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Outlier Detection with Chi-Squared Test
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:doc:`/SingleStepClassifiers/CausalStep/index`

This step detects outliers in multivariate data by applying the modified version of *Chi-Squared Test*. The basic formula is as follows:



.. math::

   {\chi^2 = \sum_{i=1}^{N} \frac{(o_{i} - E_i)^2}{E_i}}\quad\text{,}

where :math:`o` is the object to be tested and :math:`o_i` is the value of :math:`o` on the :math:`i`\ th dimension. :math:`E_i` is the mean value on the :math:`i`\ th dimension among all objects. The object may be identified as an outlier if the Chi-value is larger than a threshold value.

.. rubric:: Input Parameters

1. Multivariate data including outliers

.. rubric:: Output Parameters

1. Original data with outliers marked

.. rubric:: Workflow

.. image:: workflow.svg


.. rubric:: Algorithm

:doc:`/Algorithms/ChiSquaredTest/index`

.. rubric:: References

- J.\  Han, M. Kamber and J. Pei, Data Mining - Concepts and Techniques, 3rd ed., Amsterdam: Morgan Kaufmann Publishers, 2012.