In this chapter we consider data that consist of counts. We begin in Section 5.1 by examining a set of data on the number of females admitted into graduate school at the University of California, Berkeley. A key feature of these data is that only two outcomes are possible: admittance or rejection. Data with only two outcomes are referred to as binary (or dichotomous) data. Often the two outcomes are referred to generically as success and failure. In Section 5.2, we expand our discussion by comparing two sets of dichotomous data; we compare Berkeley graduate admission rates for females and males. Section 5.3 examines polytomous data, i.e., count data in which there are more than two possible outcomes. For example, numbers of Swedish females born in the various months of the year involve counts for 12 possible outcomes. Section 5.4 examines comparisons between two samples of polytomous data, e.g., comparing the numbers of females and males that are born in the different months of the year. Section 5.5 looks at comparisons among more than two samples of polytomous data. The last section considers a method of reducing large tables of counts that involve several samples of polytomous data into smaller more interpretable tables.