Correlation Critical Values Table: When Is r Significant?

How to read this table

Each cell is the smallest absolute correlation, |r|, that counts as statistically significant for a sample of n pairs, at the two-tailed level heading the column. Compute your r, find your n, and compare: above the cell value, the correlation is significant; below it, a sample this size cannot distinguish your r from zero at that level.

The pattern down the 0.05 column is the lesson: n = 10 demands |r| of 0.632, n = 20 needs 0.444, n = 30 needs 0.361, and by n = 50 the bar is 0.279. Small samples must shout; large samples can whisper. A correlation of 0.45 is a finding with 20 pairs (it clears 0.444, exact p about 0.047) and a shrug with 12.

n	0.1	0.05	0.02	0.01
3	0.988	0.997	1.000	1.000
4	0.900	0.950	0.980	0.990
5	0.805	0.878	0.934	0.959
6	0.729	0.811	0.882	0.917
7	0.669	0.754	0.833	0.875
8	0.621	0.707	0.789	0.834
9	0.582	0.666	0.750	0.798
10	0.549	0.632	0.715	0.765
11	0.521	0.602	0.685	0.735
12	0.497	0.576	0.658	0.708
13	0.476	0.553	0.634	0.684
14	0.458	0.532	0.612	0.661
15	0.441	0.514	0.592	0.641
16	0.426	0.497	0.574	0.623
17	0.412	0.482	0.558	0.606
18	0.400	0.468	0.543	0.590
19	0.389	0.456	0.529	0.575
20	0.378	0.444	0.516	0.561
21	0.369	0.433	0.503	0.549
22	0.360	0.423	0.492	0.537
23	0.352	0.413	0.482	0.526
24	0.344	0.404	0.472	0.515
25	0.337	0.396	0.462	0.505
26	0.330	0.388	0.453	0.496
27	0.323	0.381	0.445	0.487
28	0.317	0.374	0.437	0.479
29	0.311	0.367	0.430	0.471
30	0.306	0.361	0.423	0.463
32	0.296	0.349	0.409	0.449
34	0.287	0.339	0.397	0.436
36	0.279	0.329	0.386	0.424
38	0.271	0.320	0.376	0.413
40	0.264	0.312	0.367	0.403
45	0.248	0.294	0.346	0.380
50	0.235	0.279	0.328	0.361

Where the numbers come from

The table is the t distribution in disguise. A correlation r on n pairs converts to t = r√(n − 2) ÷ √(1 − r²) with n − 2 degrees of freedom. Setting t equal to its two-tailed critical value and solving back for r gives every cell: r = t ÷ √(t² + df). That is why the correlation significance test calculator and this table never disagree.

Worked example

A class study finds r = 0.71 between practice tests and final scores, n = 12 pairs. Row 12, 0.05 column: 0.576. The observed 0.71 clears it: significant at 5%. The 0.01 column at n = 12 reads 0.708, and 0.71 clears that too, just barely: significant at 1%. Two brackets from one row.

Significance is not size

The table answers "could this be chance?", never "does this matter?". With n in the thousands, r = 0.05 becomes significant while explaining a quarter of one percent of the variance. With n = 8, a genuinely strong r = 0.6 cannot clear the bar. Quote r and n together, always: the pair is the finding.

Frequently asked questions

What correlation is significant with n = 25 at the 5% level?

Row 25, column 0.05: 0.396. An |r| of 0.396 or more is significant; below that, 25 pairs cannot rule out zero at 5%.

Does the table work for Spearman's rho?

Approximately, for n of about 10 or more the same critical values serve as a working guide for Spearman's rho. Exact Spearman tables differ slightly at small n.

Why two-tailed columns?

Most correlation claims do not predict a direction in advance, so significance is judged in both tails. If a direction was fixed before seeing data, a one-tailed judgement halves the p-value; the calculator reports the p itself, which keeps the choice visible.

My n is bigger than 50. What is the critical value?

Use the correlation significance test calculator, which converts your r and n to an exact p-value for any sample size.

Correlation Critical Values Table