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Spearman’s rank order correlation coefficient test (Spearman’s rho) is a:

To find the correct critical value when calculating whether results are statistically significant using Spearman’s rho, you need to know:

Your results are statistically significant if the observed value is equal to or greater than the critical value.

Note: Tables like the ones below will be provided in the exam – you don’t have to memorise all these critical values!

One-tailed Spearman’s rho

One-tailed: The experimental hypothesis predicts a change in only one direction (also called a directional hypothesis).

The following are critical values of Spearman’s rho for one-tailed experiments where the sample size (n) ranges between 5-20 and for p values of 0.1, 0.05 and 0.01.

n p = 0.1 p = 0.05 p = 0.01
5 0.8 0.9 1
6 0.657 0.829 0.943
7 0.571 0.714 0.893
8 0.524 0.643 0.833
9 0.483 0.6 0.783
10 0.455 0.564 0.745
11 0.427 0.563 0.709
12 0.406 0.503 0.671
13 0.385 0.484 0.648
14 0.367 0.464 0.622
15 0.354 0.446 0.604
16 0.341 0.429 0.582
17 0.328 0.414 0.566
18 0.317 0.401 0.55
19 0.309 0.391 0.535
20 0.299 0.38 0.52

Your results are statistically significant if the observed value is equal to or greater than the critical value.

Two-tailed Spearman’s rho

Two-tailed: The experimental hypothesis predicts a change in either direction (also called a non-directional hypothesis).

The following are critical values of Spearman’s rho for two-tailed experiments where the sample size (n) ranges between 5-20 and for p values of 0.1, 0.05 and 0.01.

n p = 0.1 p = 0.05 p = 0.01
5 0.9 1 –
6 0.829 0.886 1
7 0.714 0.786 0.929
8 0.643 0.738 0.881
9 0.6 0.7 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 0.56 0.703
14 0.464 0.538 0.675
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 0.6
19 0.391 0.46 0.584
20 0.38 0.447 0.57

Your results are statistically significant if the observed value is equal to or greater than the critical value.

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