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 rS (rS critical) using a Critical Value Table such as the one below (e.g. if α = 0.05 and df = 10, then rScritical = 0.648).

Second, compare rS critical with the value for the rS statistic calculated in Step 3.

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

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

For example, if rS = 0.701 and rS critical = 0.648 then reject the Null Hypothesis.

Table of Critical Values for Critical Significance Levels (α) of 0.1, 0.05 and 0.01 for the rS statistic where degrees of freedom (df) is the number of pairs of data points minus two for a Spearman correlation.

 degrees of freedom α = 0.10 α = 0.05 α = 0.01 1 2 3 4 1.000 5 0.900 1.000 6 0.829 0.886 1.000 7 0.714 0.786 0.929 8 0.643 0.738 0.881 9 0.600 0.700 0.833 10 0.564 0.648 0.794 11 0.536 0.618 0.755 12 0.503 0.587 0.727 13 0.484 0.560 0.703 14 0.464 0.538 0.679 15 0.446 0.521 0.654 16 0.429 0.503 0.635 17 0.414 0.485 0.615 18 0.401 0.472 0.600 19 0.391 0.460 0.584 20 0.380 0.447 0.570 21 0.370 0.435 0.556 22 0.361 0.425 0.544 23 0.353 0.415 0.532 24 0.344 0.406 0.521 25 0.337 0.398 0.511 26 0.331 0.390 0.501 27 0.324 0.382 0.491 28 0.317 0.375 0.483 29 0.312 0.368 0.475 30 0.306 0.362 0.467 31 0.301 0.356 0.459 32 0.296 0.350 0.452 33 0.291 0.345 0.446 34 0.287 0.340 0.439 35 0.283 0.335 0.433 36 0.279 0.330 0.427 37 0.275 0.325 0.421 38 0.271 0.321 0.415 39 0.267 0.317 0.410 40 0.264 0.313 0.405

Critical values of the Spearman rank-order correlation coefficient, rS, based on Zar (1999) and sources therein.
Zar, JH (1999) Biostatistical Analysis 4th edition. Prentice-Hall, New Jersey.