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

- Test of correlation
- On data in the interval format

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.*