Skip to main content
Chemistry LibreTexts

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 Qij 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 Q10, where

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

The suspected outlier is rejected if Qexp 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-Test of a Single Outlier (Q10)

α

n

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