z, t, F, and r all come from a family of tests called parametric tests. Parametric tests should only be used when assumptions about the population, about the parameters, are met. In contrast, nonparametric tests don’t have to meet the same assumptions. There are two situations where nonparametric tests are used:

Nonparametric tests are desirable because they are less restricted by assumptions. However, this comes at a cost—nonparametric statistical tests are usually less powerful than parametric tests. This is a problem because a test with less power is less likely to succeed in rejecting the null hypothesis, the usual goal of hypothesis testing. Also, nonparametric tests work with nominal- or ordinal-level data, not interval/ratio. Nominal- and ordinal-level numbers contain less information than do interval- and ratio-level numbers and this can make it harder to find an effect.

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To see how less information means less power, imagine a medication that is only slightly effective in reducing fever. This small effect would be more evident if the temperature were measured to a hundredth of a degree than simply measuring whether or not a person has a fever. The more precisely a researcher can measure the outcome, the greater the ability to find an effect.

Statisticians prefer parametric tests because of their greater power. But, when parametric tests can’t be used, when their assumptions are not met, or when the outcome variable is nominal or ordinal, it is time for a nonparametric test. Our primary focus in this chapter will be two different versions of the most commonly used nonparametric test, the chi-square. (The “chi” in chi-square is abbreviated with an uppercase Greek letter, χ, pronounced “kai,” so chi-square is written χ².) Then, at the end of the chapter, the nonparametric version of a Pearson r and nonparametric version of an independent-samples t test are explored.