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.