Statistics for People Who (Think They) Hate Statistics

by Neil J. Salkind

Almost every statistical test that we’ve covered so far in Statistics for People Who (Think They) Hate Statistics assumes that the data set with which you are working has certain characteristics. For example, one assumption underlying a t test between means is that the variances of each group are homogeneous, or similar. And this assumption can be tested. Another assumption of many parametric statistics is that the sample is large enough to represent the population. Statisticians have found that it takes a sample size of about 30 to fulfill this assumption. Many of the statistical tests we’ve covered so far are also robust, which means that violating one or more assumptions just a little doesn’t hurt the validity of analyses a lot. But what do you do when these assumptions may be violated? The original research questions are certainly still worth asking and answering. That’s when we use nonparametric statistics (also called distribution-free statistics). These tests don’t follow the same “rules” (meaning they don’t require the same, possibly restrictive assumptions as the parametric tests we’ve reviewed). The use of nonparametric tests also allows us to analyze data that come as frequencies, such as the number of children in different grades or the percentage of people receiving Social Security. And very often, these variables are measured at the nominal (or categorical) level. (See Chapter 2 for more information about nominal scales of measurement.) For example, if we wan...