Wilcoxon Signed-Rank Test Critical Values Table

Wilcoxon signed-rank table provides critical values for the Wilcoxon signed-rank test. Use this table to determine the critical value for your test statistic. Reject $H_0$ if the test value is less than or equal to the value given in the table.

n	α = 0.05	α = 0.025	α = 0.01	α = 0.005
1	--	--	--	--
2	--	--	--	--
3	0	0	0	0
4	0	0	0	0
5	2	0	0	0
6	3	2	0	0
7	5	3	1	0
8	8	5	3	1
9	10	8	5	3
10	13	10	8	5
11	17	13	10	8
12	21	17	13	10
13	25	21	17	13
14	30	25	20	17
15	35	30	24	20
16	41	35	28	24
17	47	41	33	28
18	53	47	38	33
19	60	53	43	38
20	67	60	49	43
21	75	67	55	49
22	83	75	62	55
23	91	83	69	62
24	100	91	76	69
25	110	100	84	76
26	120	110	92	84
27	130	120	101	92
28	141	130	110	101
29	152	141	120	110
30	163	152	130	120
31	175	163	141	130
32	188	175	152	141
33	201	188	163	152
34	214	201	175	163
35	228	214	188	175
36	242	228	201	188
37	256	242	214	201
38	271	256	228	214
39	286	271	242	228
40	302	286	257	242
41	319	302	272	257
42	336	319	288	272
43	353	336	304	288
44	371	353	321	304
45	389	371	338	321
46	408	389	356	338
47	427	408	374	356
48	446	427	392	374
49	466	446	412	392
50	486	466	431	412

Note: '--' indicates that the critical value is not available for the given sample size and significance level.

How to Use This Table

Determine your sample size (n)
Choose between one-tailed or two-tailed test
Select your desired significance level (α)
Find the critical value in the table
Compare your calculated test statistic with the critical value

Generating This Table in R

You can generate the Wilcoxon signed-rank critical values table using R with the following code:

# Function to generate Wilcoxon signed rank critical values table for one-sided tests
generate_wilcoxon_critical_values_one_sided <- function(max_n = 50) {
  alpha_levels <- c(0.05, 0.025, 0.01, 0.005)
  result <- data.frame(n = 1:max_n)
  
  for (alpha in alpha_levels) {
    col_name <- paste0("alpha_", alpha)
    result[[col_name]] <- numeric(max_n)
    
    for (n in 1:max_n) {
      # For small n, qsignrank may not be able to compute exact values
      tryCatch({
        result[n, col_name] <- qsignrank(alpha, n)
      }, error = function(e) {
        result[n, col_name] <- "--"
      })
    }
  }
  
  return(result)
}

# Generate the table
critical_values_one_sided <- generate_wilcoxon_critical_values_one_sided(50)
print(critical_values_one_sided)

This code uses R's qsignrank function to compute the critical values for different sample sizes and significance levels. For two-tailed tests, you would need to adjust the alpha values accordingly.

Wilcoxon Signed-Rank Test Critical Values Table

How to Use This Table

Generating This Table in R

Related Calculators

Wilcoxon Signed-Rank Test Calculator

Mann-Whitney U Test Calculator

n	α = 0.05	α = 0.025	α = 0.01	α = 0.005
1	--	--	--	--
2	--	--	--	--
3	0	0	0	0
4	0	0	0	0
5	2	0	0	0
6	3	2	0	0
7	5	3	1	0
8	8	5	3	1
9	10	8	5	3
10	13	10	8	5
11	17	13	10	8
12	21	17	13	10
13	25	21	17	13
14	30	25	20	17
15	35	30	24	20
16	41	35	28	24
17	47	41	33	28
18	53	47	38	33
19	60	53	43	38
20	67	60	49	43
21	75	67	55	49
22	83	75	62	55
23	91	83	69	62
24	100	91	76	69
25	110	100	84	76
26	120	110	92	84
27	130	120	101	92
28	141	130	110	101
29	152	141	120	110
30	163	152	130	120
31	175	163	141	130
32	188	175	152	141
33	201	188	163	152
34	214	201	175	163
35	228	214	188	175
36	242	228	201	188
37	256	242	214	201
38	271	256	228	214
39	286	271	242	228
40	302	286	257	242
41	319	302	272	257
42	336	319	288	272
43	353	336	304	288
44	371	353	321	304
45	389	371	338	321
46	408	389	356	338
47	427	408	374	356
48	446	427	392	374
49	466	446	412	392
50	486	466	431	412

n	α = 0.05	α = 0.025	α = 0.01	α = 0.005
1	--	--	--	--
2	--	--	--	--
3	0	0	0	0
4	0	0	0	0
5	2	0	0	0
6	3	2	0	0
7	5	3	1	0
8	8	5	3	1
9	10	8	5	3
10	13	10	8	5
11	17	13	10	8
12	21	17	13	10
13	25	21	17	13
14	30	25	20	17
15	35	30	24	20
16	41	35	28	24
17	47	41	33	28
18	53	47	38	33
19	60	53	43	38
20	67	60	49	43
21	75	67	55	49
22	83	75	62	55
23	91	83	69	62
24	100	91	76	69
25	110	100	84	76
26	120	110	92	84
27	130	120	101	92
28	141	130	110	101
29	152	141	120	110
30	163	152	130	120
31	175	163	141	130
32	188	175	152	141
33	201	188	163	152
34	214	201	175	163
35	228	214	188	175
36	242	228	201	188
37	256	242	214	201
38	271	256	228	214
39	286	271	242	228
40	302	286	257	242
41	319	302	272	257
42	336	319	288	272
43	353	336	304	288
44	371	353	321	304
45	389	371	338	321
46	408	389	356	338
47	427	408	374	356
48	446	427	392	374
49	466	446	412	392
50	486	466	431	412

n	α = 0.05	α = 0.025	α = 0.01	α = 0.005
1	--	--	--	--
2	--	--	--	--
3	0	0	0	0
4	0	0	0	0
5	2	0	0	0
6	3	2	0	0
7	5	3	1	0
8	8	5	3	1
9	10	8	5	3
10	13	10	8	5
11	17	13	10	8
12	21	17	13	10
13	25	21	17	13
14	30	25	20	17
15	35	30	24	20
16	41	35	28	24
17	47	41	33	28
18	53	47	38	33
19	60	53	43	38
20	67	60	49	43
21	75	67	55	49
22	83	75	62	55
23	91	83	69	62
24	100	91	76	69
25	110	100	84	76
26	120	110	92	84
27	130	120	101	92
28	141	130	110	101
29	152	141	120	110
30	163	152	130	120
31	175	163	141	130
32	188	175	152	141
33	201	188	163	152
34	214	201	175	163
35	228	214	188	175
36	242	228	201	188
37	256	242	214	201
38	271	256	228	214
39	286	271	242	228
40	302	286	257	242
41	319	302	272	257
42	336	319	288	272
43	353	336	304	288
44	371	353	321	304
45	389	371	338	321
46	408	389	356	338
47	427	408	374	356
48	446	427	392	374
49	466	446	412	392
50	486	466	431	412