Dixon Type (Q) TestsΒΆ

Local Algorithm - One-Dimensional Algorithm

Dixon Q-test algorithm uses the ratio of the gap between the possible a value outside the region of interest and the next closest value to it to the total range of the data set. This value is compared to a set of statistically determined values for a variety of confidence intervals. The basic formula is as follows:

\[(1) \quad Q^{\text{test}} = \frac{Y_N - Y_{N-1}}{Y_N - Y_1} \, \text{,}\]

and

\[(2) \quad Q^{\text{test}} = \frac{Y_2 - Y_1}{Y_N - Y_1} \, \text{,}\]

where (1) is used to test whether the largest value is a value outside the region of interest, and (2) is used to test whether the smallest value in the data set of length \(N\) is a value outside the region of interest. If \(Q^{\text{test}} > Q^{\text{table}}\), the value in question is a value outside the region of interest.

Input Parameters

Parameter Type Constraint Description Remarks
\(Y\) \(Y \in \mathbb R^N\) \(N \in \mathbb{N}\) Input data sequenceof length \(N\)  
\(Q^{\text{table}}\)     A table of calculated \(Q^{\text{table}}\) values for a specific confidence level, e.g. \(90\) %, \(95\) % or \(99\) %  

Output Parameters

Parameter Type Constraint Description Remarks
\(\hat{Y}\) \(\hat{Y} \in \mathbb R^N\)   Values in the \(Y\) list which are outside the region of interest are marked  

Single Steps using the Algorithm

References

  • D.B. Rorabacher, Statistical Treatment for Rejection of Deviant Values: Critical Values of Dixon Q Parameter and Related Subrange Ratios at the 95 percent Confidence Level, Anal. Chem., vol. 63(2), pp. 139-146, 1991.

    http://pubs.acs.org/doi/pdf/10.1021/ac00002a010

  • S. Walfish, A review of statistical outlier methods. Pharmaceutical Technology, 2006. Retrieved from www.pharmtech.com.