# 12.4: Critical Values for Dixon's Q-Test

- Page ID
- 319711

The following table provides critical values for \(Q(\alpha, n)\), where \(\alpha\) 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 critical values for *Q *here are for a single outlier, *Q*_{10}, where

\[Q_\text{exp} = Q_{10} = \frac {|\text{outlier's value} - \text{nearest value}|} {\text{largest value} - \text{smallest value}} \nonumber\]

The suspected outlier is rejected if *Q*_{exp} is greater than \(Q(\alpha, n)\). 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.

\(\frac {\alpha \ce{->}} {n \ce{ v }}\) | 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 |