Critical Values for Mann-Whitney U Test

USE THIS TABLE TO FIND OUT IF YOUR VALUE FOR (Mann-Whitney) U IS SIGNIFICANT.

The value you obtained must be less than or equal to the value given in the table for your sample sizes (N) in order to be significant.
Level of significance: 5% (P = 0.05 two-tailed, and p=0.025 one-tailed test)

		Size of the largest sample (NB)
		5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
Size of the smallest sample (NA)	3	0	1	1	2	2	3	3	4	4	5	5	6	6	7	7	8	8	9	9	10	10	11	11	12	13	13
	4	1	2	3	4	4	5	6	7	8	9	10	11	11	12	13	14	15	16	17	17	18	19	20	21	22	23
	5	2	3	5	6	7	8	9	11	12	13	14	15	17	18	19	20	22	23	24	25	27	28	29	30	32	33
	6		5	6	8	10	11	13	14	16	17	19	21	22	24	25	27	29	30	32	33	35	37	38	40	42	43
	7			8	10	12	14	16	18	20	22	24	26	28	30	32	34	36	38	40	42	44	46	48	50	52	54
	8				13	15	17	19	22	24	26	29	31	34	36	38	41	43	45	48	50	53	55	57	60	62	65
	9					17	20	23	26	28	31	34	37	39	42	45	48	50	53	56	59	62	64	67	70	73	76
	10						23	26	29	33	36	39	42	45	48	52	55	58	61	64	67	71	74	77	80	83	87
	11							30	33	37	40	44	47	51	55	58	62	65	69	73	76	80	83	87	90	94	98
	12								37	41	45	49	53	57	61	65	69	73	77	81	85	89	93	97	101	105	109
	13									45	50	54	59	63	67	72	76	80	85	89	94	98	102	107	111	116	120
	14										55	59	64	67	74	78	83	88	93	98	102	107	112	118	122	127	131
	15											64	70	75	80	85	90	96	101	106	111	117	122	125	132	138	143
	16												75	81	86	92	98	103	109	115	120	126	132	138	143	149	154
	17													87	93	99	105	111	117	123	129	135	141	147	154	160	166
	18														99	106	112	119	125	132	138	145	151	158	164	171	177
	19															113	119	126	133	140	147	154	161	168	175	182	189
	20																127	134	141	149	156	163	171	178	186	193	200
	21																	142	150	157	165	173	181	188	196	204	212
	22																		158	166	174	182	191	199	207	215	223
	23																			175	183	192	200	209	218	226	235
	24																				192	201	210	219	228	238	247
	25																					211	220	230	239	249	258
	26																						230	240	250	260	270
	27																							250	261	271	282
	28																								272	282	293
	29																									294	305
	30																										317

Critical Values for Wilcoxon's T Test

USE THIS TABLE TO FIND OUT IF YOUR VALUE FOR (Wilcoxon) T IS SIGNIFICANT. The value you obtained must be less than or equal to  the value given in the table for your sample sizes (N) in order to be significant. p is the probability of your results occurring by chance (as stated by the null hypothesis), so the lower the value of p, the more certain you can be that your result is significant. eg. p=0.10 means a 1 in 10 probability the result occurred by chance, whereas p=0.025 mean a 25 in a 1000 (1 in 40) probability the result occurred by chance.

1 tailed 2 tailed 0.05 0.10 0.025 0.05 0.01 0.02 0.001 0.002 N         6 2 0     7 3 2 0   8 5 3 1   9 8 5 3   10 10 8 5 0 11 13 10 7 1 12 17 13 9 2 13 21 17 12 4 14 25 21 15 6 15 30 25 19 8 16 35 29 23 11 17 41 34 27 14 18 47 40 32 18 19 53 46 37 21

1 tailed 2 tailed 0.05 0.10 0.025 0.05 0.01 0.02 0.001 0.002 N         20 60 52 43 26 21 67 58 49 30 22 75 65 55 35 23 83 73 62 40 24 91 81 69 45 25 100 89 76 51 26 110 98 84 58 27 119 107 92 64 28 130 116 101 71 29 141 125 111 78 30 151 137 120 86 31 163 147 130 94 32 175 159 140 103 33 187 170 151 112

Critical Values for Spearman's Rho

To use this table: compare your obtained value of rho to the value in the appropriate column, taking into account how many pairs of scores you have. e.g. an obtained rho of .75, with 18 pairs of scores, is larger than the critical value of rho at the 0.01 level of significance (0.625). You would conclude that your obtained value of rho is likely to occur by chance less than 1 time in a hundred (i.e. it is highly significant). If your N is not in the table, use the next one down - e.g., for an N of 17, use the table values for 16.
N (the number of pairs of scores):	0.05	0.02	0.01
5	1.000	1.000
6	0.886	0.943	1.000
7	0.786	0.893	0.929
8	0.738	0.833	0.881
9	0.683	0.783	0.833
10	0.648	0.746	0.794
12	0.591	0.712	0.777
14	0.544	0.645	0.715
16	0.506	0.601	0.665
18	0.475	0.564	0.625
20	0.45	0.534	0.591
22	0.428	0.508	0.562
24	0.409	0.485	0.537
26	0.392	0.465	0.515
28	0.377	0.448	0.496
30	0.364	0.432	0.478

Formulae

Mann-Whitney U Test NA= number of scores in condition one NB= number of scores in condition two 1. Rank all of the scores in both conditions together, from 1st place to lowest value. Make sure that if there is more than one value that is the same that they all share the mid rank position: eg. values of 4 5 5 6 6 6 6 7 8 9 9 9 10 10 11 12 13 15 18 19 would be ranked 1 2.5 2.5 5.5 5.5 5.5 5.5 8 9 11 11 11 13.5 13.5 15 16 17 18 19 20 2. Sigma RA = the total of the ranks for the scores from condition one. 3. Substitute values into formula 4. Look up value of U in table
Wilcoxon's T Test 1. Subtract the values in column 2 from their matched values in column 1 (D=A-B) 2. Rank the differences obtained in step one, lowest difference = 1st place (ignoring whether these are positive or negative - based only on the number and discarding any differences of 0) 3. Add together the ranks for all of the positive differences 4. Add together the ranks for all the negative differences 5. Whichever of these totals is smallest = T 6. Look up the value of T in the table	This isn't a formula as such, but... T = the sum of the ranks for the negative differences OR the sum of the ranks for the positive differences, depending on which is smaller.
Spearman's Rho N = total of scores D = difference between the ranks of IV1 and IV2   1. Rank the values for IV1 2. Rank the values for IV2 3. Subtract the ranks for IV2 from IV1 (D=RA-RB) 4. Square the differences from step 3 5. Total the values obtained in step 4. 6. Substitute values into formula 7. Look up value of rs in table

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Last Update: Monday, 01 March, 2010