Chi-Square Test (with the help of Collaborative Statistics, Barbara Illowsky, Ph.D., Susan Dean)

A chi-square test (pronounced Ki - square) is used to determine if there is independence of categorical data (i.e. if there an association between two categories of data). It is known by many other names: Pearson chi-square, cross tabulation, contingency table.

Note: There are other tests that use a chi-square distribution.
One is to see if there is a difference between two standard deviations, another is for goodness of fit.
However, the major use of a chi-square test is to determine if a statistically significant difference exists between the observed (or actual frequencies) and expected frequencies (or hypothesized, give the null hypothesis that no association exists) of variables presented in a cross-tabulation or contingency table; the larger the difference between the observed and expected frequency, the larger the chi-square statistic, and the more likely that the difference is significant.