Table 1. Power analysis assuming a binomial distribution to determine minimum number of seeds required to detect at least one GE seed for different frequency of gene flow; four α values (α=5, 2.5, 1.0, 0.05%); and three power (1−β) values (0.80, 0.85, 0.95).

Hoa frequency of gene flow p(x)	α Value (α)
	α=5%	α=2.5%	α=1%	α=0.05%	α=5%	α=2.5%	α=1%	α=0.05%	α=5%	α=2.5%	α=1%	α=0.05%
	Minimum sample size (n)b for power=0.80c				Minimum sample size (n)b for power=0.85c				Minimum sample size (n)b for power=0.95c
0.01	1989	2588	3383	3985	2242	2875	3710	4340	3128	3869	4829	5544
0.005	3996	5199	6797	8007	4503	5776	7454	8719	6282	7771	9700	11136
0.0025	8010	10 422	13 625	16 051	9026	11 577	14 941	17 477	12 590	15 573	19 441	22 319
0.001	20 052	26 090	34 109	40 183	22 595	28 980	37 402	43 750	31 513	38 982	48 664	55 870
0.0005	40 122	52 204	68 248	80 402	45 209	57 985	74 837	87 540	63 051	77 995	97 368	111 788
0.00025	80 262	104 431	136 528	160 841	90 437	115 996	149 707	175 120	126 127	156 023	194 777	223 624
0.0001	200 681	261 114	341 367	402 159	226 123	290 028	374 319	437 860	315 356	390 106	487 005	559 132
0.00005	401 379	522 251	682 765	804 355	452 266	580 082	748 671	875 759	630 737	780 244	974 051	1 118 312
0.000025	802 776	1 044 526	1 365 561	1 608 746	904 551	1 160 190	1 497 376	1 751 558	1 261 500	1 560 519	1 948 144	2 236 672
0.00001	2 006 968	2 611 350	3 413 949	4 021 921	2 261 406	2 900 514	3 743 490	4 378 955	3 153 787	3 901 347	4 870 422	5 591 751
0.000005	4 013 954	5 222 724	6 827 930	8 043 879	4 522 833	5 801 054	7 487 013	8 757 949	6 307 600	7 802 726	9 740 884	11 183 549
0.0000025	8 027 925	10 445 471	13 655 891	16 087 794	9 045 685	11 602 134	14 974 060	17 515 937	12 615 225	15 605 485	19 481 810	22 367 146

Abbreviation: GE, genetically engineered.

^aNull hypothesis: theoretical value of frequency of gene flow.

^bMinimum sample size required to detect one or more GE seeds at a given theoretical frequency of gene flow and different values of α and power (1−β). Null hypothesis that the frequency X⩾P is rejected at a given α value, when no GE seeds were found in a sample size of n or greater.

^cValue of power to ascertain how much power (1−β) would be available for a given sample size and confidence interval.