Statistical Tables · free & public domain

Tukey Studentized Range (q) Table

Critical values of the studentized range q for Tukey’s HSD post-hoc comparisons.

How to use this table

Use this after a significant ANOVA, to find which pairs of means actually differ. Choose the α block, then read the error degrees of freedom down the side and the number of means being compared across the top. Example: 4 groups with 20 error d.f. at α = 0.05 → 3.96. Multiply by √(MS_within/n) to get the honestly significant difference.

The table

α 0.1

Tukey Studentized Range (q) Table — 0.1
error d.f. / number of means (k)	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
1	8.93	13.44	16.36	18.49	20.15	21.50	22.64	23.62	24.48	25.24	25.92	26.54	27.10	27.62	28.10	28.54	28.96	29.35	29.71
2	4.13	5.73	6.77	7.54	8.14	8.63	9.05	9.41	9.72	10.01	10.26	10.49	10.70	10.89	11.07	11.24	11.39	11.54	11.68
3	3.33	4.47	5.20	5.74	6.16	6.51	6.81	7.06	7.29	7.49	7.67	7.83	7.98	8.12	8.25	8.37	8.48	8.58	8.68
4	3.01	3.98	4.59	5.03	5.39	5.68	5.93	6.14	6.33	6.49	6.65	6.78	6.91	7.02	7.13	7.23	7.33	7.41	7.50
5	2.85	3.72	4.26	4.66	4.98	5.24	5.46	5.65	5.82	5.97	6.10	6.22	6.34	6.44	6.54	6.63	6.71	6.79	6.86
6	2.75	3.56	4.07	4.44	4.73	4.97	5.17	5.34	5.50	5.64	5.76	5.87	5.98	6.07	6.16	6.25	6.32	6.40	6.47
7	2.68	3.45	3.93	4.28	4.55	4.78	4.97	5.14	5.28	5.41	5.53	5.64	5.74	5.83	5.91	5.99	6.06	6.13	6.19
8	2.63	3.37	3.83	4.17	4.43	4.65	4.83	4.99	5.13	5.25	5.36	5.46	5.56	5.64	5.72	5.80	5.87	5.93	6.00
9	2.59	3.32	3.76	4.08	4.34	4.54	4.72	4.87	5.01	5.13	5.23	5.33	5.42	5.51	5.58	5.65	5.72	5.79	5.85
10	2.56	3.27	3.70	4.02	4.26	4.47	4.64	4.78	4.91	5.03	5.13	5.23	5.32	5.40	5.47	5.54	5.61	5.67	5.73
11	2.54	3.23	3.66	3.96	4.20	4.40	4.57	4.71	4.84	4.95	5.05	5.15	5.23	5.31	5.38	5.45	5.51	5.57	5.63
12	2.52	3.20	3.62	3.92	4.16	4.35	4.51	4.65	4.78	4.89	4.99	5.08	5.16	5.24	5.31	5.37	5.44	5.49	5.55
13	2.50	3.18	3.59	3.88	4.12	4.30	4.46	4.60	4.72	4.83	4.93	5.02	5.10	5.18	5.25	5.31	5.37	5.43	5.48
14	2.49	3.16	3.56	3.85	4.08	4.27	4.42	4.56	4.68	4.79	4.88	4.97	5.05	5.12	5.19	5.26	5.32	5.37	5.43
15	2.48	3.14	3.54	3.83	4.05	4.23	4.39	4.52	4.64	4.75	4.84	4.93	5.01	5.08	5.15	5.21	5.27	5.32	5.38
16	2.47	3.12	3.52	3.80	4.03	4.21	4.36	4.49	4.61	4.71	4.80	4.89	4.97	5.04	5.11	5.17	5.23	5.28	5.33
17	2.46	3.11	3.50	3.78	4.00	4.18	4.33	4.46	4.58	4.68	4.77	4.86	4.93	5.01	5.07	5.13	5.19	5.24	5.30
18	2.45	3.10	3.49	3.77	3.98	4.16	4.31	4.44	4.55	4.65	4.75	4.83	4.90	4.97	5.04	5.10	5.16	5.21	5.26
19	2.45	3.09	3.47	3.75	3.97	4.14	4.29	4.42	4.53	4.63	4.72	4.80	4.88	4.95	5.01	5.07	5.13	5.18	5.23
20	2.44	3.08	3.46	3.74	3.95	4.12	4.27	4.40	4.51	4.61	4.70	4.78	4.85	4.92	4.99	5.05	5.10	5.16	5.20
22	2.43	3.06	3.44	3.71	3.92	4.09	4.24	4.36	4.47	4.57	4.66	4.74	4.81	4.88	4.94	5.00	5.06	5.11	5.16
24	2.42	3.05	3.42	3.69	3.90	4.07	4.21	4.34	4.44	4.54	4.63	4.71	4.78	4.85	4.91	4.97	5.02	5.07	5.12
26	2.41	3.04	3.41	3.67	3.88	4.05	4.19	4.31	4.42	4.52	4.60	4.68	4.75	4.82	4.88	4.94	4.99	5.04	5.09
28	2.41	3.03	3.40	3.66	3.86	4.03	4.17	4.29	4.40	4.49	4.58	4.66	4.73	4.79	4.85	4.91	4.96	5.01	5.06
30	2.40	3.02	3.39	3.65	3.85	4.02	4.16	4.28	4.38	4.47	4.56	4.64	4.71	4.77	4.83	4.89	4.94	4.99	5.03
35	2.39	3.00	3.36	3.62	3.82	3.99	4.12	4.24	4.34	4.44	4.52	4.59	4.66	4.73	4.79	4.84	4.89	4.94	4.99
40	2.38	2.99	3.35	3.60	3.80	3.96	4.10	4.21	4.32	4.41	4.49	4.56	4.63	4.69	4.75	4.81	4.86	4.90	4.95
50	2.37	2.97	3.33	3.58	3.77	3.93	4.06	4.18	4.28	4.37	4.45	4.52	4.59	4.65	4.71	4.76	4.81	4.85	4.90
60	2.36	2.96	3.31	3.56	3.75	3.91	4.04	4.16	4.25	4.34	4.42	4.49	4.56	4.62	4.67	4.73	4.78	4.82	4.86
80	2.35	2.94	3.29	3.54	3.73	3.89	4.01	4.13	4.22	4.31	4.39	4.46	4.52	4.58	4.64	4.69	4.73	4.78	4.82
120	2.34	2.93	3.28	3.52	3.71	3.86	3.99	4.10	4.19	4.28	4.35	4.42	4.48	4.54	4.60	4.65	4.69	4.74	4.78
240	2.34	2.92	3.26	3.50	3.68	3.83	3.96	4.07	4.16	4.24	4.32	4.39	4.45	4.51	4.56	4.61	4.65	4.70	4.74

α 0.05

Tukey Studentized Range (q) Table — 0.05
error d.f. / number of means (k)	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
1	17.97	26.98	32.82	37.08	40.41	43.12	45.40	47.36	49.07	50.59	51.96	53.19	54.32	55.36	56.32	57.21	58.04	58.82	59.56
2	6.08	8.33	9.80	10.88	11.73	12.43	13.03	13.54	13.99	14.39	14.75	15.08	15.37	15.65	15.91	16.14	16.36	16.57	16.77
3	4.50	5.91	6.82	7.50	8.04	8.48	8.85	9.18	9.46	9.72	9.95	10.15	10.35	10.52	10.69	10.84	10.98	11.11	11.24
4	3.93	5.04	5.76	6.29	6.71	7.05	7.35	7.60	7.83	8.03	8.21	8.37	8.52	8.66	8.79	8.91	9.03	9.13	9.23
5	3.64	4.60	5.22	5.67	6.03	6.33	6.58	6.80	6.99	7.17	7.32	7.47	7.60	7.72	7.83	7.93	8.03	8.12	8.21
6	3.46	4.34	4.90	5.30	5.63	5.90	6.12	6.32	6.49	6.65	6.79	6.92	7.03	7.14	7.24	7.34	7.43	7.51	7.59
7	3.34	4.16	4.68	5.06	5.36	5.61	5.82	6.00	6.16	6.30	6.43	6.55	6.66	6.76	6.85	6.94	7.02	7.10	7.17
8	3.26	4.04	4.53	4.89	5.17	5.40	5.60	5.77	5.92	6.05	6.18	6.29	6.39	6.48	6.57	6.65	6.73	6.80	6.87
9	3.20	3.95	4.41	4.76	5.02	5.24	5.43	5.59	5.74	5.87	5.98	6.09	6.19	6.28	6.36	6.44	6.51	6.58	6.64
10	3.15	3.88	4.33	4.65	4.91	5.12	5.30	5.46	5.60	5.72	5.83	5.93	6.03	6.11	6.19	6.27	6.34	6.40	6.47
11	3.11	3.82	4.26	4.57	4.82	5.03	5.20	5.35	5.49	5.61	5.71	5.81	5.90	5.98	6.06	6.13	6.20	6.27	6.33
12	3.08	3.77	4.20	4.51	4.75	4.95	5.12	5.27	5.39	5.51	5.61	5.71	5.80	5.88	5.95	6.02	6.09	6.15	6.21
13	3.06	3.73	4.15	4.45	4.69	4.88	5.05	5.19	5.32	5.43	5.53	5.63	5.71	5.79	5.86	5.93	5.99	6.05	6.11
14	3.03	3.70	4.11	4.41	4.64	4.83	4.99	5.13	5.25	5.36	5.46	5.55	5.64	5.71	5.79	5.85	5.91	5.97	6.03
15	3.01	3.67	4.08	4.37	4.59	4.78	4.94	5.08	5.20	5.31	5.40	5.49	5.57	5.65	5.72	5.78	5.85	5.90	5.96
16	3.00	3.65	4.05	4.33	4.56	4.74	4.90	5.03	5.15	5.26	5.35	5.44	5.52	5.59	5.66	5.73	5.79	5.84	5.90
17	2.98	3.63	4.02	4.30	4.52	4.70	4.86	4.99	5.11	5.21	5.31	5.39	5.47	5.54	5.61	5.67	5.73	5.79	5.84
18	2.97	3.61	4.00	4.28	4.49	4.67	4.82	4.96	5.07	5.17	5.27	5.35	5.43	5.50	5.57	5.63	5.69	5.74	5.79
19	2.96	3.59	3.98	4.25	4.47	4.65	4.79	4.92	5.04	5.14	5.23	5.31	5.39	5.46	5.53	5.59	5.65	5.70	5.75
20	2.95	3.58	3.96	4.23	4.45	4.62	4.77	4.90	5.01	5.11	5.20	5.28	5.36	5.43	5.49	5.55	5.61	5.66	5.71
22	2.93	3.55	3.93	4.20	4.41	4.58	4.72	4.85	4.96	5.06	5.14	5.23	5.30	5.37	5.43	5.49	5.55	5.60	5.65
24	2.92	3.53	3.90	4.17	4.37	4.54	4.68	4.81	4.92	5.01	5.10	5.18	5.25	5.32	5.38	5.44	5.49	5.55	5.59
26	2.91	3.51	3.88	4.14	4.35	4.51	4.65	4.77	4.88	4.98	5.06	5.14	5.21	5.28	5.34	5.40	5.45	5.50	5.55
28	2.90	3.50	3.86	4.12	4.32	4.49	4.62	4.74	4.85	4.94	5.03	5.11	5.18	5.24	5.30	5.36	5.41	5.46	5.51
30	2.89	3.49	3.85	4.10	4.30	4.46	4.60	4.72	4.82	4.92	5.00	5.08	5.15	5.21	5.27	5.33	5.38	5.43	5.47
35	2.87	3.46	3.81	4.07	4.26	4.42	4.56	4.67	4.77	4.86	4.95	5.02	5.09	5.15	5.21	5.26	5.31	5.36	5.41
40	2.86	3.44	3.79	4.04	4.23	4.39	4.52	4.63	4.73	4.82	4.90	4.98	5.04	5.11	5.16	5.22	5.27	5.31	5.36
50	2.84	3.42	3.76	4.00	4.19	4.34	4.47	4.58	4.68	4.77	4.85	4.92	4.98	5.04	5.10	5.15	5.20	5.24	5.29
60	2.83	3.40	3.74	3.98	4.16	4.31	4.44	4.55	4.65	4.73	4.81	4.88	4.94	5.00	5.06	5.11	5.15	5.20	5.24
80	2.81	3.38	3.71	3.95	4.13	4.28	4.40	4.51	4.60	4.69	4.76	4.83	4.89	4.95	5.00	5.05	5.10	5.14	5.18
120	2.80	3.36	3.68	3.92	4.10	4.24	4.36	4.47	4.56	4.64	4.71	4.78	4.84	4.90	4.95	5.00	5.04	5.09	5.13
240	2.79	3.34	3.66	3.89	4.06	4.21	4.32	4.43	4.52	4.60	4.67	4.73	4.79	4.85	4.90	4.94	4.99	5.03	5.07

α 0.025

Tukey Studentized Range (q) Table — 0.025
error d.f. / number of means (k)	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
1	35.99	54.00	65.69	74.22	80.87	86.29	90.85	94.77	98.20	101.24	103.97	106.45	108.71	110.78	112.70	114.49	116.15	117.71	119.18
2	8.78	11.94	14.01	15.54	16.75	17.74	18.58	19.31	19.95	20.51	21.02	21.49	21.91	22.30	22.67	23.00	23.32	23.61	23.89
3	5.91	7.66	8.81	9.66	10.33	10.89	11.36	11.77	12.14	12.46	12.75	13.01	13.26	13.48	13.69	13.88	14.06	14.23	14.39
4	4.94	6.24	7.09	7.72	8.21	8.62	8.98	9.28	9.55	9.79	10.00	10.20	10.38	10.55	10.70	10.85	10.99	11.11	11.23
5	4.47	5.56	6.26	6.77	7.19	7.53	7.82	8.07	8.29	8.49	8.67	8.83	8.98	9.12	9.25	9.37	9.49	9.59	9.69
6	4.20	5.16	5.77	6.23	6.59	6.88	7.14	7.36	7.55	7.73	7.89	8.03	8.16	8.29	8.40	8.51	8.60	8.70	8.79
7	4.02	4.90	5.46	5.87	6.19	6.46	6.69	6.89	7.07	7.23	7.37	7.50	7.62	7.74	7.84	7.93	8.03	8.11	8.19
8	3.89	4.71	5.23	5.62	5.92	6.17	6.38	6.57	6.73	6.88	7.01	7.13	7.24	7.35	7.44	7.53	7.62	7.69	7.77
9	3.80	4.58	5.07	5.43	5.71	5.95	6.15	6.32	6.48	6.62	6.74	6.86	6.96	7.06	7.15	7.23	7.31	7.38	7.46
10	3.72	4.47	4.94	5.29	5.56	5.78	5.97	6.14	6.28	6.42	6.53	6.64	6.74	6.83	6.92	7.00	7.07	7.15	7.21
11	3.67	4.39	4.84	5.17	5.43	5.65	5.83	5.99	6.13	6.26	6.37	6.47	6.57	6.66	6.74	6.81	6.89	6.95	7.02
12	3.62	4.32	4.76	5.08	5.33	5.54	5.72	5.87	6.00	6.12	6.23	6.33	6.43	6.51	6.59	6.66	6.73	6.80	6.86
13	3.58	4.27	4.69	5.00	5.25	5.45	5.62	5.77	5.90	6.02	6.12	6.22	6.31	6.39	6.47	6.54	6.61	6.67	6.73
14	3.55	4.22	4.64	4.94	5.18	5.37	5.54	5.68	5.81	5.93	6.03	6.12	6.21	6.29	6.36	6.43	6.50	6.56	6.62
15	3.52	4.18	4.59	4.89	5.12	5.31	5.47	5.61	5.74	5.85	5.95	6.04	6.12	6.20	6.28	6.34	6.41	6.47	6.52
16	3.50	4.15	4.55	4.84	5.07	5.25	5.41	5.55	5.67	5.78	5.88	5.97	6.05	6.13	6.20	6.27	6.33	6.39	6.44
17	3.48	4.12	4.51	4.80	5.02	5.20	5.36	5.50	5.61	5.72	5.82	5.91	5.99	6.06	6.13	6.20	6.26	6.32	6.37
18	3.46	4.09	4.48	4.76	4.98	5.16	5.31	5.45	5.57	5.67	5.76	5.85	5.93	6.00	6.07	6.14	6.20	6.25	6.31
19	3.44	4.07	4.45	4.73	4.95	5.12	5.27	5.41	5.52	5.62	5.72	5.80	5.88	5.95	6.02	6.08	6.14	6.20	6.25
20	3.43	4.05	4.43	4.70	4.91	5.09	5.24	5.37	5.48	5.58	5.68	5.76	5.84	5.91	5.97	6.04	6.09	6.15	6.20
22	3.40	4.01	4.38	4.65	4.86	5.03	5.18	5.30	5.41	5.51	5.60	5.68	5.76	5.83	5.89	5.95	6.01	6.06	6.11
24	3.38	3.98	4.35	4.61	4.82	4.98	5.13	5.25	5.36	5.46	5.54	5.62	5.70	5.76	5.83	5.89	5.94	5.99	6.04
26	3.36	3.96	4.32	4.58	4.78	4.94	5.08	5.20	5.31	5.41	5.49	5.57	5.64	5.71	5.77	5.83	5.88	5.93	5.98
28	3.35	3.94	4.29	4.55	4.75	4.91	5.05	5.17	5.27	5.37	5.45	5.53	5.60	5.66	5.72	5.78	5.83	5.88	5.93
30	3.34	3.92	4.27	4.52	4.72	4.88	5.02	5.13	5.24	5.33	5.41	5.49	5.56	5.62	5.68	5.74	5.79	5.84	5.89
35	3.31	3.88	4.23	4.47	4.67	4.82	4.96	5.07	5.17	5.26	5.34	5.42	5.48	5.55	5.60	5.66	5.71	5.76	5.80
40	3.29	3.86	4.20	4.44	4.63	4.78	4.91	5.02	5.12	5.21	5.29	5.36	5.43	5.49	5.54	5.60	5.65	5.69	5.74
50	3.27	3.82	4.15	4.39	4.57	4.72	4.85	4.96	5.05	5.14	5.21	5.28	5.35	5.41	5.46	5.51	5.56	5.60	5.65
60	3.25	3.80	4.12	4.36	4.54	4.68	4.81	4.91	5.01	5.09	5.16	5.23	5.29	5.35	5.41	5.46	5.50	5.55	5.59
80	3.23	3.77	4.09	4.32	4.49	4.63	4.75	4.86	4.95	5.03	5.10	5.17	5.23	5.29	5.34	5.39	5.43	5.47	5.51
120	3.21	3.74	4.05	4.28	4.45	4.59	4.70	4.81	4.89	4.97	5.04	5.11	5.17	5.22	5.27	5.32	5.36	5.40	5.44
240	3.19	3.71	4.02	4.24	4.40	4.54	4.65	4.75	4.84	4.91	4.98	5.05	5.10	5.16	5.20	5.25	5.29	5.33	5.37

α 0.01

Tukey Studentized Range (q) Table — 0.01
error d.f. / number of means (k)	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
1	90.02	135.04	164.26	185.58	202.21	215.77	227.17	236.97	245.54	253.15	259.98	266.16	271.81	277.00	281.80	286.26	290.43	294.33	298.00
2	14.04	19.02	22.29	24.72	26.63	28.20	29.53	30.68	31.69	32.59	33.40	34.13	34.81	35.43	36.00	36.53	37.03	37.50	37.94
3	8.26	10.62	12.17	13.32	14.24	15.00	15.64	16.20	16.69	17.13	17.53	17.89	18.22	18.52	18.80	19.07	19.31	19.55	19.76
4	6.51	8.12	9.17	9.96	10.58	11.10	11.54	11.93	12.26	12.57	12.84	13.09	13.32	13.53	13.73	13.91	14.08	14.24	14.39
5	5.70	6.98	7.80	8.42	8.91	9.32	9.67	9.97	10.24	10.48	10.70	10.89	11.08	11.24	11.40	11.55	11.68	11.81	11.93
6	5.24	6.33	7.03	7.56	7.97	8.32	8.61	8.87	9.10	9.30	9.48	9.65	9.81	9.95	10.08	10.21	10.32	10.43	10.54
7	4.95	5.92	6.54	7.00	7.37	7.68	7.94	8.17	8.37	8.55	8.71	8.86	9.00	9.12	9.24	9.35	9.46	9.55	9.65
8	4.75	5.64	6.20	6.62	6.96	7.24	7.47	7.68	7.86	8.03	8.18	8.31	8.44	8.55	8.66	8.76	8.85	8.94	9.03
9	4.60	5.43	5.96	6.35	6.66	6.91	7.13	7.33	7.49	7.65	7.78	7.91	8.03	8.13	8.23	8.33	8.41	8.49	8.57
10	4.48	5.27	5.77	6.14	6.43	6.67	6.87	7.05	7.21	7.36	7.49	7.60	7.71	7.81	7.91	7.99	8.08	8.15	8.23
11	4.39	5.15	5.62	5.97	6.25	6.48	6.67	6.84	6.99	7.13	7.25	7.36	7.46	7.56	7.65	7.73	7.81	7.88	7.95
12	4.32	5.05	5.50	5.84	6.10	6.32	6.51	6.67	6.81	6.94	7.06	7.17	7.26	7.36	7.44	7.52	7.59	7.66	7.73
13	4.26	4.96	5.40	5.73	5.98	6.19	6.37	6.53	6.67	6.79	6.90	7.01	7.10	7.19	7.27	7.35	7.42	7.48	7.55
14	4.21	4.89	5.32	5.63	5.88	6.08	6.26	6.41	6.54	6.66	6.77	6.87	6.96	7.05	7.13	7.20	7.27	7.33	7.39
15	4.17	4.84	5.25	5.56	5.80	5.99	6.16	6.31	6.44	6.55	6.66	6.76	6.84	6.93	7.00	7.07	7.14	7.20	7.26
16	4.13	4.79	5.19	5.49	5.72	5.92	6.08	6.22	6.35	6.46	6.56	6.66	6.74	6.82	6.90	6.97	7.03	7.09	7.15
17	4.10	4.74	5.14	5.43	5.66	5.85	6.01	6.15	6.27	6.38	6.48	6.57	6.66	6.73	6.81	6.87	6.94	7.00	7.05
18	4.07	4.70	5.09	5.38	5.60	5.79	5.94	6.08	6.20	6.31	6.41	6.50	6.58	6.65	6.73	6.79	6.85	6.91	6.97
19	4.05	4.67	5.05	5.33	5.55	5.73	5.89	6.02	6.14	6.25	6.34	6.43	6.51	6.58	6.65	6.72	6.78	6.84	6.89
20	4.02	4.64	5.02	5.29	5.51	5.69	5.84	5.97	6.09	6.19	6.28	6.37	6.45	6.52	6.59	6.65	6.71	6.77	6.82
22	3.99	4.59	4.96	5.22	5.43	5.61	5.75	5.88	5.99	6.10	6.19	6.27	6.35	6.42	6.48	6.54	6.60	6.66	6.71
24	3.96	4.55	4.91	5.17	5.37	5.54	5.69	5.81	5.92	6.02	6.11	6.19	6.26	6.33	6.39	6.45	6.51	6.56	6.61
26	3.93	4.51	4.87	5.12	5.32	5.49	5.63	5.75	5.86	5.95	6.04	6.12	6.19	6.26	6.32	6.38	6.43	6.48	6.53
28	3.91	4.48	4.83	5.08	5.28	5.44	5.58	5.70	5.80	5.90	5.98	6.06	6.13	6.20	6.26	6.31	6.37	6.42	6.47
30	3.89	4.45	4.80	5.05	5.24	5.40	5.54	5.65	5.76	5.85	5.93	6.01	6.08	6.14	6.20	6.26	6.31	6.36	6.41
35	3.85	4.40	4.74	4.98	5.17	5.32	5.45	5.57	5.67	5.75	5.84	5.91	5.98	6.04	6.10	6.15	6.20	6.25	6.29
40	3.82	4.37	4.70	4.93	5.11	5.26	5.39	5.50	5.60	5.69	5.76	5.83	5.90	5.96	6.02	6.07	6.12	6.16	6.21
50	3.79	4.32	4.63	4.86	5.04	5.19	5.31	5.41	5.51	5.59	5.67	5.73	5.80	5.85	5.91	5.96	6.01	6.05	6.09
60	3.76	4.28	4.59	4.82	4.99	5.13	5.25	5.36	5.45	5.53	5.60	5.67	5.73	5.78	5.84	5.89	5.93	5.97	6.01
80	3.73	4.24	4.55	4.76	4.93	5.07	5.18	5.28	5.37	5.45	5.52	5.59	5.64	5.70	5.75	5.80	5.84	5.88	5.92
120	3.70	4.20	4.50	4.71	4.87	5.01	5.12	5.21	5.30	5.37	5.44	5.50	5.56	5.61	5.66	5.71	5.75	5.79	5.83
240	3.67	4.16	4.45	4.66	4.81	4.94	5.05	5.15	5.23	5.30	5.37	5.43	5.48	5.53	5.58	5.62	5.66	5.70	5.74

Four α levels including 0.025, and error d.f. on my own ladder out to 240.

How these values were produced

Studentized range distribution (SciPy 1.17). Tabulated by Harter (1960), Ann. Math. Statist. 31(4), 1122–1147.

Every one of these 2,432 values was computed from the underlying distribution — none was transcribed from a printed table. Values of this kind are mathematical facts: they come out the same for anyone who computes them correctly.

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