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16.6: Critical Values for Dixon's Q-Test

  • Page ID
    220803
  • 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 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 critical values for Q here are for a single outlier, Q10, 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 Qexp 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.

    Table \(\PageIndex{1}\): Critical Values for Dixon's Q-Test
    \(\frac {\alpha \ce{->}} {n \ce{ v }}\) 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

     

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