In the previous sections, all of the methods we derived were based on making some sort of underlying assumptions about the data − for example, "the data are normally distributed," or the "population variances are equal." How do we go about using our data to answer our scientific questions if the assumptions on which our methods are based don't hold? That's what we'll tackle in this section. Specifically, we will:

• learn how to use the chi-square goodness of fit test to test whether random categorical variables follow a particular probability distribution
• learn how to use the chi-square test for testing whether two or more multinomial distributions are equal
• learn how to use the chi-square test to test whether two (or more) random categorical variables are independent
• define, determine, and use order statistics to draw conclusions about a median, as well as other percentiles
• learn how to use the Wilcoxon test to conduct a hypothesis test for the median of a population
• learn how to use a run test to test the equality of two distribution functions
• learn how to use a run test to test for the randomness of a sequence of events
• learn how to use the Kolmogorov-Smirnov goodness-of-fit test to test how well an empirical distribution function fits a hypothesized distribution function
• learn how to use resampling methods to find approximate distributions of statistics that are used to make statistical inference