## T distribution table

### From OPOSSEM

This table presents the appropriate critical values of the Student's t statistic for a number of common confidence levels and degrees of freedom. To use this table, identify the column with the appropriate confidence level and then find the row with the number of degrees of freedom appropriate for the statistical test (for example, in the difference of means t test, this would be <math>n_1 + n_2 - 2</math>).

If there is no row for the exact number of degrees of freedom for your test, read the row with the number of degrees of freedom *rounded down*. For very large numbers of degrees of freedom (over 300 or so), it is acceptable to use the row labeled ∞, which is equivalent to the standard normal distribution (Z table).

This table is designed for use with two-tailed tests and confidence intervals. The one-tailed confidence levels presented here are 95%, 97.5%, and 99.5% respectively.

df | 90% | 95% | 99% |
---|---|---|---|

1 | 6.314 | 12.706 | 63.657 |

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 |

50 | 1.676 | 2.009 | 2.678 |

60 | 1.671 | 2.000 | 2.660 |

70 | 1.667 | 1.994 | 2.648 |

80 | 1.664 | 1.990 | 2.639 |

90 | 1.662 | 1.987 | 2.632 |

100 | 1.660 | 1.984 | 2.626 |

110 | 1.659 | 1.982 | 2.621 |

120 | 1.658 | 1.980 | 2.617 |

200 | 1.653 | 1.972 | 2.601 |

∞ | 1.645 | 1.960 | 2.576 |