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

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.

Critical Values for the Q_{10}) |
|||||
---|---|---|---|---|---|

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

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 |