Statistical Tables · free & public domain

Pearson Correlation Critical Values (PPMC)

Critical values of Pearson’s r by sample size, for testing H₀: ρ = 0.

How to use this table

Read down to your sample size n, across to your two-tailed α. Reject H₀: ρ = 0 — that is, call the correlation significant — if |r| exceeds the value. Example: n = 20 at α = 0.05 → 0.444, so an observed r of 0.52 is significant but 0.41 is not. Indexed by n directly, so there is no d.f. conversion to get wrong.

The table

Pearson Correlation Critical Values (PPMC)
n / two-tail α	0.1	0.05	0.02	0.01	0.001
3	0.988	0.997	1.000	1.000	1.000
4	0.900	0.950	0.980	0.990	0.999
5	0.805	0.878	0.934	0.959	0.991
6	0.729	0.811	0.882	0.917	0.974
7	0.669	0.754	0.833	0.875	0.951
8	0.621	0.707	0.789	0.834	0.925
9	0.582	0.666	0.750	0.798	0.898
10	0.549	0.632	0.715	0.765	0.872
11	0.521	0.602	0.685	0.735	0.847
12	0.497	0.576	0.658	0.708	0.823
13	0.476	0.553	0.634	0.684	0.801
14	0.458	0.532	0.612	0.661	0.780
15	0.441	0.514	0.592	0.641	0.760
16	0.426	0.497	0.574	0.623	0.742
17	0.412	0.482	0.558	0.606	0.725
18	0.400	0.468	0.543	0.590	0.708
19	0.389	0.456	0.529	0.575	0.693
20	0.378	0.444	0.516	0.561	0.679
21	0.369	0.433	0.503	0.549	0.665
22	0.360	0.423	0.492	0.537	0.652
23	0.352	0.413	0.482	0.526	0.640
24	0.344	0.404	0.472	0.515	0.629
25	0.337	0.396	0.462	0.505	0.618
26	0.330	0.388	0.453	0.496	0.607
27	0.323	0.381	0.445	0.487	0.597
28	0.317	0.374	0.437	0.479	0.588
29	0.311	0.367	0.430	0.471	0.579
30	0.306	0.361	0.423	0.463	0.570
32	0.296	0.349	0.409	0.449	0.554
34	0.287	0.339	0.397	0.436	0.539
36	0.279	0.329	0.386	0.424	0.525
38	0.271	0.320	0.376	0.413	0.513
40	0.264	0.312	0.367	0.403	0.501
45	0.248	0.294	0.346	0.380	0.474
50	0.235	0.279	0.328	0.361	0.451
60	0.214	0.254	0.300	0.330	0.414
70	0.198	0.235	0.278	0.306	0.385
80	0.185	0.220	0.260	0.286	0.361
90	0.174	0.207	0.245	0.270	0.341
100	0.165	0.197	0.232	0.256	0.324
150	0.135	0.160	0.190	0.210	0.266
200	0.117	0.139	0.164	0.182	0.231

Indexed by sample size n (not d.f.), with a 0.001 column and n to 200.

How these values were produced

r = t/√(t² + d.f.) with d.f. = n − 2 — the exact equivalence between the t test and the correlation test (SciPy 1.17).

Every one of these 210 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.

Need the test run rather than the critical value looked up? The Proof Workbench computes t, r, χ² and ANOVA in your browser with assumption checks and a re-verifiable receipt.

Use it freely

This table is dedicated to the public domain under CC0 1.0. No attribution required, no signup, no limits — copy it into a lecture, a textbook, or your own site. A link back is welcome but not asked for.

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