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 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.