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Pearson’s product-moment correlation coefficient (Pearson’s r) is a:

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

  • Whether your experimental hypothesis is one-tailed or two-tailed
  • The degrees of freedom (df)
    • This will be given to you in the exam, but is calculated as follows:
      • (Sample size – 2)
  • The level of significance (p)
    • This will be given to you in the exam

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 Pearson’s r

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

The following are critical values of Pearson’s r for one-tailed experiments where the degrees of freedom (df) range between 5-20 and for p values of 0.1, 0.05 and 0.01.

df p = 0.1 p = 0.05 p = 0.01
5 0.551 0.669 0.833
6 0.507 0.622 0.789
7 0.472 0.582 0.750
8 0.443 0.549 0.716
9 0.419 0.521 0.685
10 0.398 0.497 0.658
11 0.380 0.476 0.634
12 0.365 0.458 0.612
13 0.351 0.441 0.592
14 0.338 0.426 0.574
15 0.327 0.412 0.558
16 0.317 0.400 0.543
17 0.308 0.389 0.529
18 0.229 0.378 0.516
19 0.291 0.369 0.503
20 0.284 0.360 0.492

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

Two-tailed Pearson’s r

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

The following are critical values of Pearson’s r for two-tailed experiments where the degrees of freedom (df) range between 5-20 and for p values of 0.1, 0.05 and 0.01.

df p = 0.1 p = 0.05 p = 0.01
5 0.669 0.754 0.874
6 0.622 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

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

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