0.054	0.044	0.055	0.05
50	0.039	0.031	0.042	0.042	0.036	0.043
100	0.027	0.027	0.036	0.05	0.033	0.037
200	0.033	0.023	0.03	0.041	0.025	0.032
300	0.042	0.018	0.029	0.038	0.023	0.032
400	0.041	0.012	0.02	0.046	0.017	0.021
500	0.053	0.013	0.026	0.054	0.02	0.028
Correlated 0.5 Uniform (0,1) ± 0.5Beta (6,3), $ρ = Beta (2, 5)$
n	KS	Inverse chi	Inverse norm	Tippett	Wilcoxon	Logit
20	0.02	0.006	0.008	0.03	0.006	0.009
50	0.051	0	0	0.031	0	0
100	*0.123*	0	0.003	0.023	0.001	0.004
200	*0.271*	0	0	0.021	0	0
300	*0.414*	0	0	0.033	0	0
400	*0.552*	0	0	0.024	0	0
500	*0.663*	0	0	0.028	0	0
Correlated Uniform (0,1) ± 0.1Beta (5,1), $ρ = Uniform (0.1, 0.9)$
n	KS	Inverse chi	Inverse norm	Tippett	Wilcoxon	Logit
20	0.036	0.041	0.034	0.048	0.031	0.038
50	0.042	0.039	0.043	0.054	0.039	0.048
100	0.028	0.03	0.029	0.054	0.028	0.029
200	0.037	0.018	0.023	0.045	0.021	0.025
300	0.016	0.012	0.013	0.025	0.015	0.014
400	0.034	0.008	0.017	0.045	0.015	0.019
500	0.031	0.006	0.014	0.046	0.005	0.016
Correlated 0.5 Uniform (0,1) ± 0.5Beta (5,1), $ρ = Uniform (0.1, 0.9)$
n	KS	Inverse chi	Inverse norm	Tippett	Wilcoxon	Logit
20	0.011	0.005	0.002	0.017	0.001	0.002
50	0.029	0.002	0.003	0.022	0.001	0.003
100	0.048	0	0	0.023	0.001	0.001
200	0.099	0	0	0.023	0.000	0
300	*0.161*	0	0	0.026	0.000	0
400	*0.176*	0	0	0.016	0.000	0
500	*0.218*	0	0	0.024	0.001	0
Correlated 0.9 Uniform (0,1) ± 0.1Beta (6,3), $ρ = Uniform (0.1, 0.9)$
n	KS	Inverse chi	Inverse norm	Tippett	Wilcoxon	Logit
20	0.05	0.036	0.038	0.033	0.044	0.039
50	0.054	0.031	0.047	0.043	0.045	0.044
100	0.044	0.031	0.048	0.05	0.045	0.056
200	0.091	0.034	0.057	0.047	0.058	0.058
300	*0.117*	0.024	0.054	0.049	0.054	0.05 s8
400	0.097	0.022	0.048	0.048	0.048	0.05
500	*0.116*	0.014	0.042	0.035	0.043	0.043
Correlated 0.5 Uniform (0,1) ± 0.5Beta (5,1), $ρ = Uniform (0.1, 0.9)$
n	KS	Inverse chi	Inverse norm	Tippett	Wilcoxon	Logit
20	*0.108*	0.009	0.016	0.027	0.017	0.016
50	*0.298*	0.002	0.014	0.025	0.013	0.014
100	*0.459*	0.002	0.014	0.024	0.016	0.014
200	*0.774*	0	0.016	0.017	0.022	0.017
300	*0.908*	0	0.016	0.023	0.023	0.015
400	*0.933*	0	0.024	0.024	0.029	0.019
500	*0.975*	0	0.016	0.02	0.032	0.013

Uniform distributions have random correlation matrices. The nominal Type I error rate is 0.05 and the severe inflation of Type I error with simulated error rate > 0.1 is written in bold italic).

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ISSN: 1756-0381

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