# Appendix 06: Critical Values for Dixon’s Q-Test

- Page ID
- 6642

The following table provides critical values for *Q*(α, *n*), where α is the probability of incorrectly rejecting the suspected outlier and *n* is the number of samples in the data set. There are several versions of Dixon’s Q-Test, each of which calculates a value for *Q*_{ij} where *i* is the number of suspected outliers on one end of the data set and *j* is the number of suspected outliers on the opposite end of the data set. The values given here are for *Q*_{10}, where

\[Q_\ce{exp} = Q_{10} = \mathrm{\dfrac{|\textrm{outlier's value} - nearest\: value|}{largest\: value - smallest\: value}}\]

The suspected outlier is rejected if *Q*_{exp} is greater than *Q*(α, *n*). For additional information consult Rorabacher, D. B. “Statistical Treatment for Rejection of Deviant Values: Critical Values of Dixon’s ‘*Q*’ Parameter and Related Subrange Ratios at the 95% confidence Level,” *Anal. Chem.* **1991**, *63*, 139–146.

α⇒ | 0.1 | 0.05 | 0.04 | 0.02 | 0.01 |
---|---|---|---|---|---|

⇓n |
|||||

3 | 0.941 | 0.970 | 0.976 | 0.988 | 0.994 |

4 | 0.765 | 0.829 | 0.846 | 0.889 | 0.926 |

5 | 0.642 | 0.710 | 0.729 | 0.780 | 0.821 |

6 | 0.560 | 0.625 | 0.644 | 0.698 | 0.740 |

7 | 0.507 | 0.568 | 0.586 | 0.637 | 0.680 |

8 | 0.468 | 0.526 | 0.543 | 0.590 | 0.634 |

9 | 0.437 | 0.493 | 0.510 | 0.555 | 0.598 |

10 | 0.412 | 0.466 | 0.483 | 0.527 | 0.568 |