Power: fixed tests and Levene-first gate

1,000 replications per cell; four groups; significance level 5%. All tests use the same simulated samples within each cell.

L+SW: Levene on internally studentised model residuals first. If Levene does not reject, pooled residual Shapiro-Wilk selects F or KW. If Levene rejects, Holm-adjusted groupwise Shapiro-Wilk selects W or KW.

F: Fisher ANOVA; W: Welch ANOVA; KW: Kruskal-Wallis. Positive differences mean higher rejection probability for the gate; negative differences mean lower rejection probability. Differences are in percentage points, with ± one paired Monte Carlo standard error. These simulations alone do not establish Type I error control.

The inputs are the vignette's normal and Fleishman distributions. Skewness and excess kurtosis identify each base distribution. SD factors and mean shifts are listed for every block. n denotes each group size in balanced designs and average group size in unbalanced designs; the complete group-size vector is shown. Routing percentages are separate from final-test rejection percentages.

ordered

balanced n, equal SD

Means: (0.00, 0.25, 0.50, 0.75); SD: (1,1,1,1).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	10, 10, 10, 10	Normal	24.2	22.7	22.0	24.1	90.3	6.4	3.3	-0.10 ± 0.36	+1.40 ± 0.85	+2.10 ± 0.68
0; 0	20	20, 20, 20, 20	Normal	50.3	48.1	46.8	50.8	91.7	3.9	4.4	+0.50 ± 0.33	+2.70 ± 0.83	+4.00 ± 0.89
0; 0	30	30, 30, 30, 30	Normal	71.9	70.1	68.1	72.0	91.7	3.8	4.5	+0.10 ± 0.33	+1.90 ± 0.74	+3.90 ± 0.89
0; 0	50	50, 50, 50, 50	Normal	92.4	92.5	90.8	92.4	91.3	4.4	4.3	+0.00 ± 0.00	-0.10 ± 0.33	+1.60 ± 0.51
0; 0	100	100, 100, 100, 100	Normal	100.0	100.0	99.9	100.0	90.4	4.0	5.6	+0.00 ± 0.00	+0.00 ± 0.00	+0.10 ± 0.10
0; 0	200	200, 200, 200, 200	Normal	100.0	100.0	100.0	100.0	88.7	5.5	5.8	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
0; 6	10	10, 10, 10, 10	Fleishman	28.8	32.4	37.7	37.6	51.6	7.7	40.7	+8.80 ± 1.02	+5.20 ± 1.05	-0.10 ± 0.67
0; 6	20	20, 20, 20, 20	Fleishman	55.5	57.4	69.8	68.4	23.4	3.1	73.5	+12.90 ± 1.17	+11.00 ± 1.11	-1.40 ± 0.56
0; 6	30	30, 30, 30, 30	Fleishman	72.7	73.9	87.9	87.1	10.3	2.5	87.2	+14.40 ± 1.15	+13.20 ± 1.13	-0.80 ± 0.28
0; 6	50	50, 50, 50, 50	Fleishman	92.4	92.5	98.6	98.6	1.8	0.9	97.3	+6.20 ± 0.76	+6.10 ± 0.76	+0.00 ± 0.00
0; 6	100	100, 100, 100, 100	Fleishman	99.6	99.6	100.0	100.0	0.0	0.1	99.9	+0.40 ± 0.20	+0.40 ± 0.20	+0.00 ± 0.00
0; 6	200	200, 200, 200, 200	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
0.5; 1	10	10, 10, 10, 10	Fleishman	24.9	24.8	24.5	26.1	74.4	8.0	17.6	+1.20 ± 0.51	+1.30 ± 0.87	+1.60 ± 0.73
0.5; 1	20	20, 20, 20, 20	Fleishman	52.2	50.7	52.4	54.3	64.4	5.1	30.5	+2.10 ± 0.60	+3.60 ± 0.90	+1.90 ± 0.83
0.5; 1	30	30, 30, 30, 30	Fleishman	71.9	70.6	73.3	74.1	49.9	4.0	46.1	+2.20 ± 0.66	+3.50 ± 0.77	+0.80 ± 0.58
0.5; 1	50	50, 50, 50, 50	Fleishman	92.6	92.7	94.2	94.3	34.3	3.4	62.3	+1.70 ± 0.54	+1.60 ± 0.55	+0.10 ± 0.22
0.5; 1	100	100, 100, 100, 100	Fleishman	99.9	99.9	100.0	100.0	9.6	1.4	89.0	+0.10 ± 0.10	+0.10 ± 0.10	+0.00 ± 0.00
0.5; 1	200	200, 200, 200, 200	Fleishman	100.0	100.0	100.0	100.0	0.2	0.0	99.8	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
1; 1.6	10	10, 10, 10, 10	Fleishman	28.0	25.8	28.4	30.7	51.4	8.1	40.5	+2.70 ± 0.72	+4.90 ± 0.95	+2.30 ± 0.67
1; 1.6	20	20, 20, 20, 20	Fleishman	50.3	48.7	55.2	55.7	16.8	5.7	77.5	+5.40 ± 0.93	+7.00 ± 1.03	+0.50 ± 0.36
1; 1.6	30	30, 30, 30, 30	Fleishman	70.7	70.9	77.8	77.6	3.1	4.0	92.9	+6.90 ± 0.95	+6.70 ± 0.97	-0.20 ± 0.14
1; 1.6	50	50, 50, 50, 50	Fleishman	92.0	92.5	95.3	95.3	0.2	1.0	98.8	+3.30 ± 0.68	+2.80 ± 0.64	+0.00 ± 0.00
1; 1.6	100	100, 100, 100, 100	Fleishman	99.7	99.8	99.9	99.9	0.0	0.0	100.0	+0.20 ± 0.14	+0.10 ± 0.10	+0.00 ± 0.00
1; 1.6	200	200, 200, 200, 200	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
2; 6.6	10	10, 10, 10, 10	Fleishman	29.7	31.3	42.5	43.0	8.2	9.5	82.3	+13.30 ± 1.24	+11.70 ± 1.18	+0.50 ± 0.46
2; 6.6	20	20, 20, 20, 20	Fleishman	55.0	55.5	80.8	80.8	0.0	1.7	98.3	+25.80 ± 1.40	+25.30 ± 1.40	+0.00 ± 0.00
2; 6.6	30	30, 30, 30, 30	Fleishman	70.2	71.2	92.0	92.0	0.0	0.0	100.0	+21.80 ± 1.31	+20.80 ± 1.31	+0.00 ± 0.00
2; 6.6	50	50, 50, 50, 50	Fleishman	91.3	92.2	99.7	99.7	0.0	0.0	100.0	+8.40 ± 0.88	+7.50 ± 0.83	+0.00 ± 0.00
2; 6.6	100	100, 100, 100, 100	Fleishman	99.8	99.8	100.0	100.0	0.0	0.0	100.0	+0.20 ± 0.14	+0.20 ± 0.14	+0.00 ± 0.00
2; 6.6	200	200, 200, 200, 200	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00

unbalanced n, equal SD

Means: (0.00, 0.25, 0.50, 0.75); SD: (1,1,1,1).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	5, 8, 12, 15	Normal	22.8	20.4	20.2	23.5	89.0	5.1	5.9	+0.70 ± 0.41	+3.10 ± 0.99	+3.30 ± 0.76
0; 0	20	10, 16, 24, 30	Normal	45.1	44.2	42.0	46.0	88.2	6.2	5.6	+0.90 ± 0.46	+1.80 ± 0.97	+4.00 ± 0.89
0; 0	30	15, 24, 36, 45	Normal	64.0	61.3	60.2	64.2	90.0	4.9	5.1	+0.20 ± 0.35	+2.90 ± 0.86	+4.00 ± 0.89
0; 0	50	25, 40, 60, 75	Normal	88.3	86.6	86.5	88.2	91.1	3.8	5.1	-0.10 ± 0.10	+1.60 ± 0.56	+1.70 ± 0.61
0; 0	100	50, 80, 120, 150	Normal	99.7	99.5	99.6	99.8	90.0	4.4	5.6	+0.10 ± 0.10	+0.30 ± 0.17	+0.20 ± 0.14
0; 0	200	100, 160, 240, 300	Normal	100.0	100.0	100.0	100.0	91.1	4.4	4.5	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
0; 6	10	5, 8, 12, 15	Fleishman	23.9	24.8	29.0	29.1	53.2	6.4	40.4	+5.20 ± 0.88	+4.30 ± 1.17	+0.10 ± 0.76
0; 6	20	10, 16, 24, 30	Fleishman	45.9	47.5	60.4	59.1	22.7	5.2	72.1	+13.20 ± 1.18	+11.60 ± 1.23	-1.30 ± 0.54
0; 6	30	15, 24, 36, 45	Fleishman	67.1	68.2	82.2	81.6	8.0	2.3	89.7	+14.50 ± 1.26	+13.40 ± 1.19	-0.60 ± 0.28
0; 6	50	25, 40, 60, 75	Fleishman	88.7	89.5	97.6	97.6	1.3	0.5	98.2	+8.90 ± 0.93	+8.10 ± 0.87	+0.00 ± 0.00
0; 6	100	50, 80, 120, 150	Fleishman	99.2	99.2	100.0	100.0	0.0	0.0	100.0	+0.80 ± 0.28	+0.80 ± 0.28	+0.00 ± 0.00
0; 6	200	100, 160, 240, 300	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
0.5; 1	10	5, 8, 12, 15	Fleishman	23.2	25.3	22.5	24.9	74.7	8.8	16.5	+1.70 ± 0.52	-0.40 ± 1.04	+2.40 ± 0.74
0.5; 1	20	10, 16, 24, 30	Fleishman	47.4	47.6	49.0	49.7	63.5	6.7	29.8	+2.30 ± 0.64	+2.10 ± 0.95	+0.70 ± 0.61
0.5; 1	30	15, 24, 36, 45	Fleishman	63.6	63.5	65.2	65.7	52.6	5.4	42.0	+2.10 ± 0.68	+2.20 ± 0.91	+0.50 ± 0.67
0.5; 1	50	25, 40, 60, 75	Fleishman	86.4	85.4	86.3	86.4	33.9	3.3	62.8	+0.00 ± 0.57	+1.00 ± 0.71	+0.10 ± 0.39
0.5; 1	100	50, 80, 120, 150	Fleishman	99.6	99.4	99.7	99.7	9.7	2.3	88.0	+0.10 ± 0.17	+0.30 ± 0.22	+0.00 ± 0.00
0.5; 1	200	100, 160, 240, 300	Fleishman	100.0	100.0	100.0	100.0	0.1	0.3	99.6	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
1; 1.6	10	5, 8, 12, 15	Fleishman	23.6	27.8	25.4	27.2	49.3	9.8	40.9	+3.60 ± 0.79	-0.60 ± 1.02	+1.80 ± 0.65
1; 1.6	20	10, 16, 24, 30	Fleishman	47.9	48.8	51.8	52.4	15.9	5.9	78.2	+4.50 ± 0.94	+3.60 ± 1.08	+0.60 ± 0.35
1; 1.6	30	15, 24, 36, 45	Fleishman	65.9	64.9	70.7	70.9	4.4	3.8	91.8	+5.00 ± 0.96	+6.00 ± 1.01	+0.20 ± 0.14
1; 1.6	50	25, 40, 60, 75	Fleishman	88.3	87.7	91.4	91.3	0.1	1.1	98.8	+3.00 ± 0.67	+3.60 ± 0.71	-0.10 ± 0.10
1; 1.6	100	50, 80, 120, 150	Fleishman	99.1	99.0	99.7	99.7	0.0	0.0	100.0	+0.60 ± 0.24	+0.70 ± 0.26	+0.00 ± 0.00
1; 1.6	200	100, 160, 240, 300	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
2; 6.6	10	5, 8, 12, 15	Fleishman	27.1	39.5	43.3	43.5	9.2	11.5	79.3	+16.40 ± 1.24	+4.00 ± 1.17	+0.20 ± 0.35
2; 6.6	20	10, 16, 24, 30	Fleishman	47.9	54.6	72.5	72.4	0.1	1.4	98.5	+24.50 ± 1.41	+17.80 ± 1.33	-0.10 ± 0.10
2; 6.6	30	15, 24, 36, 45	Fleishman	64.3	68.0	87.5	87.5	0.0	0.0	100.0	+23.20 ± 1.36	+19.50 ± 1.31	+0.00 ± 0.00
2; 6.6	50	25, 40, 60, 75	Fleishman	86.6	86.4	98.8	98.8	0.0	0.0	100.0	+12.20 ± 1.05	+12.40 ± 1.05	+0.00 ± 0.00
2; 6.6	100	50, 80, 120, 150	Fleishman	99.7	99.7	100.0	100.0	0.0	0.0	100.0	+0.30 ± 0.17	+0.30 ± 0.17	+0.00 ± 0.00
2; 6.6	200	100, 160, 240, 300	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00

balanced n, unequal SD

Means: (0.00, 0.25, 0.50, 0.75); SD: (1.000000000000000,1.414213562373095,2.000000000000000,2.236067977499790).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	10, 10, 10, 10	Normal	11.3	11.8	9.9	12.0	48.9	41.2	9.9	+0.70 ± 0.67	+0.20 ± 0.57	+2.10 ± 0.65
0; 0	20	20, 20, 20, 20	Normal	18.8	20.8	17.7	21.0	15.8	76.8	7.4	+2.20 ± 0.97	+0.20 ± 0.40	+3.30 ± 0.87
0; 0	30	30, 30, 30, 30	Normal	26.9	30.6	28.2	30.5	4.1	91.2	4.7	+3.60 ± 0.96	-0.10 ± 0.26	+2.30 ± 0.92
0; 0	50	50, 50, 50, 50	Normal	43.4	51.8	44.0	51.4	0.0	95.6	4.4	+8.00 ± 1.18	-0.40 ± 0.20	+7.40 ± 1.17
0; 0	100	100, 100, 100, 100	Normal	78.8	85.3	77.5	84.7	0.0	94.4	5.6	+5.90 ± 0.90	-0.60 ± 0.24	+7.20 ± 0.95
0; 0	200	200, 200, 200, 200	Normal	98.1	99.5	98.7	99.5	0.0	94.5	5.5	+1.40 ± 0.37	+0.00 ± 0.00	+0.80 ± 0.32
0; 6	10	10, 10, 10, 10	Fleishman	13.0	15.0	16.8	17.6	29.7	26.6	43.7	+4.60 ± 0.94	+2.60 ± 0.83	+0.80 ± 0.62
0; 6	20	20, 20, 20, 20	Fleishman	21.1	25.6	31.4	30.1	5.6	29.7	64.7	+9.00 ± 1.20	+4.50 ± 0.94	-1.30 ± 0.59
0; 6	30	30, 30, 30, 30	Fleishman	30.7	37.8	45.3	44.3	0.7	20.9	78.4	+13.60 ± 1.29	+6.50 ± 1.03	-1.00 ± 0.58
0; 6	50	50, 50, 50, 50	Fleishman	48.5	56.1	70.8	70.2	0.0	6.8	93.2	+21.70 ± 1.41	+14.10 ± 1.27	-0.60 ± 0.32
0; 6	100	100, 100, 100, 100	Fleishman	78.2	85.3	95.5	95.5	0.0	0.1	99.9	+17.30 ± 1.20	+10.20 ± 0.98	+0.00 ± 0.00
0; 6	200	200, 200, 200, 200	Fleishman	97.7	99.6	100.0	100.0	0.0	0.0	100.0	+2.30 ± 0.47	+0.40 ± 0.20	+0.00 ± 0.00
0.5; 1	10	10, 10, 10, 10	Fleishman	11.9	11.4	10.8	13.8	43.8	38.4	17.8	+1.90 ± 0.79	+2.40 ± 0.72	+3.00 ± 0.73
0.5; 1	20	20, 20, 20, 20	Fleishman	16.5	18.1	13.4	17.6	11.5	63.7	24.8	+1.10 ± 0.94	-0.50 ± 0.48	+4.20 ± 0.78
0.5; 1	30	30, 30, 30, 30	Fleishman	25.8	29.5	20.9	27.7	2.7	65.9	31.4	+1.90 ± 1.09	-1.80 ± 0.66	+6.80 ± 0.91
0.5; 1	50	50, 50, 50, 50	Fleishman	42.9	48.5	35.1	41.8	0.0	55.7	44.3	-1.10 ± 1.19	-6.70 ± 0.89	+6.70 ± 0.94
0.5; 1	100	100, 100, 100, 100	Fleishman	78.1	84.3	66.5	71.1	0.0	28.1	71.9	-7.00 ± 1.11	-13.20 ± 1.10	+4.60 ± 0.68
0.5; 1	200	200, 200, 200, 200	Fleishman	98.6	99.4	94.4	94.8	0.0	6.2	93.8	-3.80 ± 0.60	-4.60 ± 0.66	+0.40 ± 0.20
1; 1.6	10	10, 10, 10, 10	Fleishman	8.8	7.7	6.1	8.8	31.1	38.5	30.4	+0.00 ± 0.74	+1.10 ± 0.54	+2.70 ± 0.63
1; 1.6	20	20, 20, 20, 20	Fleishman	16.4	18.5	10.4	14.9	4.6	40.2	55.2	-1.50 ± 0.98	-3.60 ± 0.71	+4.50 ± 0.69
1; 1.6	30	30, 30, 30, 30	Fleishman	25.6	29.3	14.6	20.0	0.4	30.8	68.8	-5.60 ± 1.14	-9.30 ± 1.04	+5.40 ± 0.74
1; 1.6	50	50, 50, 50, 50	Fleishman	45.4	51.8	21.7	24.4	0.0	8.8	91.2	-21.00 ± 1.39	-27.40 ± 1.44	+2.70 ± 0.51
1; 1.6	100	100, 100, 100, 100	Fleishman	76.6	83.4	41.9	41.9	0.0	0.0	100.0	-34.70 ± 1.53	-41.50 ± 1.57	+0.00 ± 0.00
1; 1.6	200	200, 200, 200, 200	Fleishman	99.0	99.3	73.8	73.8	0.0	0.0	100.0	-25.20 ± 1.37	-25.50 ± 1.38	+0.00 ± 0.00
2; 6.6	10	10, 10, 10, 10	Fleishman	8.9	8.0	6.6	8.6	6.2	23.1	70.7	-0.30 ± 0.88	+0.60 ± 0.69	+2.00 ± 0.49
2; 6.6	20	20, 20, 20, 20	Fleishman	18.0	18.6	8.5	10.4	0.1	4.9	95.0	-7.60 ± 1.05	-8.20 ± 1.08	+1.90 ± 0.43
2; 6.6	30	30, 30, 30, 30	Fleishman	25.1	28.7	10.7	10.8	0.0	0.1	99.9	-14.30 ± 1.18	-17.90 ± 1.29	+0.10 ± 0.10
2; 6.6	50	50, 50, 50, 50	Fleishman	44.3	49.1	15.3	15.3	0.0	0.0	100.0	-29.00 ± 1.49	-33.80 ± 1.56	+0.00 ± 0.00
2; 6.6	100	100, 100, 100, 100	Fleishman	78.7	84.1	23.6	23.6	0.0	0.0	100.0	-55.10 ± 1.58	-60.50 ± 1.55	+0.00 ± 0.00
2; 6.6	200	200, 200, 200, 200	Fleishman	98.4	99.3	44.6	44.6	0.0	0.0	100.0	-53.80 ± 1.58	-54.70 ± 1.57	+0.00 ± 0.00

unbalanced n, larger n with larger SD

Means: (0.00, 0.25, 0.50, 0.75); SD: (1.000000000000000,1.414213562373095,2.000000000000000,2.236067977499790).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	5, 8, 12, 15	Normal	4.4	13.7	4.7	8.4	69.7	22.5	7.8	+4.00 ± 0.65	-5.30 ± 0.83	+3.70 ± 0.72
0; 0	20	10, 16, 24, 30	Normal	9.7	18.7	10.8	17.5	36.8	54.2	9.0	+7.80 ± 0.96	-1.20 ± 0.51	+6.70 ± 0.93
0; 0	30	15, 24, 36, 45	Normal	14.9	31.0	18.2	28.8	14.4	79.1	6.5	+13.90 ± 1.18	-2.20 ± 0.54	+10.60 ± 1.15
0; 0	50	25, 40, 60, 75	Normal	25.4	48.3	29.0	47.3	0.4	93.9	5.7	+21.90 ± 1.35	-1.00 ± 0.31	+18.30 ± 1.29
0; 0	100	50, 80, 120, 150	Normal	57.3	81.7	66.3	81.0	0.0	95.0	5.0	+23.70 ± 1.37	-0.70 ± 0.26	+14.70 ± 1.21
0; 0	200	100, 160, 240, 300	Normal	93.8	98.5	95.9	98.4	0.0	95.8	4.2	+4.60 ± 0.66	-0.10 ± 0.10	+2.50 ± 0.49
0; 6	10	5, 8, 12, 15	Fleishman	7.4	12.8	8.8	10.3	42.2	10.0	47.8	+2.90 ± 0.62	-2.50 ± 0.86	+1.50 ± 0.54
0; 6	20	10, 16, 24, 30	Fleishman	8.9	22.1	18.8	20.9	11.7	18.3	70.0	+12.00 ± 1.08	-1.20 ± 1.01	+2.10 ± 0.60
0; 6	30	15, 24, 36, 45	Fleishman	15.5	33.1	31.2	31.8	2.0	15.5	82.5	+16.30 ± 1.25	-1.30 ± 1.08	+0.60 ± 0.45
0; 6	50	25, 40, 60, 75	Fleishman	27.9	53.0	55.0	56.1	0.1	7.2	92.7	+28.20 ± 1.46	+3.10 ± 1.23	+1.10 ± 0.33
0; 6	100	50, 80, 120, 150	Fleishman	60.1	82.3	92.0	92.0	0.0	0.2	99.8	+31.90 ± 1.49	+9.70 ± 1.08	+0.00 ± 0.00
0; 6	200	100, 160, 240, 300	Fleishman	93.3	99.0	99.8	99.8	0.0	0.0	100.0	+6.50 ± 0.78	+0.80 ± 0.28	+0.00 ± 0.00
0.5; 1	10	5, 8, 12, 15	Fleishman	4.4	11.2	4.9	7.8	58.2	21.2	20.6	+3.40 ± 0.61	-3.40 ± 0.67	+2.90 ± 0.65
0.5; 1	20	10, 16, 24, 30	Fleishman	8.1	20.7	9.8	17.2	28.5	43.1	28.4	+9.10 ± 0.98	-3.50 ± 0.73	+7.40 ± 0.92
0.5; 1	30	15, 24, 36, 45	Fleishman	12.2	30.9	13.7	24.7	8.5	58.9	32.6	+12.50 ± 1.10	-6.20 ± 0.81	+11.00 ± 1.09
0.5; 1	50	25, 40, 60, 75	Fleishman	28.3	52.1	29.2	41.8	0.5	55.6	43.9	+13.50 ± 1.33	-10.30 ± 0.99	+12.60 ± 1.09
0.5; 1	100	50, 80, 120, 150	Fleishman	59.4	85.6	55.2	62.8	0.0	28.0	72.0	+3.40 ± 1.28	-22.80 ± 1.33	+7.60 ± 0.84
0.5; 1	200	100, 160, 240, 300	Fleishman	92.3	98.9	87.9	88.4	0.0	4.6	95.4	-3.90 ± 0.82	-10.50 ± 0.97	+0.50 ± 0.22
1; 1.6	10	5, 8, 12, 15	Fleishman	4.3	12.9	4.7	8.2	41.0	23.5	35.5	+3.90 ± 0.70	-4.70 ± 0.79	+3.50 ± 0.68
1; 1.6	20	10, 16, 24, 30	Fleishman	7.6	21.3	6.9	13.9	9.0	30.8	60.2	+6.30 ± 0.93	-7.40 ± 0.90	+7.00 ± 0.83
1; 1.6	30	15, 24, 36, 45	Fleishman	13.1	31.0	10.4	17.2	0.6	25.4	74.0	+4.10 ± 1.03	-13.80 ± 1.14	+6.80 ± 0.81
1; 1.6	50	25, 40, 60, 75	Fleishman	26.7	50.7	14.4	17.6	0.0	8.0	92.0	-9.10 ± 1.15	-33.10 ± 1.49	+3.20 ± 0.56
1; 1.6	100	50, 80, 120, 150	Fleishman	59.1	82.8	31.5	31.5	0.0	0.0	100.0	-27.60 ± 1.43	-51.30 ± 1.58	+0.00 ± 0.00
1; 1.6	200	100, 160, 240, 300	Fleishman	92.6	97.8	60.8	60.8	0.0	0.0	100.0	-31.80 ± 1.47	-37.00 ± 1.53	+0.00 ± 0.00
2; 6.6	10	5, 8, 12, 15	Fleishman	3.9	14.5	4.8	7.6	6.2	14.1	79.7	+3.70 ± 0.76	-6.90 ± 0.97	+2.80 ± 0.58
2; 6.6	20	10, 16, 24, 30	Fleishman	7.9	23.9	4.7	5.6	0.1	2.3	97.6	-2.30 ± 0.77	-18.30 ± 1.26	+0.90 ± 0.30
2; 6.6	30	15, 24, 36, 45	Fleishman	9.9	31.9	5.1	5.1	0.0	0.1	99.9	-4.80 ± 0.81	-26.80 ± 1.44	+0.00 ± 0.00
2; 6.6	50	25, 40, 60, 75	Fleishman	24.2	53.3	10.0	10.0	0.0	0.0	100.0	-14.20 ± 1.19	-43.30 ± 1.60	+0.00 ± 0.00
2; 6.6	100	50, 80, 120, 150	Fleishman	59.6	81.0	20.4	20.4	0.0	0.0	100.0	-39.20 ± 1.56	-60.60 ± 1.55	+0.00 ± 0.00
2; 6.6	200	100, 160, 240, 300	Fleishman	95.4	98.5	40.7	40.7	0.0	0.0	100.0	-54.70 ± 1.58	-57.80 ± 1.56	+0.00 ± 0.00

unbalanced n, larger n with smaller SD

Means: (0.00, 0.25, 0.50, 0.75); SD: (2.236067977499790,2.000000000000000,1.414213562373095,1.000000000000000).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	5, 8, 12, 15	Normal	18.9	9.8	13.8	14.5	40.1	53.5	6.4	-4.40 ± 0.75	+4.70 ± 0.78	+0.70 ± 0.74
0; 0	20	10, 16, 24, 30	Normal	29.4	18.2	22.1	19.9	10.2	83.7	6.1	-9.50 ± 1.12	+1.70 ± 0.46	-2.20 ± 0.85
0; 0	30	15, 24, 36, 45	Normal	36.0	24.5	28.5	24.5	2.8	92.8	4.4	-11.50 ± 1.17	+0.00 ± 0.25	-4.00 ± 0.98
0; 0	50	25, 40, 60, 75	Normal	50.9	39.5	44.7	39.6	0.1	95.7	4.2	-11.30 ± 1.27	+0.10 ± 0.17	-5.10 ± 1.05
0; 0	100	50, 80, 120, 150	Normal	81.4	75.3	74.7	75.3	0.0	94.0	6.0	-6.10 ± 0.96	+0.00 ± 0.20	+0.60 ± 0.96
0; 0	200	100, 160, 240, 300	Normal	97.7	97.0	96.6	97.0	0.0	94.7	5.3	-0.70 ± 0.39	+0.00 ± 0.00	+0.40 ± 0.49
0; 6	10	5, 8, 12, 15	Fleishman	20.9	11.5	19.4	17.4	27.8	36.1	36.1	-3.50 ± 1.09	+5.90 ± 0.89	-2.00 ± 0.79
0; 6	20	10, 16, 24, 30	Fleishman	27.9	18.9	30.7	28.2	5.5	28.7	65.8	+0.30 ± 1.23	+9.30 ± 1.03	-2.50 ± 0.62
0; 6	30	15, 24, 36, 45	Fleishman	38.1	28.7	42.5	40.4	1.1	21.5	77.4	+2.30 ± 1.28	+11.70 ± 1.12	-2.10 ± 0.53
0; 6	50	25, 40, 60, 75	Fleishman	56.0	46.7	68.0	66.5	0.0	7.7	92.3	+10.50 ± 1.38	+19.80 ± 1.34	-1.50 ± 0.41
0; 6	100	50, 80, 120, 150	Fleishman	80.7	76.9	93.9	93.9	0.0	0.8	99.2	+13.20 ± 1.12	+17.00 ± 1.20	+0.00 ± 0.00
0; 6	200	100, 160, 240, 300	Fleishman	98.4	97.6	100.0	100.0	0.0	0.0	100.0	+1.60 ± 0.40	+2.40 ± 0.48	+0.00 ± 0.00
0.5; 1	10	5, 8, 12, 15	Fleishman	21.6	12.5	17.2	18.1	36.4	50.3	13.3	-3.50 ± 0.87	+5.60 ± 0.83	+0.90 ± 0.78
0.5; 1	20	10, 16, 24, 30	Fleishman	27.7	20.5	28.7	24.8	10.3	69.3	20.4	-2.90 ± 1.11	+4.30 ± 0.69	-3.90 ± 0.88
0.5; 1	30	15, 24, 36, 45	Fleishman	36.3	28.1	42.3	34.7	2.9	67.5	29.6	-1.60 ± 1.20	+6.60 ± 0.87	-7.60 ± 1.00
0.5; 1	50	25, 40, 60, 75	Fleishman	56.1	48.5	64.1	57.3	0.1	54.9	45.0	+1.20 ± 1.26	+8.80 ± 0.95	-6.80 ± 0.90
0.5; 1	100	50, 80, 120, 150	Fleishman	79.4	75.0	90.5	87.1	0.0	29.9	70.1	+7.70 ± 1.14	+12.10 ± 1.06	-3.40 ± 0.59
0.5; 1	200	100, 160, 240, 300	Fleishman	97.4	97.1	99.7	99.7	0.0	4.8	95.2	+2.30 ± 0.49	+2.60 ± 0.52	+0.00 ± 0.00
1; 1.6	10	5, 8, 12, 15	Fleishman	22.8	17.3	22.2	23.9	24.8	46.3	28.9	+1.10 ± 0.95	+6.60 ± 0.88	+1.70 ± 0.74
1; 1.6	20	10, 16, 24, 30	Fleishman	29.9	25.4	38.8	35.9	3.4	44.8	51.8	+6.00 ± 1.20	+10.50 ± 1.02	-2.90 ± 0.63
1; 1.6	30	15, 24, 36, 45	Fleishman	40.3	31.5	54.2	50.7	0.5	27.6	71.9	+10.40 ± 1.38	+19.20 ± 1.29	-3.50 ± 0.63
1; 1.6	50	25, 40, 60, 75	Fleishman	53.3	48.6	76.1	74.8	0.0	6.9	93.1	+21.50 ± 1.37	+26.20 ± 1.41	-1.30 ± 0.39
1; 1.6	100	50, 80, 120, 150	Fleishman	81.5	76.8	97.2	97.2	0.0	0.0	100.0	+15.70 ± 1.16	+20.40 ± 1.27	+0.00 ± 0.00
1; 1.6	200	100, 160, 240, 300	Fleishman	98.6	97.9	100.0	100.0	0.0	0.0	100.0	+1.40 ± 0.37	+2.10 ± 0.45	+0.00 ± 0.00
2; 6.6	10	5, 8, 12, 15	Fleishman	26.2	28.5	37.8	36.9	6.2	26.6	67.2	+10.70 ± 1.19	+8.40 ± 1.05	-0.90 ± 0.54
2; 6.6	20	10, 16, 24, 30	Fleishman	33.7	37.4	67.2	66.8	0.2	3.3	96.5	+33.10 ± 1.54	+29.40 ± 1.48	-0.40 ± 0.24
2; 6.6	30	15, 24, 36, 45	Fleishman	43.1	43.6	84.4	84.4	0.0	0.1	99.9	+41.30 ± 1.60	+40.80 ± 1.57	+0.00 ± 0.00
2; 6.6	50	25, 40, 60, 75	Fleishman	57.6	56.0	97.4	97.4	0.0	0.0	100.0	+39.80 ± 1.56	+41.40 ± 1.56	+0.00 ± 0.00
2; 6.6	100	50, 80, 120, 150	Fleishman	78.3	78.5	99.9	99.9	0.0	0.0	100.0	+21.60 ± 1.30	+21.40 ± 1.30	+0.00 ± 0.00
2; 6.6	200	100, 160, 240, 300	Fleishman	97.4	96.9	100.0	100.0	0.0	0.0	100.0	+2.60 ± 0.50	+3.10 ± 0.55	+0.00 ± 0.00

onepoint_0.5

balanced n, equal SD

Means: (0.00, 0.00, 0.00, 0.50); SD: (1,1,1,1).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	10, 10, 10, 10	Normal	16.3	14.4	14.0	16.7	91.0	4.5	4.5	+0.40 ± 0.32	+2.30 ± 0.77	+2.70 ± 0.71
0; 0	20	20, 20, 20, 20	Normal	32.6	32.5	30.4	32.7	91.5	5.0	3.5	+0.10 ± 0.30	+0.20 ± 0.81	+2.30 ± 0.79
0; 0	30	30, 30, 30, 30	Normal	48.2	46.6	43.8	48.3	89.3	5.9	4.8	+0.10 ± 0.30	+1.70 ± 0.75	+4.50 ± 0.92
0; 0	50	50, 50, 50, 50	Normal	72.5	72.5	69.8	73.0	90.5	4.8	4.7	+0.50 ± 0.30	+0.50 ± 0.61	+3.20 ± 0.84
0; 0	100	100, 100, 100, 100	Normal	96.5	96.5	95.8	96.3	90.8	4.1	5.1	-0.20 ± 0.14	-0.20 ± 0.32	+0.50 ± 0.39
0; 6	10	10, 10, 10, 10	Fleishman	17.7	17.9	21.7	22.4	48.5	7.2	44.3	+4.70 ± 0.79	+4.50 ± 0.89	+0.70 ± 0.52
0; 6	20	20, 20, 20, 20	Fleishman	32.8	34.4	48.0	48.0	23.9	3.9	72.2	+15.20 ± 1.24	+13.60 ± 1.20	+0.00 ± 0.53
0; 6	30	30, 30, 30, 30	Fleishman	48.1	49.8	64.9	64.6	9.1	2.7	88.2	+16.50 ± 1.26	+14.80 ± 1.23	-0.30 ± 0.33
0; 6	50	50, 50, 50, 50	Fleishman	73.6	75.0	89.1	89.1	1.3	0.7	98.0	+15.50 ± 1.19	+14.10 ± 1.16	+0.00 ± 0.00
0; 6	100	100, 100, 100, 100	Fleishman	96.9	97.1	99.6	99.6	0.0	0.1	99.9	+2.70 ± 0.51	+2.50 ± 0.49	+0.00 ± 0.00
0.5; 1	10	10, 10, 10, 10	Fleishman	16.3	15.9	15.8	17.4	77.0	7.1	15.9	+1.10 ± 0.46	+1.50 ± 0.85	+1.60 ± 0.65
0.5; 1	20	20, 20, 20, 20	Fleishman	33.0	33.1	34.9	36.5	64.1	4.7	31.2	+3.50 ± 0.63	+3.40 ± 0.92	+1.60 ± 0.72
0.5; 1	30	30, 30, 30, 30	Fleishman	44.5	48.1	48.2	49.0	53.7	5.2	41.1	+4.50 ± 0.78	+0.90 ± 0.85	+0.80 ± 0.76
0.5; 1	50	50, 50, 50, 50	Fleishman	71.0	71.6	74.6	74.7	33.7	3.0	63.3	+3.70 ± 0.72	+3.10 ± 0.72	+0.10 ± 0.50
0.5; 1	100	100, 100, 100, 100	Fleishman	96.3	96.3	97.0	97.1	10.5	1.9	87.6	+0.80 ± 0.45	+0.80 ± 0.45	+0.10 ± 0.10
1; 1.6	10	10, 10, 10, 10	Fleishman	16.6	14.9	16.0	17.6	48.9	9.8	41.3	+1.00 ± 0.65	+2.70 ± 0.83	+1.60 ± 0.63
1; 1.6	20	20, 20, 20, 20	Fleishman	29.6	30.2	33.5	34.5	16.1	6.7	77.2	+4.90 ± 1.03	+4.30 ± 0.98	+1.00 ± 0.42
1; 1.6	30	30, 30, 30, 30	Fleishman	46.0	45.8	52.2	52.0	3.6	3.7	92.7	+6.00 ± 1.12	+6.20 ± 1.07	-0.20 ± 0.20
1; 1.6	50	50, 50, 50, 50	Fleishman	74.7	76.5	81.3	81.3	0.3	1.0	98.7	+6.60 ± 1.00	+4.80 ± 0.86	+0.00 ± 0.00
1; 1.6	100	100, 100, 100, 100	Fleishman	96.8	97.5	98.6	98.6	0.0	0.0	100.0	+1.80 ± 0.42	+1.10 ± 0.33	+0.00 ± 0.00
2; 6.6	10	10, 10, 10, 10	Fleishman	18.9	20.8	25.4	27.3	8.8	12.4	78.8	+8.40 ± 1.06	+6.50 ± 0.99	+1.90 ± 0.55
2; 6.6	20	20, 20, 20, 20	Fleishman	33.3	38.0	59.1	59.1	0.0	1.2	98.8	+25.80 ± 1.43	+21.10 ± 1.43	+0.00 ± 0.00
2; 6.6	30	30, 30, 30, 30	Fleishman	48.1	56.2	78.7	78.7	0.0	0.0	100.0	+30.60 ± 1.47	+22.50 ± 1.37	+0.00 ± 0.00
2; 6.6	50	50, 50, 50, 50	Fleishman	74.9	80.4	98.1	98.1	0.0	0.0	100.0	+23.20 ± 1.34	+17.70 ± 1.21	+0.00 ± 0.00
2; 6.6	100	100, 100, 100, 100	Fleishman	97.1	98.5	100.0	100.0	0.0	0.0	100.0	+2.90 ± 0.53	+1.50 ± 0.38	+0.00 ± 0.00

unbalanced n, equal SD

Means: (0.00, 0.00, 0.00, 0.50); SD: (1,1,1,1).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	5, 8, 12, 15	Normal	19.8	17.9	18.4	20.4	89.0	7.2	3.8	+0.60 ± 0.40	+2.50 ± 0.80	+2.00 ± 0.69
0; 0	20	10, 16, 24, 30	Normal	40.3	35.5	37.4	40.2	90.0	5.0	5.0	-0.10 ± 0.33	+4.70 ± 0.85	+2.80 ± 0.89
0; 0	30	15, 24, 36, 45	Normal	56.4	54.9	53.6	56.8	89.1	6.7	4.2	+0.40 ± 0.28	+1.90 ± 0.62	+3.20 ± 0.90
0; 0	50	25, 40, 60, 75	Normal	83.7	82.5	82.1	83.7	90.0	5.4	4.6	+0.00 ± 0.25	+1.20 ± 0.51	+1.60 ± 0.63
0; 0	100	50, 80, 120, 150	Normal	99.2	99.3	98.7	99.3	90.7	4.6	4.7	+0.10 ± 0.10	+0.00 ± 0.00	+0.60 ± 0.24
0; 6	10	5, 8, 12, 15	Fleishman	22.6	20.6	27.7	28.3	48.9	7.9	43.2	+5.70 ± 0.88	+7.70 ± 1.11	+0.60 ± 0.63
0; 6	20	10, 16, 24, 30	Fleishman	42.2	41.1	55.7	55.0	21.0	4.4	74.6	+12.80 ± 1.17	+13.90 ± 1.16	-0.70 ± 0.50
0; 6	30	15, 24, 36, 45	Fleishman	57.9	57.4	75.4	75.3	9.5	1.7	88.8	+17.40 ± 1.26	+17.90 ± 1.27	-0.10 ± 0.39
0; 6	50	25, 40, 60, 75	Fleishman	81.8	81.7	95.0	94.8	1.6	1.1	97.3	+13.00 ± 1.08	+13.10 ± 1.09	-0.20 ± 0.14
0; 6	100	50, 80, 120, 150	Fleishman	98.8	98.9	100.0	100.0	0.0	0.1	99.9	+1.20 ± 0.34	+1.10 ± 0.33	+0.00 ± 0.00
0.5; 1	10	5, 8, 12, 15	Fleishman	21.3	19.6	20.9	22.9	76.0	7.1	16.9	+1.60 ± 0.44	+3.30 ± 0.92	+2.00 ± 0.68
0.5; 1	20	10, 16, 24, 30	Fleishman	40.1	39.3	42.2	42.9	62.8	7.3	29.9	+2.80 ± 0.69	+3.60 ± 0.88	+0.70 ± 0.73
0.5; 1	30	15, 24, 36, 45	Fleishman	55.5	55.9	58.2	58.3	49.5	4.9	45.6	+2.80 ± 0.72	+2.40 ± 0.77	+0.10 ± 0.56
0.5; 1	50	25, 40, 60, 75	Fleishman	83.1	82.7	86.8	85.9	32.9	3.5	63.6	+2.80 ± 0.72	+3.20 ± 0.73	-0.90 ± 0.50
0.5; 1	100	50, 80, 120, 150	Fleishman	99.1	99.1	99.1	99.1	8.5	1.8	89.7	+0.00 ± 0.14	+0.00 ± 0.14	+0.00 ± 0.00
1; 1.6	10	5, 8, 12, 15	Fleishman	20.0	22.1	21.2	23.1	50.3	9.3	40.4	+3.10 ± 0.65	+1.00 ± 0.91	+1.90 ± 0.59
1; 1.6	20	10, 16, 24, 30	Fleishman	39.0	39.7	44.4	45.3	15.6	5.8	78.6	+6.30 ± 1.04	+5.60 ± 1.08	+0.90 ± 0.41
1; 1.6	30	15, 24, 36, 45	Fleishman	59.9	61.3	67.3	67.5	4.4	3.6	92.0	+7.60 ± 1.03	+6.20 ± 1.00	+0.20 ± 0.14
1; 1.6	50	25, 40, 60, 75	Fleishman	82.7	83.5	88.9	88.9	0.0	0.4	99.6	+6.20 ± 0.90	+5.40 ± 0.88	+0.00 ± 0.00
1; 1.6	100	50, 80, 120, 150	Fleishman	99.3	99.3	99.7	99.7	0.0	0.0	100.0	+0.40 ± 0.20	+0.40 ± 0.20	+0.00 ± 0.00
2; 6.6	10	5, 8, 12, 15	Fleishman	23.4	30.0	37.0	37.9	10.0	11.1	78.9	+14.50 ± 1.26	+7.90 ± 1.18	+0.90 ± 0.50
2; 6.6	20	10, 16, 24, 30	Fleishman	44.3	50.2	70.4	70.5	0.0	1.3	98.7	+26.20 ± 1.42	+20.30 ± 1.37	+0.10 ± 0.10
2; 6.6	30	15, 24, 36, 45	Fleishman	60.3	65.4	87.2	87.2	0.0	0.0	100.0	+26.90 ± 1.42	+21.80 ± 1.33	+0.00 ± 0.00
2; 6.6	50	25, 40, 60, 75	Fleishman	82.4	86.4	99.1	99.1	0.0	0.0	100.0	+16.70 ± 1.18	+12.70 ± 1.05	+0.00 ± 0.00
2; 6.6	100	50, 80, 120, 150	Fleishman	98.8	99.4	100.0	100.0	0.0	0.0	100.0	+1.20 ± 0.34	+0.60 ± 0.24	+0.00 ± 0.00

balanced n, unequal SD

Means: (0.00, 0.00, 0.00, 0.50); SD: (1.000000000000000,1.414213562373095,2.000000000000000,2.236067977499790).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	10, 10, 10, 10	Normal	10.5	7.4	7.8	10.1	46.3	45.7	8.0	-0.40 ± 0.51	+2.70 ± 0.60	+2.30 ± 0.60
0; 0	20	20, 20, 20, 20	Normal	15.0	11.1	13.5	12.5	14.0	79.5	6.5	-2.50 ± 0.80	+1.40 ± 0.47	-1.00 ± 0.71
0; 0	30	30, 30, 30, 30	Normal	19.3	12.8	15.6	12.8	3.0	92.8	4.2	-6.50 ± 0.98	+0.00 ± 0.25	-2.80 ± 0.88
0; 0	50	50, 50, 50, 50	Normal	27.2	19.0	22.7	19.0	0.1	93.9	6.0	-8.20 ± 1.07	+0.00 ± 0.25	-3.70 ± 0.93
0; 0	100	100, 100, 100, 100	Normal	49.4	40.0	43.8	40.5	0.0	96.0	4.0	-8.90 ± 1.02	+0.50 ± 0.30	-3.30 ± 1.13
0; 6	10	10, 10, 10, 10	Fleishman	10.4	8.2	11.1	11.6	31.3	24.5	44.2	+1.20 ± 0.69	+3.40 ± 0.73	+0.50 ± 0.62
0; 6	20	20, 20, 20, 20	Fleishman	16.7	11.7	18.6	16.9	5.8	26.2	68.0	+0.20 ± 0.99	+5.20 ± 0.84	-1.70 ± 0.52
0; 6	30	30, 30, 30, 30	Fleishman	18.0	14.2	23.8	22.6	1.3	20.2	78.5	+4.60 ± 1.11	+8.40 ± 1.00	-1.20 ± 0.55
0; 6	50	50, 50, 50, 50	Fleishman	29.0	20.9	35.8	35.4	0.0	7.2	92.8	+6.40 ± 1.26	+14.50 ± 1.23	-0.40 ± 0.28
0; 6	100	100, 100, 100, 100	Fleishman	51.1	41.2	65.8	65.7	0.0	0.4	99.6	+14.60 ± 1.36	+24.50 ± 1.45	-0.10 ± 0.10
0.5; 1	10	10, 10, 10, 10	Fleishman	7.7	5.6	7.2	8.2	41.2	41.3	17.5	+0.50 ± 0.59	+2.60 ± 0.59	+1.00 ± 0.49
0.5; 1	20	20, 20, 20, 20	Fleishman	13.0	9.4	10.0	10.6	11.8	63.1	25.1	-2.40 ± 0.74	+1.20 ± 0.49	+0.60 ± 0.55
0.5; 1	30	30, 30, 30, 30	Fleishman	18.2	12.4	12.6	12.9	2.7	68.3	29.0	-5.30 ± 0.98	+0.50 ± 0.50	+0.30 ± 0.66
0.5; 1	50	50, 50, 50, 50	Fleishman	28.3	21.4	22.0	22.0	0.1	57.1	42.8	-6.30 ± 0.99	+0.60 ± 0.63	+0.00 ± 0.71
0.5; 1	100	100, 100, 100, 100	Fleishman	51.2	40.8	37.9	38.8	0.0	28.0	72.0	-12.40 ± 1.24	-2.00 ± 0.99	+0.90 ± 0.56
1; 1.6	10	10, 10, 10, 10	Fleishman	8.8	7.6	8.0	8.9	29.8	37.4	32.8	+0.10 ± 0.74	+1.30 ± 0.54	+0.90 ± 0.52
1; 1.6	20	20, 20, 20, 20	Fleishman	14.3	9.1	11.3	11.3	5.4	45.7	48.9	-3.00 ± 0.98	+2.20 ± 0.72	+0.00 ± 0.53
1; 1.6	30	30, 30, 30, 30	Fleishman	16.2	12.3	12.3	13.4	0.8	27.6	71.6	-2.80 ± 0.95	+1.10 ± 0.69	+1.10 ± 0.48
1; 1.6	50	50, 50, 50, 50	Fleishman	26.6	18.1	18.3	18.6	0.0	10.0	90.0	-8.00 ± 1.20	+0.50 ± 0.99	+0.30 ± 0.33
1; 1.6	100	100, 100, 100, 100	Fleishman	48.7	37.2	28.8	28.8	0.0	0.1	99.9	-19.90 ± 1.35	-8.40 ± 1.30	+0.00 ± 0.00
2; 6.6	10	10, 10, 10, 10	Fleishman	7.8	7.2	8.4	9.4	7.3	23.5	69.2	+1.60 ± 0.75	+2.20 ± 0.63	+1.00 ± 0.37
2; 6.6	20	20, 20, 20, 20	Fleishman	13.3	8.7	13.4	13.5	0.1	3.5	96.4	+0.20 ± 1.05	+4.80 ± 0.93	+0.10 ± 0.17
2; 6.6	30	30, 30, 30, 30	Fleishman	17.1	10.7	18.4	18.4	0.0	0.3	99.7	+1.30 ± 1.30	+7.70 ± 1.23	+0.00 ± 0.00
2; 6.6	50	50, 50, 50, 50	Fleishman	25.1	18.1	25.0	25.0	0.0	0.0	100.0	-0.10 ± 1.44	+6.90 ± 1.44	+0.00 ± 0.00
2; 6.6	100	100, 100, 100, 100	Fleishman	49.9	40.6	52.2	52.2	0.0	0.0	100.0	+2.30 ± 1.74	+11.60 ± 1.84	+0.00 ± 0.00

unbalanced n, larger n with larger SD

Means: (0.00, 0.00, 0.00, 0.50); SD: (1.000000000000000,1.414213562373095,2.000000000000000,2.236067977499790).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	5, 8, 12, 15	Normal	5.8	7.9	5.3	7.2	69.5	24.3	6.2	+1.40 ± 0.45	-0.70 ± 0.54	+1.90 ± 0.57
0; 0	20	10, 16, 24, 30	Normal	8.2	12.1	9.2	12.0	37.4	55.2	7.4	+3.80 ± 0.79	-0.10 ± 0.46	+2.80 ± 0.81
0; 0	30	15, 24, 36, 45	Normal	15.4	17.1	13.5	17.1	15.4	80.0	4.6	+1.70 ± 0.85	+0.00 ± 0.35	+3.60 ± 0.83
0; 0	50	25, 40, 60, 75	Normal	23.7	26.5	23.9	26.7	0.6	94.3	5.1	+3.00 ± 0.97	+0.20 ± 0.24	+2.80 ± 0.90
0; 0	100	50, 80, 120, 150	Normal	50.9	52.1	49.1	52.1	0.0	93.7	6.3	+1.20 ± 1.01	+0.00 ± 0.37	+3.00 ± 1.01
0; 6	10	5, 8, 12, 15	Fleishman	5.9	6.0	7.8	7.7	40.2	11.2	48.6	+1.80 ± 0.51	+1.70 ± 0.70	-0.10 ± 0.39
0; 6	20	10, 16, 24, 30	Fleishman	12.5	13.4	17.3	17.3	11.8	14.8	73.4	+4.80 ± 0.85	+3.90 ± 0.83	+0.00 ± 0.47
0; 6	30	15, 24, 36, 45	Fleishman	17.1	16.7	23.5	23.2	2.6	12.8	84.6	+6.10 ± 1.05	+6.50 ± 1.02	-0.30 ± 0.44
0; 6	50	25, 40, 60, 75	Fleishman	27.3	29.0	39.5	39.6	0.2	5.9	93.9	+12.30 ± 1.27	+10.60 ± 1.29	+0.10 ± 0.26
0; 6	100	50, 80, 120, 150	Fleishman	49.6	51.4	73.0	72.9	0.0	0.5	99.5	+23.30 ± 1.45	+21.50 ± 1.40	-0.10 ± 0.10
0.5; 1	10	5, 8, 12, 15	Fleishman	4.7	6.8	4.8	6.0	59.5	18.9	21.6	+1.30 ± 0.39	-0.80 ± 0.60	+1.20 ± 0.51
0.5; 1	20	10, 16, 24, 30	Fleishman	9.1	11.6	9.1	11.6	26.6	43.0	30.4	+2.50 ± 0.71	+0.00 ± 0.55	+2.50 ± 0.55
0.5; 1	30	15, 24, 36, 45	Fleishman	12.1	14.6	11.3	13.3	9.8	56.2	34.0	+1.20 ± 0.81	-1.30 ± 0.54	+2.00 ± 0.73
0.5; 1	50	25, 40, 60, 75	Fleishman	25.5	29.2	22.2	26.4	0.8	56.2	43.0	+0.90 ± 1.01	-2.80 ± 0.74	+4.20 ± 0.79
0.5; 1	100	50, 80, 120, 150	Fleishman	47.1	49.4	37.7	39.4	0.0	27.5	72.5	-7.70 ± 1.11	-10.00 ± 1.10	+1.70 ± 0.54
1; 1.6	10	5, 8, 12, 15	Fleishman	4.9	7.9	5.4	7.5	38.7	21.6	39.7	+2.60 ± 0.64	-0.40 ± 0.60	+2.10 ± 0.57
1; 1.6	20	10, 16, 24, 30	Fleishman	9.5	13.2	8.7	11.9	9.7	35.7	54.6	+2.40 ± 0.77	-1.30 ± 0.62	+3.20 ± 0.61
1; 1.6	30	15, 24, 36, 45	Fleishman	12.2	14.4	8.9	10.6	1.6	23.1	75.3	-1.60 ± 0.75	-3.80 ± 0.83	+1.70 ± 0.46
1; 1.6	50	25, 40, 60, 75	Fleishman	22.7	27.2	17.2	18.1	0.0	6.6	93.4	-4.60 ± 0.95	-9.10 ± 1.11	+0.90 ± 0.33
1; 1.6	100	50, 80, 120, 150	Fleishman	47.7	52.3	32.8	32.8	0.0	0.1	99.9	-14.90 ± 1.35	-19.50 ± 1.45	+0.00 ± 0.00
2; 6.6	10	5, 8, 12, 15	Fleishman	4.2	7.9	5.7	7.9	6.3	15.4	78.3	+3.70 ± 0.70	+0.00 ± 0.75	+2.20 ± 0.49
2; 6.6	20	10, 16, 24, 30	Fleishman	8.3	14.2	11.7	12.0	0.1	2.3	97.6	+3.70 ± 0.83	-2.20 ± 1.04	+0.30 ± 0.17
2; 6.6	30	15, 24, 36, 45	Fleishman	12.4	18.7	15.1	15.1	0.0	0.0	100.0	+2.70 ± 0.96	-3.60 ± 1.19	+0.00 ± 0.00
2; 6.6	50	25, 40, 60, 75	Fleishman	24.2	29.4	26.5	26.5	0.0	0.0	100.0	+2.30 ± 1.32	-2.90 ± 1.52	+0.00 ± 0.00
2; 6.6	100	50, 80, 120, 150	Fleishman	49.7	56.1	51.6	51.6	0.0	0.0	100.0	+1.90 ± 1.56	-4.50 ± 1.79	+0.00 ± 0.00

unbalanced n, larger n with smaller SD

Means: (0.00, 0.00, 0.00, 0.50); SD: (2.236067977499790,2.000000000000000,1.414213562373095,1.000000000000000).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	5, 8, 12, 15	Normal	20.9	12.5	16.2	17.8	43.4	50.0	6.6	-3.10 ± 0.84	+5.30 ± 0.79	+1.60 ± 0.80
0; 0	20	10, 16, 24, 30	Normal	25.6	20.5	23.0	21.7	12.3	81.1	6.6	-3.90 ± 0.94	+1.20 ± 0.40	-1.30 ± 0.77
0; 0	30	15, 24, 36, 45	Normal	34.8	34.5	34.1	35.4	2.8	90.5	6.7	+0.60 ± 1.16	+0.90 ± 0.41	+1.30 ± 1.00
0; 0	50	25, 40, 60, 75	Normal	51.7	57.8	53.7	57.7	0.2	95.4	4.4	+6.00 ± 1.18	-0.10 ± 0.17	+4.00 ± 1.03
0; 0	100	50, 80, 120, 150	Normal	82.6	88.3	85.3	88.3	0.0	94.7	5.3	+5.70 ± 0.81	+0.00 ± 0.00	+3.00 ± 0.73
0; 6	10	5, 8, 12, 15	Fleishman	16.7	10.6	18.5	18.1	27.7	34.0	38.3	+1.40 ± 1.02	+7.50 ± 0.90	-0.40 ± 0.71
0; 6	20	10, 16, 24, 30	Fleishman	26.7	24.2	34.9	33.5	5.7	28.7	65.6	+6.80 ± 1.32	+9.30 ± 0.98	-1.40 ± 0.62
0; 6	30	15, 24, 36, 45	Fleishman	37.0	37.6	52.0	50.6	1.4	19.6	79.0	+13.60 ± 1.38	+13.00 ± 1.18	-1.40 ± 0.53
0; 6	50	25, 40, 60, 75	Fleishman	53.7	61.0	75.8	75.0	0.0	7.2	92.8	+21.30 ± 1.49	+14.00 ± 1.22	-0.80 ± 0.32
0; 6	100	50, 80, 120, 150	Fleishman	83.6	88.4	98.2	98.2	0.0	0.0	100.0	+14.60 ± 1.13	+9.80 ± 0.94	+0.00 ± 0.00
0.5; 1	10	5, 8, 12, 15	Fleishman	19.8	15.7	19.3	20.0	36.2	50.2	13.6	+0.20 ± 0.83	+4.30 ± 0.80	+0.70 ± 0.73
0.5; 1	20	10, 16, 24, 30	Fleishman	28.0	26.5	32.1	30.6	9.7	64.2	26.1	+2.60 ± 1.07	+4.10 ± 0.72	-1.50 ± 0.83
0.5; 1	30	15, 24, 36, 45	Fleishman	31.2	33.5	42.1	37.6	1.9	70.4	27.7	+6.40 ± 1.22	+4.10 ± 0.66	-4.50 ± 0.92
0.5; 1	50	25, 40, 60, 75	Fleishman	50.3	57.5	67.4	64.4	0.2	57.2	42.6	+14.10 ± 1.32	+6.90 ± 0.83	-3.00 ± 0.73
0.5; 1	100	50, 80, 120, 150	Fleishman	84.1	89.3	95.0	93.9	0.0	29.7	70.3	+9.80 ± 0.99	+4.60 ± 0.68	-1.10 ± 0.33
1; 1.6	10	5, 8, 12, 15	Fleishman	19.7	18.2	21.9	22.5	21.8	49.4	28.8	+2.80 ± 0.98	+4.30 ± 0.80	+0.60 ± 0.75
1; 1.6	20	10, 16, 24, 30	Fleishman	27.3	30.9	40.5	37.8	4.2	45.4	50.4	+10.50 ± 1.20	+6.90 ± 0.94	-2.70 ± 0.71
1; 1.6	30	15, 24, 36, 45	Fleishman	35.5	42.9	57.7	55.8	0.6	28.1	71.3	+20.30 ± 1.41	+12.90 ± 1.16	-1.90 ± 0.61
1; 1.6	50	25, 40, 60, 75	Fleishman	53.3	62.7	83.6	82.4	0.0	6.6	93.4	+29.10 ± 1.50	+19.70 ± 1.28	-1.20 ± 0.34
1; 1.6	100	50, 80, 120, 150	Fleishman	82.5	90.4	99.3	99.3	0.0	0.1	99.9	+16.80 ± 1.18	+8.90 ± 0.90	+0.00 ± 0.00
2; 6.6	10	5, 8, 12, 15	Fleishman	21.8	27.3	39.4	39.6	6.0	25.2	68.8	+17.80 ± 1.34	+12.30 ± 1.12	+0.20 ± 0.47
2; 6.6	20	10, 16, 24, 30	Fleishman	32.5	39.8	68.3	68.6	0.0	3.3	96.7	+36.10 ± 1.57	+28.80 ± 1.47	+0.30 ± 0.17
2; 6.6	30	15, 24, 36, 45	Fleishman	38.8	49.2	86.1	86.1	0.0	0.0	100.0	+47.30 ± 1.59	+36.90 ± 1.53	+0.00 ± 0.00
2; 6.6	50	25, 40, 60, 75	Fleishman	55.0	65.8	98.3	98.3	0.0	0.0	100.0	+43.30 ± 1.57	+32.50 ± 1.48	+0.00 ± 0.00
2; 6.6	100	50, 80, 120, 150	Fleishman	81.7	90.8	100.0	100.0	0.0	0.0	100.0	+18.30 ± 1.22	+9.20 ± 0.91	+0.00 ± 0.00

onepoint_1

balanced n, equal SD

Means: (0.00, 0.00, 0.00, 1.00); SD: (1,1,1,1).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	10, 10, 10, 10	Normal	55.3	50.9	49.9	55.0	89.5	5.9	4.6	-0.30 ± 0.39	+4.10 ± 1.02	+5.10 ± 0.90
0; 0	20	20, 20, 20, 20	Normal	91.9	89.0	89.9	91.9	89.6	5.0	5.4	+0.00 ± 0.25	+2.90 ± 0.62	+2.00 ± 0.53
0; 0	30	30, 30, 30, 30	Normal	98.0	97.5	97.4	98.0	91.4	4.6	4.0	+0.00 ± 0.00	+0.50 ± 0.26	+0.60 ± 0.32
0; 0	50	50, 50, 50, 50	Normal	99.9	100.0	99.8	99.9	91.3	4.3	4.4	+0.00 ± 0.00	-0.10 ± 0.10	+0.10 ± 0.10
0; 0	100	100, 100, 100, 100	Normal	100.0	100.0	100.0	100.0	90.9	5.3	3.8	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
0; 6	10	10, 10, 10, 10	Fleishman	61.4	61.6	70.5	71.2	49.9	7.0	43.1	+9.80 ± 1.03	+9.60 ± 1.20	+0.70 ± 0.77
0; 6	20	20, 20, 20, 20	Fleishman	89.3	88.6	95.8	95.1	22.2	5.6	72.2	+5.80 ± 0.77	+6.50 ± 0.82	-0.70 ± 0.30
0; 6	30	30, 30, 30, 30	Fleishman	97.0	96.4	99.7	99.5	10.6	2.4	87.0	+2.50 ± 0.49	+3.10 ± 0.55	-0.20 ± 0.14
0; 6	50	50, 50, 50, 50	Fleishman	99.9	99.9	100.0	100.0	0.8	0.9	98.3	+0.10 ± 0.10	+0.10 ± 0.10	+0.00 ± 0.00
0; 6	100	100, 100, 100, 100	Fleishman	100.0	100.0	100.0	100.0	0.1	0.0	99.9	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
0.5; 1	10	10, 10, 10, 10	Fleishman	58.7	55.8	56.2	60.3	75.9	7.0	17.1	+1.60 ± 0.58	+4.50 ± 1.07	+4.10 ± 0.88
0.5; 1	20	20, 20, 20, 20	Fleishman	90.9	91.0	91.7	92.1	66.6	6.2	27.2	+1.20 ± 0.40	+1.10 ± 0.66	+0.40 ± 0.62
0.5; 1	30	30, 30, 30, 30	Fleishman	98.7	98.9	98.7	98.8	56.4	4.2	39.4	+0.10 ± 0.17	-0.10 ± 0.17	+0.10 ± 0.10
0.5; 1	50	50, 50, 50, 50	Fleishman	100.0	100.0	100.0	100.0	32.7	4.4	62.9	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
0.5; 1	100	100, 100, 100, 100	Fleishman	100.0	100.0	100.0	100.0	9.3	2.5	88.2	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
1; 1.6	10	10, 10, 10, 10	Fleishman	60.1	61.9	61.0	64.1	49.9	10.2	39.9	+4.00 ± 0.89	+2.20 ± 0.95	+3.10 ± 0.71
1; 1.6	20	20, 20, 20, 20	Fleishman	90.9	93.3	95.5	95.5	15.1	7.1	77.8	+4.60 ± 0.71	+2.20 ± 0.58	+0.00 ± 0.20
1; 1.6	30	30, 30, 30, 30	Fleishman	97.9	99.1	99.5	99.5	3.3	3.7	93.0	+1.60 ± 0.40	+0.40 ± 0.20	+0.00 ± 0.00
1; 1.6	50	50, 50, 50, 50	Fleishman	100.0	100.0	100.0	100.0	0.2	1.1	98.7	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
1; 1.6	100	100, 100, 100, 100	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
2; 6.6	10	10, 10, 10, 10	Fleishman	58.1	69.2	77.0	78.1	8.1	10.6	81.3	+20.00 ± 1.33	+8.90 ± 1.24	+1.10 ± 0.43
2; 6.6	20	20, 20, 20, 20	Fleishman	90.6	95.8	99.6	99.6	0.2	1.6	98.2	+9.00 ± 0.91	+3.80 ± 0.60	+0.00 ± 0.00
2; 6.6	30	30, 30, 30, 30	Fleishman	98.3	99.8	100.0	100.0	0.0	0.0	100.0	+1.70 ± 0.41	+0.20 ± 0.14	+0.00 ± 0.00
2; 6.6	50	50, 50, 50, 50	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
2; 6.6	100	100, 100, 100, 100	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00

unbalanced n, equal SD

Means: (0.00, 0.00, 0.00, 1.00); SD: (1,1,1,1).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	5, 8, 12, 15	Normal	66.8	56.0	60.7	66.8	86.9	7.9	5.2	+0.00 ± 0.42	+10.80 ± 1.07	+6.10 ± 0.90
0; 0	20	10, 16, 24, 30	Normal	94.4	92.9	93.1	94.0	90.0	5.0	5.0	-0.40 ± 0.24	+1.10 ± 0.41	+0.90 ± 0.41
0; 0	30	15, 24, 36, 45	Normal	99.7	99.6	99.5	99.6	91.0	4.9	4.1	-0.10 ± 0.10	+0.00 ± 0.14	+0.10 ± 0.10
0; 0	50	25, 40, 60, 75	Normal	100.0	100.0	100.0	100.0	89.2	6.0	4.8	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
0; 0	100	50, 80, 120, 150	Normal	100.0	100.0	100.0	100.0	90.1	4.2	5.7	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
0; 6	10	5, 8, 12, 15	Fleishman	73.9	68.3	82.7	82.1	50.8	8.0	41.2	+8.20 ± 0.92	+13.80 ± 1.14	-0.60 ± 0.58
0; 6	20	10, 16, 24, 30	Fleishman	94.9	95.9	98.9	98.2	25.3	4.0	70.7	+3.30 ± 0.57	+2.30 ± 0.51	-0.70 ± 0.26
0; 6	30	15, 24, 36, 45	Fleishman	99.3	99.2	99.9	99.9	10.4	2.2	87.4	+0.60 ± 0.24	+0.70 ± 0.26	+0.00 ± 0.00
0; 6	50	25, 40, 60, 75	Fleishman	100.0	100.0	100.0	100.0	1.5	0.7	97.8	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
0; 6	100	50, 80, 120, 150	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
0.5; 1	10	5, 8, 12, 15	Fleishman	68.5	63.7	67.9	70.9	76.5	5.9	17.6	+2.40 ± 0.52	+7.20 ± 0.98	+3.00 ± 0.76
0.5; 1	20	10, 16, 24, 30	Fleishman	96.2	96.1	97.4	97.4	61.2	7.2	31.6	+1.20 ± 0.34	+1.30 ± 0.41	+0.00 ± 0.32
0.5; 1	30	15, 24, 36, 45	Fleishman	99.6	99.6	99.7	99.6	52.2	5.7	42.1	+0.00 ± 0.00	+0.00 ± 0.00	-0.10 ± 0.17
0.5; 1	50	25, 40, 60, 75	Fleishman	100.0	100.0	100.0	100.0	31.6	3.8	64.6	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
0.5; 1	100	50, 80, 120, 150	Fleishman	100.0	100.0	100.0	100.0	8.0	1.5	90.5	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
1; 1.6	10	5, 8, 12, 15	Fleishman	70.0	68.0	73.7	74.9	49.7	10.7	39.6	+4.90 ± 0.77	+6.90 ± 1.02	+1.20 ± 0.62
1; 1.6	20	10, 16, 24, 30	Fleishman	94.8	96.1	97.3	97.3	17.6	6.4	76.0	+2.50 ± 0.53	+1.20 ± 0.34	+0.00 ± 0.14
1; 1.6	30	15, 24, 36, 45	Fleishman	99.7	99.8	99.9	99.9	4.7	3.2	92.1	+0.20 ± 0.14	+0.10 ± 0.10	+0.00 ± 0.00
1; 1.6	50	25, 40, 60, 75	Fleishman	100.0	100.0	100.0	100.0	0.1	0.9	99.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
1; 1.6	100	50, 80, 120, 150	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
2; 6.6	10	5, 8, 12, 15	Fleishman	72.7	77.9	88.0	88.1	9.2	10.5	80.3	+15.40 ± 1.18	+10.20 ± 1.03	+0.10 ± 0.33
2; 6.6	20	10, 16, 24, 30	Fleishman	95.7	96.9	99.8	99.8	0.1	1.0	98.9	+4.10 ± 0.63	+2.90 ± 0.53	+0.00 ± 0.00
2; 6.6	30	15, 24, 36, 45	Fleishman	99.4	100.0	100.0	100.0	0.0	0.0	100.0	+0.60 ± 0.24	+0.00 ± 0.00	+0.00 ± 0.00
2; 6.6	50	25, 40, 60, 75	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
2; 6.6	100	50, 80, 120, 150	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00

balanced n, unequal SD

Means: (0.00, 0.00, 0.00, 1.00); SD: (1.000000000000000,1.414213562373095,2.000000000000000,2.236067977499790).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	10, 10, 10, 10	Normal	22.7	16.3	18.8	21.4	48.7	42.7	8.6	-1.30 ± 0.71	+5.10 ± 0.84	+2.60 ± 0.81
0; 0	20	20, 20, 20, 20	Normal	39.4	29.3	32.9	31.8	16.1	75.0	8.9	-7.60 ± 1.06	+2.50 ± 0.55	-1.10 ± 0.91
0; 0	30	30, 30, 30, 30	Normal	57.0	44.9	49.1	45.3	4.2	91.3	4.5	-11.70 ± 1.17	+0.40 ± 0.35	-3.80 ± 0.96
0; 0	50	50, 50, 50, 50	Normal	79.8	69.5	71.3	69.5	0.0	96.1	3.9	-10.30 ± 1.05	+0.00 ± 0.20	-1.80 ± 0.95
0; 0	100	100, 100, 100, 100	Normal	97.1	95.1	95.4	95.2	0.0	96.4	3.6	-1.90 ± 0.48	+0.10 ± 0.10	-0.20 ± 0.42
0; 6	10	10, 10, 10, 10	Fleishman	25.8	18.3	28.1	29.0	29.7	25.3	45.0	+3.20 ± 1.13	+10.70 ± 1.07	+0.90 ± 0.67
0; 6	20	20, 20, 20, 20	Fleishman	44.3	34.4	51.6	48.6	6.6	26.8	66.6	+4.30 ± 1.35	+14.20 ± 1.19	-3.00 ± 0.66
0; 6	30	30, 30, 30, 30	Fleishman	59.5	50.0	71.4	68.5	0.7	20.5	78.8	+9.00 ± 1.33	+18.50 ± 1.28	-2.90 ± 0.62
0; 6	50	50, 50, 50, 50	Fleishman	79.1	70.6	90.5	89.4	0.1	7.7	92.2	+10.30 ± 1.10	+18.80 ± 1.25	-1.10 ± 0.33
0; 6	100	100, 100, 100, 100	Fleishman	97.9	95.1	99.7	99.7	0.0	0.3	99.7	+1.80 ± 0.42	+4.60 ± 0.66	+0.00 ± 0.00
0.5; 1	10	10, 10, 10, 10	Fleishman	21.8	15.0	17.1	19.7	43.6	39.0	17.4	-2.10 ± 0.70	+4.70 ± 0.75	+2.60 ± 0.63
0.5; 1	20	20, 20, 20, 20	Fleishman	37.2	27.8	31.3	30.8	12.2	63.6	24.2	-6.40 ± 1.10	+3.00 ± 0.61	-0.50 ± 0.84
0.5; 1	30	30, 30, 30, 30	Fleishman	58.5	46.7	47.5	49.0	2.3	65.4	32.3	-9.50 ± 1.19	+2.30 ± 0.72	+1.50 ± 0.97
0.5; 1	50	50, 50, 50, 50	Fleishman	80.1	71.1	70.8	71.6	0.0	56.2	43.8	-8.50 ± 1.08	+0.50 ± 0.78	+0.80 ± 0.69
0.5; 1	100	100, 100, 100, 100	Fleishman	98.3	96.1	95.5	95.8	0.0	30.0	70.0	-2.50 ± 0.51	-0.30 ± 0.41	+0.30 ± 0.30
1; 1.6	10	10, 10, 10, 10	Fleishman	23.2	17.0	19.2	20.1	26.4	40.0	33.6	-3.10 ± 0.97	+3.10 ± 0.75	+0.90 ± 0.77
1; 1.6	20	20, 20, 20, 20	Fleishman	39.7	28.1	29.8	31.7	6.2	44.3	49.5	-8.00 ± 1.18	+3.60 ± 0.82	+1.90 ± 0.75
1; 1.6	30	30, 30, 30, 30	Fleishman	55.1	43.2	41.8	44.4	0.1	30.6	69.3	-10.70 ± 1.24	+1.20 ± 1.00	+2.60 ± 0.64
1; 1.6	50	50, 50, 50, 50	Fleishman	81.0	73.2	68.8	69.4	0.0	7.7	92.3	-11.60 ± 1.13	-3.80 ± 1.12	+0.60 ± 0.24
1; 1.6	100	100, 100, 100, 100	Fleishman	98.1	96.9	93.2	93.2	0.0	0.1	99.9	-4.90 ± 0.71	-3.70 ± 0.68	+0.00 ± 0.00
2; 6.6	10	10, 10, 10, 10	Fleishman	19.0	15.0	19.0	20.4	5.4	22.6	72.0	+1.40 ± 1.15	+5.40 ± 0.97	+1.40 ± 0.56
2; 6.6	20	20, 20, 20, 20	Fleishman	39.6	30.7	41.5	41.4	0.1	3.8	96.1	+1.80 ± 1.36	+10.70 ± 1.43	-0.10 ± 0.22
2; 6.6	30	30, 30, 30, 30	Fleishman	56.3	47.8	59.1	59.1	0.0	0.3	99.7	+2.80 ± 1.34	+11.30 ± 1.42	+0.00 ± 0.00
2; 6.6	50	50, 50, 50, 50	Fleishman	81.6	76.3	82.5	82.5	0.0	0.1	99.9	+0.90 ± 1.24	+6.20 ± 1.29	+0.00 ± 0.00
2; 6.6	100	100, 100, 100, 100	Fleishman	99.0	98.4	99.0	99.0	0.0	0.0	100.0	+0.00 ± 0.40	+0.60 ± 0.47	+0.00 ± 0.00

unbalanced n, larger n with larger SD

Means: (0.00, 0.00, 0.00, 1.00); SD: (1.000000000000000,1.414213562373095,2.000000000000000,2.236067977499790).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	5, 8, 12, 15	Normal	18.0	18.9	15.8	19.2	69.4	23.1	7.5	+1.20 ± 0.65	+0.30 ± 0.85	+3.40 ± 0.77
0; 0	20	10, 16, 24, 30	Normal	38.0	37.5	35.9	38.9	38.0	55.6	6.4	+0.90 ± 0.74	+1.40 ± 0.63	+3.00 ± 0.99
0; 0	30	15, 24, 36, 45	Normal	56.3	57.5	55.1	58.0	15.9	79.1	5.0	+1.70 ± 0.95	+0.50 ± 0.44	+2.90 ± 0.97
0; 0	50	25, 40, 60, 75	Normal	82.6	84.6	79.2	84.7	1.4	94.4	4.2	+2.10 ± 0.78	+0.10 ± 0.17	+5.50 ± 0.92
0; 0	100	50, 80, 120, 150	Normal	99.5	99.3	99.1	99.3	0.0	95.6	4.4	-0.20 ± 0.14	+0.00 ± 0.00	+0.20 ± 0.14
0; 6	10	5, 8, 12, 15	Fleishman	21.1	21.0	28.9	28.9	41.2	12.8	46.0	+7.80 ± 0.93	+7.90 ± 1.09	+0.00 ± 0.69
0; 6	20	10, 16, 24, 30	Fleishman	39.7	40.4	57.2	56.4	11.6	16.2	72.2	+16.70 ± 1.29	+16.00 ± 1.27	-0.80 ± 0.51
0; 6	30	15, 24, 36, 45	Fleishman	61.8	62.8	79.6	78.5	2.2	15.3	82.5	+16.70 ± 1.28	+15.70 ± 1.23	-1.10 ± 0.46
0; 6	50	25, 40, 60, 75	Fleishman	82.8	86.0	95.9	95.7	0.1	6.0	93.9	+12.90 ± 1.07	+9.70 ± 0.95	-0.20 ± 0.24
0; 6	100	50, 80, 120, 150	Fleishman	98.8	98.5	99.9	99.9	0.0	0.1	99.9	+1.10 ± 0.33	+1.40 ± 0.37	+0.00 ± 0.00
0.5; 1	10	5, 8, 12, 15	Fleishman	18.8	18.9	18.5	20.3	58.4	21.1	20.5	+1.50 ± 0.68	+1.40 ± 0.89	+1.80 ± 0.72
0.5; 1	20	10, 16, 24, 30	Fleishman	39.2	40.3	36.8	41.4	28.3	42.9	28.8	+2.20 ± 0.97	+1.10 ± 0.73	+4.60 ± 0.87
0.5; 1	30	15, 24, 36, 45	Fleishman	56.1	58.7	52.1	57.0	7.7	60.0	32.3	+0.90 ± 1.05	-1.70 ± 0.71	+4.90 ± 0.92
0.5; 1	50	25, 40, 60, 75	Fleishman	83.6	85.2	79.6	82.6	0.6	52.8	46.6	-1.00 ± 0.84	-2.60 ± 0.66	+3.00 ± 0.63
0.5; 1	100	50, 80, 120, 150	Fleishman	99.4	99.4	98.6	98.7	0.0	28.8	71.2	-0.70 ± 0.33	-0.70 ± 0.33	+0.10 ± 0.10
1; 1.6	10	5, 8, 12, 15	Fleishman	16.6	18.6	15.2	19.1	39.3	22.6	38.1	+2.50 ± 0.83	+0.50 ± 0.94	+3.90 ± 0.67
1; 1.6	20	10, 16, 24, 30	Fleishman	37.2	39.8	31.1	36.9	8.0	31.9	60.1	-0.30 ± 1.15	-2.90 ± 0.93	+5.80 ± 0.80
1; 1.6	30	15, 24, 36, 45	Fleishman	56.3	60.7	50.9	55.0	1.2	24.6	74.2	-1.30 ± 1.07	-5.70 ± 1.07	+4.10 ± 0.67
1; 1.6	50	25, 40, 60, 75	Fleishman	81.8	84.8	74.5	75.6	0.0	6.8	93.2	-6.20 ± 0.97	-9.20 ± 1.10	+1.10 ± 0.33
1; 1.6	100	50, 80, 120, 150	Fleishman	99.0	99.4	97.4	97.4	0.0	0.0	100.0	-1.60 ± 0.40	-2.00 ± 0.46	+0.00 ± 0.00
2; 6.6	10	5, 8, 12, 15	Fleishman	17.8	22.0	23.1	25.6	6.5	15.3	78.2	+7.80 ± 1.07	+3.60 ± 1.12	+2.50 ± 0.59
2; 6.6	20	10, 16, 24, 30	Fleishman	38.0	45.9	49.9	50.3	0.0	2.3	97.7	+12.30 ± 1.27	+4.40 ± 1.51	+0.40 ± 0.20
2; 6.6	30	15, 24, 36, 45	Fleishman	57.4	64.4	67.7	67.7	0.0	0.0	100.0	+10.30 ± 1.39	+3.30 ± 1.54	+0.00 ± 0.00
2; 6.6	50	25, 40, 60, 75	Fleishman	83.0	89.2	90.9	90.9	0.0	0.0	100.0	+7.90 ± 1.00	+1.70 ± 0.98	+0.00 ± 0.00
2; 6.6	100	50, 80, 120, 150	Fleishman	99.3	99.8	99.9	99.9	0.0	0.0	100.0	+0.60 ± 0.24	+0.10 ± 0.10	+0.00 ± 0.00

unbalanced n, larger n with smaller SD

Means: (0.00, 0.00, 0.00, 1.00); SD: (2.236067977499790,2.000000000000000,1.414213562373095,1.000000000000000).
Simulation inputs				Final-test rejection (%)				Gate routing (%)			Gate minus fixed (pp ± MCSE)
Skew; excess kurtosis	n	Group sizes A-D	Input	F	W	KW	L+SW	F	W	KW	vs F	vs W	vs KW
0; 0	10	5, 8, 12, 15	Normal	40.8	35.5	39.5	39.8	41.2	52.0	6.8	-1.00 ± 0.86	+4.30 ± 0.76	+0.30 ± 0.85
0; 0	20	10, 16, 24, 30	Normal	71.1	75.1	75.1	75.5	13.4	79.8	6.8	+4.40 ± 1.00	+0.40 ± 0.40	+0.40 ± 0.82
0; 0	30	15, 24, 36, 45	Normal	85.7	92.0	89.1	91.7	3.2	90.5	6.3	+6.00 ± 0.82	-0.30 ± 0.17	+2.60 ± 0.67
0; 0	50	25, 40, 60, 75	Normal	99.4	99.7	99.5	99.7	0.1	95.5	4.4	+0.30 ± 0.22	+0.00 ± 0.00	+0.20 ± 0.20
0; 0	100	50, 80, 120, 150	Normal	100.0	100.0	100.0	100.0	0.0	95.6	4.4	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
0; 6	10	5, 8, 12, 15	Fleishman	44.1	41.8	56.4	52.5	27.8	37.3	34.9	+8.40 ± 1.28	+10.70 ± 1.07	-3.90 ± 0.87
0; 6	20	10, 16, 24, 30	Fleishman	71.5	79.3	89.3	87.9	5.6	29.7	64.7	+16.40 ± 1.22	+8.60 ± 0.93	-1.40 ± 0.42
0; 6	30	15, 24, 36, 45	Fleishman	90.4	93.9	98.9	98.7	1.4	21.1	77.5	+8.30 ± 0.88	+4.80 ± 0.68	-0.20 ± 0.20
0; 6	50	25, 40, 60, 75	Fleishman	98.4	99.3	100.0	100.0	0.1	7.4	92.5	+1.60 ± 0.40	+0.70 ± 0.26	+0.00 ± 0.00
0; 6	100	50, 80, 120, 150	Fleishman	100.0	100.0	100.0	100.0	0.0	0.1	99.9	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
0.5; 1	10	5, 8, 12, 15	Fleishman	46.3	43.3	51.0	49.4	37.2	47.7	15.1	+3.10 ± 1.12	+6.10 ± 0.86	-1.60 ± 0.87
0.5; 1	20	10, 16, 24, 30	Fleishman	70.7	76.3	80.7	78.8	12.5	62.2	25.3	+8.10 ± 1.01	+2.50 ± 0.59	-1.90 ± 0.75
0.5; 1	30	15, 24, 36, 45	Fleishman	85.7	92.3	95.6	94.6	2.8	67.5	29.7	+8.90 ± 0.92	+2.30 ± 0.49	-1.00 ± 0.49
0.5; 1	50	25, 40, 60, 75	Fleishman	98.7	99.6	99.9	99.8	0.4	53.1	46.5	+1.10 ± 0.33	+0.20 ± 0.14	-0.10 ± 0.10
0.5; 1	100	50, 80, 120, 150	Fleishman	100.0	100.0	100.0	100.0	0.0	29.4	70.6	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
1; 1.6	10	5, 8, 12, 15	Fleishman	42.2	44.0	52.6	51.7	24.5	47.5	28.0	+9.50 ± 1.19	+7.70 ± 0.88	-0.90 ± 0.89
1; 1.6	20	10, 16, 24, 30	Fleishman	69.7	80.3	88.2	85.9	4.2	43.5	52.3	+16.20 ± 1.26	+5.60 ± 0.82	-2.30 ± 0.60
1; 1.6	30	15, 24, 36, 45	Fleishman	88.3	93.9	97.3	96.4	0.3	26.1	73.6	+8.10 ± 0.90	+2.50 ± 0.51	-0.90 ± 0.33
1; 1.6	50	25, 40, 60, 75	Fleishman	97.5	99.3	100.0	99.9	0.0	5.5	94.5	+2.40 ± 0.48	+0.60 ± 0.24	-0.10 ± 0.10
1; 1.6	100	50, 80, 120, 150	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00
2; 6.6	10	5, 8, 12, 15	Fleishman	49.7	60.7	72.3	71.2	4.6	27.8	67.6	+21.50 ± 1.40	+10.50 ± 1.07	-1.10 ± 0.56
2; 6.6	20	10, 16, 24, 30	Fleishman	67.2	81.2	95.7	95.5	0.0	3.9	96.1	+28.30 ± 1.43	+14.30 ± 1.11	-0.20 ± 0.14
2; 6.6	30	15, 24, 36, 45	Fleishman	86.9	93.8	99.6	99.6	0.0	0.1	99.9	+12.70 ± 1.05	+5.80 ± 0.74	+0.00 ± 0.00
2; 6.6	50	25, 40, 60, 75	Fleishman	97.2	99.3	100.0	100.0	0.0	0.0	100.0	+2.80 ± 0.52	+0.70 ± 0.26	+0.00 ± 0.00
2; 6.6	100	50, 80, 120, 150	Fleishman	100.0	100.0	100.0	100.0	0.0	0.0	100.0	+0.00 ± 0.00	+0.00 ± 0.00	+0.00 ± 0.00