# Chi-Squared Test¶

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

Single Steps using the Algorithm

References

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