Correlation

Pearson Correlation Table: Critical Values of r

The smallest correlation coefficient that is statistically significant for a given sample size and significance level.

df 1 to 1000
5 significance levels
Calculator included

Pearson r Critical Values

Rows: df = n − 2 · Columns: α · Cells: critical |r|. Reject H₀ (ρ = 0) if |r| ≥ the cell.

Critical Values of the Pearson Correlation Coefficient (r Table)
Two-tailed α →	0.1	0.05	0.02	0.01	0.001
One-tailed α → df (n − 2) ↓	0.05	0.025	0.01	0.005	0.0005
1	0.9877	0.9969	0.9995	0.9999	1.0000
2	0.9000	0.9500	0.9800	0.9900	0.9990
3	0.8054	0.8783	0.9343	0.9587	0.9911
4	0.7293	0.8114	0.8822	0.9172	0.9741
5	0.6694	0.7545	0.8329	0.8745	0.9509
6	0.6215	0.7067	0.7887	0.8343	0.9249
7	0.5822	0.6664	0.7498	0.7977	0.8983
8	0.5494	0.6319	0.7155	0.7646	0.8721
9	0.5214	0.6021	0.6851	0.7348	0.8470
10	0.4973	0.5760	0.6581	0.7079	0.8233
11	0.4762	0.5529	0.6339	0.6835	0.8010
12	0.4575	0.5324	0.6120	0.6614	0.7800
13	0.4409	0.5140	0.5923	0.6411	0.7604
14	0.4259	0.4973	0.5742	0.6226	0.7419
15	0.4124	0.4821	0.5577	0.6055	0.7247
16	0.4000	0.4683	0.5425	0.5897	0.7084
17	0.3887	0.4555	0.5285	0.5751	0.6932
18	0.3783	0.4438	0.5155	0.5614	0.6788
19	0.3687	0.4329	0.5034	0.5487	0.6652
20	0.3598	0.4227	0.4921	0.5368	0.6524
21	0.3515	0.4132	0.4815	0.5256	0.6402
22	0.3438	0.4044	0.4716	0.5151	0.6287
23	0.3365	0.3961	0.4622	0.5052	0.6178
24	0.3297	0.3882	0.4534	0.4958	0.6074
25	0.3233	0.3809	0.4451	0.4869	0.5974
26	0.3172	0.3739	0.4372	0.4785	0.5880
27	0.3115	0.3673	0.4297	0.4705	0.5790
28	0.3061	0.3610	0.4226	0.4629	0.5703
29	0.3009	0.3550	0.4158	0.4556	0.5620
30	0.2960	0.3494	0.4093	0.4487	0.5541
35	0.2746	0.3246	0.3810	0.4182	0.5189
40	0.2573	0.3044	0.3578	0.3932	0.4896
45	0.2429	0.2876	0.3384	0.3721	0.4647
50	0.2306	0.2732	0.3218	0.3542	0.4432
60	0.2108	0.2500	0.2948	0.3248	0.4079
70	0.1954	0.2319	0.2737	0.3017	0.3798
80	0.1829	0.2172	0.2565	0.2830	0.3568
90	0.1726	0.2050	0.2422	0.2673	0.3375
100	0.1638	0.1946	0.2301	0.2540	0.3211
120	0.1496	0.1779	0.2104	0.2324	0.2943
150	0.1339	0.1593	0.1886	0.2083	0.2643
200	0.1161	0.1381	0.1636	0.1809	0.2298
300	0.0948	0.1129	0.1338	0.1480	0.1884
500	0.0735	0.0875	0.1038	0.1149	0.1464
1000	0.0520	0.0619	0.0735	0.0813	0.1038

Tip: click any value to highlight its row and column.

How to read this table

Compute df = n − 2, where n is the number of pairs.
Choose the column for your α (two-tailed unless you have a directional hypothesis).
The correlation is significant if |r| is greater than or equal to the table value.

Worked example

In 20 patients, the correlation between baseline biomarker level and response is r = 0.52. With df = 18, row 18, two-tailed α = 0.05 gives 0.4438. Because 0.52 ≥ 0.4438, the correlation is significant. It is below the α = 0.01 value of 0.5614, so 0.01 < p < 0.05.

Click the underlined links to highlight the value in the table.

Calculator

For values between the rows and columns of the table. Results update as you type.

Formula and how the values were computed

t = r √(df / (1 − r²)), df = n − 2 · r_crit = t_crit / √(t_crit² + df)

Critical values follow from the t-distribution: r = t / √(t² + df), where t is the two-tailed critical t with df = n − 2. They assume bivariate normality.

Frequently asked questions

Does a significant r mean a strong correlation?

No. With large samples very small correlations are significant: with df = 1000, r = 0.062 is significant at α = 0.05. Report r with a confidence interval, not just the p-value.

Can I use this table for Spearman correlation?

Only as an approximation for moderate to large samples. For small samples Spearman's rho has its own exact critical values.

Pearson Correlation Table: Critical Values of r

Pearson r Critical Values

How to read this table

Worked example

Calculator

Formula and how the values were computed

Frequently asked questions

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