Statistical Inference for the Relationship Between Two Variables

Abstract

In this chapter, we continue our discussion of hypothesis testing methods. Here, we only consider hypotheses that are expressed in terms of a relationship between two variables. We start our discussion by focusing on situations where one variable is numerical and the other variable is binary. Typically, the numerical variable, called the response variable, is regarded as the primary variable of interest that captures a specific characteristic of the population that we are investigating. The binary variable, called factor, on the other hand, divides the population into two groups. Therefore, to evaluate the hypothesis regarding the relationship between the numerical variable of interest and the binary variable that defines the two groups, we investigate the difference between the two groups with respect to the characteristic represented by the numerical variable. Next, we discuss situations where both variables are binary. Finally, we talk about the situations where both variables are numerical.