First, use the Critical Significance Level (α: *alpha*) chosen in Step 2 and the degrees of freedom (*df*) calculated in Step 3 (where *df* = the total sample size minus two) to find the Critical Value of *t* (*t*_{critical}) using a Critical Value Table such as the one below e.g., if α = 0.05 and *df* = 5, then *t*_{critical} = 2.571.

Second, compare *t*_{critical} with the value for the *t* statistic calculated in Step 3.

**Reject your Null Hypothesis** if your calculated value is greater than or equal to the critical value; *t* ≥ *t*_{critical} (significant result).

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

E.g., if t = 2.981 and *t*_{critical} = 2.571 then reject the Null Hypothesis.

df |
α = 0.10 | α = 0.05 | α = 0.01 |
---|---|---|---|

1 | 6.314 | 12.706 | 63.656 |

2 | 2.920 | 4.303 | 9.925 |

3 | 2.353 | 3.182 | 5.841 |

4 | 2.132 | 2.776 | 4.604 |

5 | 2.015 | 2.571 | 4.032 |

6 | 1.943 | 2.447 | 3.707 |

7 | 1.895 | 2.365 | 3.499 |

8 | 1.860 | 2.306 | 3.355 |

9 | 1.833 | 2.262 | 3.250 |

10 | 1.812 | 2.228 | 3.169 |

11 | 1.796 | 2.201 | 3.106 |

12 | 1.782 | 2.179 | 3.055 |

13 | 1.771 | 2.160 | 3.012 |

14 | 1.761 | 2.145 | 2.977 |

15 | 1.753 | 2.131 | 2.947 |

16 | 1.746 | 2.120 | 2.921 |

17 | 1.740 | 2.110 | 2.898 |

18 | 1.734 | 2.101 | 2.878 |

19 | 1.729 | 2.093 | 2.861 |

20 | 1.725 | 2.086 | 2.845 |

21 | 1.721 | 2.080 | 2.831 |

22 | 1.717 | 2.074 | 2.819 |

23 | 1.714 | 2.069 | 2.807 |

24 | 1.711 | 2.064 | 2.797 |

25 | 1.708 | 2.060 | 2.787 |

26 | 1.706 | 2.056 | 2.779 |

27 | 1.703 | 2.052 | 2.771 |

28 | 1.701 | 2.048 | 2.763 |

29 | 1.699 | 2.045 | 2.756 |

30 | 1.697 | 2.042 | 2.750 |

31 | 1.696 | 2.040 | 2.744 |

32 | 1.694 | 2.037 | 2.738 |

33 | 1.692 | 2.035 | 2.733 |

34 | 1.691 | 2.032 | 2.728 |

35 | 1.690 | 2.030 | 2.724 |

36 | 1.688 | 2.028 | 2.719 |

37 | 1.687 | 2.026 | 2.715 |

38 | 1.686 | 2.024 | 2.712 |

39 | 1.685 | 2.023 | 2.708 |

40 | 1.684 | 2.021 | 2.704 |