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# Hack #16. Identify Unexpected Relationships

If you want to verify whether a relationship you have observed between two variables is real, you have a variety of statistical tools available. A problem arises, though, when you have measured these variables without much precision, using categorical measurement. The solution is a two-way chi-square test, which, among other things, can be used to make unsubstantiated assumptions about the characteristics of people you have just met.

"Identify Unexpected Outcomes" [Hack #15] used the one-way chi-square test to make police scheduling decisions based on whether equal numbers of crimes were committed at different times of day. That tool works well to solve any analytical problem when:

• The data is at the categorical level of measurement (e.g., gender, political party, ethnicity).

• You want to determine whether there is a greater frequency of scores in certain categories than would be expected by chance.

You face another common analytic problem when you're curious to know whether two categorical variables are related to each other. Relationships between categorical variables can be examined with the handy two-way chi-square test.

### Tip

If two variables are measured at the interval level (many scores are possible along a continuum), the correlation coefficient [Hack #11] is the best tool to use, but it doesn't work well with categorical measurement.

We make assumptions all the time about relationships between these sorts of variables. Many of our common ...

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