First, use the Critical Significance Level (α) chosen in Step 2 and degrees of freedom (df) calculated in Step 3 (df = the number of pairs of data points minus two) to find the Critical Value of r (rcritical) using a Critical Value Table such as the one below (e.g. if α = 0.05 and df = 10, then rcritical = 0.576).

Second, compare rcritical with the value for the r statistic calculated in Step 3.

Reject your Null Hypothesis if your calculated value is greater than or equal to the Critical value; rrcritical (significant result).

Accept your Null Hypothesis if your calculated value is less than the Critical value; r < rcritical (non-significant result).

For example, if r = 0.591 and rcritical = 0.576 then reject the Null Hypothesis.

Table of Critical Values for Critical Significance Levels (α) of 0.1, 0.05 and 0.01 for the r statistic where degrees of freedom (df) is one less than the number of categories for a Pearson correlation.

 df α = 0.0 α = 0.05 α = 0.01 1 0.988 0.997 1.000 2 0.900 0.950 0.990 3 0.805 0.878 0.959 4 0.729 0.811 0.917 5 0.669 0.754 0.875 6 0.621 0.707 0.834 7 0.582 0.666 0.798 8 0.549 0.632 0.765 9 0.521 0.602 0.735 10 0.497 0.576 0.708 11 0.476 0.553 0.684 12 0.458 0.532 0.661 13 0.441 0.514 0.641 14 0.426 0.497 0.623 15 0.412 0.482 0.606 16 0.400 0.468 0.590 17 0.389 0.456 0.575 18 0.378 0.444 0.561 19 0.369 0.433 0.549 20 0.360 0.423 0.537 21 0.352 0.413 0.526 22 0.344 0.404 0.515 23 0.337 0.396 0.505 24 0.330 0.388 0.496 25 0.323 0.381 0.487 26 0.317 0.374 0.479 27 0.311 0.367 0.471 28 0.306 0.361 0.463 29 0.301 0.355 0.456 30 0.296 0.349 0.449 31 0.291 0.344 0.442 32 0.287 0.339 0.436 33 0.283 0.334 0.430 34 0.279 0.329 0.424 35 0.275 0.325 0.418 36 0.271 0.320 0.413 37 0.267 0.316 0.408 38 0.264 0.312 0.403 39 0.260 0.308 0.398 40 0.257 0.304 0.393

Critical values of the correlation coefficient, r derived from critical values of the t-distribution by Toby Carter.