Pearson R Critical Value Table
Use this Pearson correlation critical values table to compare an observed r with the critical absolute correlation for your sample size and significance level. See how degrees of freedom and one- or two-tailed tests affect the threshold.
n = 20; df = 18; total two-tailed α = 0.05
Critical correlation values are rounded to four decimal places. Values displayed as 1.0000 may be slightly below one before rounding.
Pearson R Critical Values Table
A critical r value is a cutoff for testing whether a population Pearson correlation is zero under the usual test assumptions. The cutoff depends on sample size n and the chosen significance level, and is commonly displayed as an absolute value for a two-tailed test.
| n (df = n − 2) | 0.1 | 0.05 | 0.025 | 0.01 | 0.005 | 0.001 |
|---|---|---|---|---|---|---|
| 3 (1) | ||||||
| 4 (2) | ||||||
| 5 (3) | ||||||
| 6 (4) | ||||||
| 7 (5) | ||||||
| 8 (6) | ||||||
| 9 (7) | ||||||
| 10 (8) | ||||||
| 11 (9) | ||||||
| 12 (10) | ||||||
| 13 (11) | ||||||
| 14 (12) | ||||||
| 15 (13) | ||||||
| 16 (14) | ||||||
| 17 (15) | ||||||
| 18 (16) | ||||||
| 19 (17) | ||||||
| 20 (18) | ||||||
| 21 (19) | ||||||
| 22 (20) | ||||||
| 23 (21) | ||||||
| 24 (22) | ||||||
| 25 (23) | ||||||
| 26 (24) | ||||||
| 27 (25) | ||||||
| 28 (26) | ||||||
| 29 (27) | ||||||
| 30 (28) | ||||||
| 40 (38) | ||||||
| 60 (58) | ||||||
| 100 (98) | ||||||
| 200 (198) |
Assumptions: independent paired observations and a bivariate-normal null reference for testing zero Pearson population correlation. This table is not a reference for every correlation method. For a one-sided alternative, use the threshold with the sign of that alternative; do not compare |r| in both directions.
How to Read an R Critical Value Table
Find your number of paired observations n and the column for the desired α and tail convention. Compare the magnitude |r| of the observed correlation with the critical absolute value. For n = 10 and a two-tailed α = 0.05, |rcrit| is approximately 0.6319.
Sample Size and Degrees of Freedom
For the conventional significance test of a Pearson correlation, df = n − 2. The critical threshold generally decreases in magnitude as the sample size grows at the same α.
Worked Example: Pearson r with n = 20
For 20 paired observations, df = 18. At a two-tailed α = 0.05, the critical absolute Pearson correlation is approximately 0.4438. An observed r = 0.50 exceeds this reference threshold in magnitude, provided the test assumptions hold.
Frequently Asked Questions
What is an r critical value table?
It shows correlation cutoffs for specified sample sizes and significance levels under a chosen Pearson test convention.
How do I find the critical value of Pearson r?
Choose sample size n and the significance level and tail direction. For the conventional Pearson test, degrees of freedom are n − 2.
Why are there two critical r values?
A two-tailed test is symmetric: positive and negative correlations with sufficiently large absolute value can both exceed the critical magnitude.
What is the critical r for n = 10 at 0.05?
For a two-tailed Pearson test at α = 0.05 with n = 10, the critical magnitude is approximately 0.6319.
Is a critical r table the same as a correlation calculator?
No. The table provides a reference cutoff. A correlation calculator estimates r from paired observations; statistical interpretation depends on the sampling model.
Sources
Reviewed: October 2026. Reference grids and lookups are calculated locally; no observations are sent to a server.