Statistical Tables · free & public domain

Spearman Rank Correlation Critical Values

Critical values of Spearman’s rₛ, exact permutation enumeration to n = 14.

How to use this table

Rank both variables, compute r_s on the ranks, then read down to your n and across to your α. Reject H₀: ρ = 0 if |r_s| exceeds the value. Example: n = 20 at α = 0.05 → 0.448.

The table

Spearman Rank Correlation Critical Values
n / two-tail α	0.1	0.05	0.02	0.01
5	0.900	1.000	1.000	—
6	0.829	0.886	0.943	1.000
7	0.714	0.786	0.893	0.929
8	0.643	0.738	0.833	0.881
9	0.600	0.700	0.783	0.833
10	0.564	0.648	0.745	0.794
11	0.536	0.618	0.709	0.755
12	0.503	0.587	0.678	0.727
13	0.484	0.560	0.648	0.703
14	0.464	0.538	0.626	0.679
15	0.446	0.521	0.604	0.654
16	0.429	0.503	0.585	0.635
17	0.414	0.488	0.566	0.615
18	0.404	0.474	0.550	0.600
19	0.391	0.460	0.535	0.584
20	0.380	0.448	0.522	0.570
21	0.370	0.435	0.509	0.556
22	0.361	0.425	0.496	0.544
23	0.353	0.415	0.485	0.532
24	0.344	0.406	0.476	0.521
25	0.338	0.398	0.466	0.510
26	0.330	0.390	0.457	0.501
27	0.324	0.383	0.449	0.493
28	0.318	0.375	0.440	0.483
29	0.312	0.369	0.433	0.475
30	0.306	0.362	0.425	0.467
31	0.301	0.356	0.418	0.459
32	0.296	0.350	0.411	0.452
33	0.291	0.345	0.405	0.445
34	0.287	0.340	0.399	0.439
35	0.283	0.335	0.394	0.433
36	0.279	0.330	0.388	0.427
37	0.275	0.325	0.383	0.421
38	0.271	0.321	0.378	0.416
39	0.267	0.317	0.373	0.410
40	0.264	0.313	0.368	0.405

Exact permutation distribution for n ≤ 14; 8-million-draw simulation for n ≥ 15 using the same rule, validated against the exact values at n = 10–14. n runs to 40.

How these values were produced

Exact enumeration of all n! rank permutations for n ≤ 14; 8-million-draw simulation for n ≥ 15 (NumPy PCG64), validated against the exact values at n = 10–14.

Every one of these 144 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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Use it freely

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