Chi-Square Corner Cells Test: Two Wrongs Don’t Make a Right

Paul R. Yarnold

Optimal Data Analysis, LLC

For an application involving two ordered attributes the chi-square four corner cells (CSFC) test is described as a “quick preliminary test” in lieu of factorial ANOVA. In this procedure a 2 x 2 contingency table is constructed using only the highest and lowest possible values of both measures: chi-square is used to obtain p, and phi to estimate the correlation between variables. The example used to illustrate this methodology violates two crucial assumptions underlying chi-square.

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