# Chi-square

**DOI:**https://doi.org/10.1007/978-3-319-57111-9_1179

## Definition

The chi-square (χ^{2}) test is a nonparametric statistical method primarily used to evaluate frequency data for categorical variables, by examining the differences between observed and expected frequencies for each category. A one-way chi-square test is used to determine whether differences in frequencies across levels of a nominal variable are due to chance (the null hypothesis) or represent a true difference (the alternative hypothesis). The chi-square is calculated by dividing the squared difference between the observed and expected frequency by the expected frequency in each category and summing the results (*χ*^{2} = Σ((*O* − *E*)^{2}/*E*)). When two variables are involved, a contingency table is constructed, depicting the observed frequency and the expected frequency in each cell. The chi-square is calculated again by, within each cell, squaring the difference between the observed and expected frequency and dividing by the expected frequency, and then summing each result.

## Current...

## Further Readings

- Campbell, I. (2007). Chi-squared and Fisher-Irwin tests of two-by-two tables with small sample recommendations.
*Statistics in Medicine, 26*, 3661–3675.PubMedCrossRefPubMedCentralGoogle Scholar - Cochran, W. G. (1952). The χ
^{2}test of goodness of fit.*Annals of Mathematical Statistics, 25*, 315–345.CrossRefGoogle Scholar - McHugh, M. L. (2013). The chi-square test of independence.
*Biochemical Medicine, 23*, 143–149.CrossRefGoogle Scholar