Chi-square Tests

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Chi-square tests can be used to test the association between two classifications (classifier variables) of a set of counts or frequencies. This two dimensional arrangement is commonly displayed as a contingency table or cross classification where rows represent one variable and columns represent the other. The null hypothesis is that there is no association between the two variables.

The main assumption of this group of methods is that for any observation it can only belong to one cell in the contingency table.

Row and column totals (marginal totals) are used to predict what count would be expected for each cell if the null hypothesis were true. A test statistic which is approximately distributed as a chi-square variable is calculated from the observed and expected frequencies. The larger the test statistic (for given degrees of freedom) the more likely there is to be a statistically significant association between the two variables.

This group of methods is intended for medium to large samples. Cochrane's rule states that no expected frequency should be less than 1 and at least 80% of expected frequencies should be greater than 5 (Bland, 2000).