Critical values of the correlation coefficient

The table gives critical values of the Pearson correlation coefficient r for various degrees of freedom and significance levels. Degrees of freedom df = n − 2, where n is the number of paired observations. Reject H₀ (that the population correlation coefficient is zero) if the absolute value of the calculated r is greater than or equal to the critical value in the table.

Critical values are computed from the relationship between r and the t-distribution:

$$t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}} \qquad \Leftrightarrow \qquad r = \sqrt{\frac{t^2}{t^2 + df}}$$

df (n−2)	Two-tailed significance level α
df (n−2)	0.10	0.05	0.02	0.01	0.001
1	0.9877	0.9969	0.9995	0.9999	>0.9999
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	0.6214	0.7068	0.7887	0.8343	0.9249
7	0.5823	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	0.4972	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
22	0.3438	0.4044	0.4716	0.5151	0.6291
24	0.3297	0.3882	0.4534	0.4958	0.6081
26	0.3172	0.3739	0.4372	0.4785	0.5888
28	0.3061	0.3610	0.4226	0.4629	0.5711
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	0.2428	0.2876	0.3384	0.3721	0.4648
50	0.2306	0.2732	0.3218	0.3542	0.4433
60	0.2108	0.2500	0.2948	0.3248	0.4078
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

Critical values of the correlation coefficient

See also