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The chi-square test refers to a family of statistical tests that have been utilized to determine whether the observed (sampling) distribution or outcome differs significantly from an a priori or theoretically anticipated outcome or distribution. More simply stated, the test is formulated to determine whether the difference observed was due to a chance occurrence. This entry further describes the chi-square test and looks at its basic principles, applications, and limitations.

Although the most common chi-square test statistic is Pearson’s chi-square test, there are other test statistics that exist with the same theoretical foundation including Yates’s chi-square test, Tukey’s test of additivity, Cochran–Mantel–Haenszel test, and likelihood ratio tests. Although the chi-square test has been applied to a plethora of statistical applications, the fundamental utilization has been ...

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