7.2 Describing and Examining Bivariate Associations

Before we can get to establishing statistical associations between two variables, we need to know what we are looking for (or at), as it were. Social research, especially deductive reasoning, usually starts with an idea — a research question if you will — which is frequently grounded in an empirical observation of two variables’ possible association (e.g., “Hey, it seems like all vegetarians/vegans I know tend to be well off. I wonder if income and vegetarianism/veganism are related…”) Then, if one is quantitatively inclined, a random sample can be used to “check” for such an association.

Most people conceive of that “check” as a one-step process but it actually involves two steps frequently undertaken in quick succession, so much so that to appear singular. As this is your introduction to the topic, we will take the steps slowly, one after the other.

The first step is the descriptive part: given our sample data, does it look like there is an association between the two variables of interest? This step concerns the data obtained through our sample, i.e., it describes our sample, and only our sample.

The second step is the inferential part: assuming that it looks like there is an association between the two variables of interest in the sample, is this association generalizable to the population? That is, is this a “real” association reflecting the population or is it something we have observed in our sample due to the vagaries of random chance? This is the part where we formulate and test hypotheses in or order to be able to make generalizable conclusions. We will focus on that starting with this chapter until the end of the book.

We hereby start with the first step, describing bivariate associations (again, based on sample data). What you need for this step is a recollection of the types of variables, and of the fact that we generally use both visual (graphical) and numerical descriptions.

From Chapter 3 (a long while back), recall that we univariately described a variable by 1) graphing its distribution (we used pie charts, bar graphs, and histograms, depending on level of measurement), and 2) providing numerical measures of central tendency and dispersion where applicable; this is how we used to “get a sense” of the variable and what it looked like. Similarly, we can also use graphical and numerical bivariate descriptives, this time depending on the combination of continuous-or-discrete variable type, to “get a sense” of the potential association between two variables and what it might look like.

Recall as well (from Section 1.5 (https://pressbooks.bccampus.ca/simplestats/chapter/1-5-discrete-and-continuous-variables/)), that we can classify variables as discrete and continuous^[1]  (I know, I know – it too has been awhile, but I did warn you eventually we’d get back to that).

From this chapter on, we’ll proceed by considering all three possible bivariate combinations of these: 1) associations between a discrete and a continuous variable^[2], 2) associations between two discrete variables^[3], and, finally, 3) associations between two continuous variables^[4].

I discuss describing each of the three types of associations in the following subsections.