Chi-Squared Test

Global Algorithm - Multi-Dimensional algorithm

Chi-Squared Test algorithm is used to analyze a correlation relationship between two attributes. The \(\chi^2\)-value for attributes \(A\) and \(B\) is computed as:

\[\chi^2 = \sum_{i=1}^{N} \sum_{j=1}^{M} \frac{(o_{ij} - e_{ij})^2}{e_{ij}} \, \text{,}\]

where \(o_{ij}\) is the observed frequency of the joint event of pair \((A_i, B_j)\) and \(e_{ij}\) is the corresponding expected frequency.

Input Parameters

Parameter	Type	Constraint	Description	Remarks
\(A\)	\(A = \{a_i\}, i = 1, 2, \ldots, N\)	\(N \in \mathbb{N}\)
\(B\)	\(B = \{b_i\}, i = 1, 2, \ldots, M\)	\(M \in \mathbb{N}\)
\((e_{ij})\)	\((e_{ij}) \in \mathbb N^{N \times M}\)

Output Parameters

Parameter	Type	Constraint	Description	Remarks
\(\chi^2\)	\(\chi^2 \in \mathbb R\)

Tool Support

• Matlab

  For details refer to the online documentation of the function ‘chi2gof’.

Single Steps using the Algorithm

• Data Discretization with Chi-Squared Test
• Outlier Detection with Chi-Squared Test
• Redundancy Detection with Chi-Squared Test

References

• P.E. Greenwood, M.S. Nikulin, A guide to chi-squared testing, Wiley, New York, 1996.