Sample Size Calculation for Controlling False Discovery Proportion

Table 2

Sample size calculation for controlling FDP and FDR to achieve overall power, blockwise correlation structure.

𝜋0	𝜌𝑢	𝜌𝑣	𝑝𝑢	𝑝𝑣	𝑚 = 2000		𝑚 = 10000
					FDP	FDR	FDP	FDR
0.9	0.2	0.2	0.1	0.1	75	66	68	65
	0.5	0.5	0.1	0.1	77	66	70	65
	0.8	0.8	0.1	0.1	81	67	74	66
	0	0.2	0	0.3	76	66	68	64
	0	0.5	0	0.3	78	66	71	64
	0	0.6	0	0.3	81	66	73	64
	0.2	0	1	0	77 (74)	67	70	67
	0.5	0	1	0	79 (75)	69	72	69
	0.8	0	1	0	82 (77)	72	75	72
0.7	0.2	0.2	0.1	0.1	53	49	50	48
	0.5	0.5	0.1	0.1	54	49	51	48
	0.8	0.8	0.1	0.1	55	49	53	49
	0	0.2	0	0.3	53	48	50	48
	0	0.5	0	0.3	55	48	52	48
	0	0.8	0	0.3	58	48	56	48
	0.2	0	1	0	54 (53)	49	50	49
	0.5	0	1	0	55 (54)	50	50	50
	0.8	0	1	0	56 (55)	52	50	52

𝜌_𝑢: correlation between test statistics for which the alternative hypotheses are true; 𝜌_𝑣: correlation between test statistics for which the null hypotheses are true; 𝑝_𝑢: proportion of correlated test statistics for which the alternative hypotheses are true; 𝑝_𝑣: proportion of correlated test statistics for which the null hypotheses are true.