==================== Dixon Type (Q) Tests ==================== :doc:/WorkProcessClassifiers/LocalAlgorithm/index - :doc:/WorkProcessClassifiers/OneDimensionalAlgorithm/index *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: .. math:: (1) \quad Q^{\text{test}} = \frac{Y_N - Y_{N-1}}{Y_N - Y_1} \, \text{,} and .. math:: (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 :math:N is a value outside the region of interest. If :math:Q^{\text{test}} > Q^{\text{table}}\ , the value in question is a value outside the region of interest. .. rubric:: Input Parameters +----------------------------------------+--------------------------------------------+----------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------+ | Parameter | Type | Constraint | Description | Remarks | +========================================+============================================+========================================+=====================================================================================================================================================================================================================+=========+ | :math:Y | :math:Y \in \mathbb R^N | :math:N \in \mathbb{N} | Input data sequenceof length :math:N | | +----------------------------------------+--------------------------------------------+----------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------+ | :math:Q^{\text{table}} | | | A table of calculated :math:Q^{\text{table}} values for a specific confidence level, e.g. :math:90 \ %, :math:95 \ % or :math:99 \ % | | +----------------------------------------+--------------------------------------------+----------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------+ .. rubric:: Output Parameters +----------------------------+----------------------------------------------------+------------+-------------------------------------------------------------------------------------------+---------+ | Parameter | Type | Constraint | Description | Remarks | +============================+====================================================+============+===========================================================================================+=========+ | :math:\hat{Y} | :math:\hat{Y} \in \mathbb R^N | | Values in the :math:Y list which are outside the region of interest are marked | | +----------------------------+----------------------------------------------------+------------+-------------------------------------------------------------------------------------------+---------+ .. rubric:: Single Steps using the Algorithm * :doc:/DataPreprocessing/DataCleaning/OutlierDetection/OutlierDetectionWithDixonTypeQTests/index .. rubric:: 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.