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The chi-square statistic is used to test goodness of fit, homogeneity of proportions, and independence. Although the first two uses were at least somewhat new to my students, the concept of independence was not. This article begins by reviewing the use of the chi-square statistic for goodness of fit and then looks at how I have helped my students relate their earlier work with independence to the use of the chi-square statistic.

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Many people know very little about finance. Few people, for example, can answer a finance question as natural and useful as, If I set aside $100 a month for 20 years at 5 percent annual interest, how much