Table 1:

Power and type I error for the 2-sided Wilcoxon Mann-Whitney rank-sum test, α = 0.05

Sample Size	Method	Effect Size
		p=0.5	p=0.7	p=0.75	p=0.8	p=0.85	p=0.9
n=6, m=6	Noether	3	22	32	44	56	67
	O’Brien-Castelloe	n/a	26	39	54	69	82
	Rosner-Glynn	5	19	27	38	53	74
	Empirical - Normal	4	18	28	40	56	75
	Empirical - Exp	4	18	28	40	56	74
	Empirical - Laplace	4	18	28	39	55	72
	Shieh - Normal	5	18	27	38	53	74
	Shieh - Shifted Exp	5	19	28	39	53	72
	Shieh - Laplace	5	19	27	38	53	72
n=15, m=15	Noether	3	48	66	81	91	97
	O’Brien-Castelloe	n/a	52	72	87	96	99
	Rosner-Glynn	5	46	67	87	98	>99
	Empirical - Normal	5	47	67	85	96	>99
	Empirical - Exp	5	46	68	86	96	>99
	Empirical - Laplace	5	46	68	85	95	99
	Shieh - Normal	5	46	67	86	98	>99
	Shieh - Shifted Exp	5	46	67	85	97	>99
	Shieh - Laplace	5	46	67	86	97	>99
n=6, m=12	Rosner-Glynn	5	25	37	53	73	92
	Empirical - Exp	4	24	37	54	73	90
	Shieh - Shifted Exp	5	23	36	54	74	93
n=12, m=6	Rosner-Glynn	5	25	37	53	73	92
	Empirical - Exp	4	26	39	55	72	86
	Shieh - Shifted Exp	5	27	39	53	69	86

Above, n and m are the two sample sizes. p is a measure of effect size, i.e., the probability that the first random variable is less than the second variable, P(Y > X). Statistical power (%) is displayed rounded to the nearest whole percentage. Effect size H₀ : p = 0.5 presents type I error. Exp=Exponential