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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 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