First, use the Critical Significance Level (α: *alpha*) chosen in Step 2 and degrees of freedom (*df*) calculated in Step 3 (where *df* = the number of pairs of data points minus two) to find the Critical Value of *r* (*r*_{critical}) using a Critical Value Table such as the one below e.g., if α = 0.05 and *df* = 10, then *r*_{critical} = 0.576.

Second, compare *r*_{critical} 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; *r* ≥ *r*_{critical} (significant result).

**Accept your Null Hypothesis** if your calculated value is less than the critical value; *r* < *r*_{critical} (non-significant result).

E.g., if *r* = 0.591 and *r*_{critical} = 0.576 then reject the Null Hypothesis.

df |
α = 0.10 | 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 |