OVERVIEW

Once we have set up a hypothesis test and collected data, how do we evaluate what we have found? In this chapter we provide hands-on discussions of the basic building blocks used to make statistical inferences about the relationship between two variables. We deal with the often misunderstood topic of “statistical significance” – focusing both on what it is and what it is not – as well as the nature of statistical uncertainty. We introduce three ways to examine relationships between two variables: tabular analysis (crosstabs), difference of means tests, and correlation coefficients. (We will introduce a fourth technique, bivariate regression analysis, in Chapter 9.)

BIVARIATE HYPOTHESIS TESTS AND ESTABLISHING CAUSAL RELATIONSHIPS

In the preceding chapters we introduced the core concepts of hypothesis testing. In this chapter we discuss the basic mechanics of hypothesis testing with three different examples of bivariate hypothesis testing. It is worth noting that, although this type of analysis was the main form of hypothesis testing in the professional journals up through the 1970s, it is seldom used as the primary means of hypothesis testing in the professional journals today. This is the case because these techniques are good at helping us with only the first principle for establishing causal relationships. Namely, bivariate hypothesis tests help us to answer the question, “Are X and Y related?” By definition – “bivariate” means “two variables” – these tests cannot help us with the important question, “Is there some confounding variable Z that is related to both X and Y and makes the observed association between X and Y spurious?”