NUMBAT OER - Open Educational Resources

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.