Chapter 7 Variables Associations

Statistical inference is hardly only a matter of estimating single variable means and proportions, and of constructing confidence intervals around them. Rather, quantitative sociologists (and other social scientists), like all scientists trying to explain the world around them, study associations between variables. Does class attendance affect students marks? Are male professors praised more highly in student evaluations than female professors? Are children of more educated parents more likely to earn post-secondary degrees? Does abstinence-only sex education lead to higher teen pregnancy (and abortion) rates? Are rich people more likely to vote? Are religious people more likely to espouse more socially conservative values? Does playing violent video-games increase incidence of real-life violence and crime? Does race/ethnicity affect one’s educational attainment and/or income?

All of these questions reflect variable associations. Every time we hypothesize that two characteristics are related, or think that something causes change in another, every time we ask why something is the way it is and what makes it to be that way, we already speak the language of variable associations, even without acknowledging it as such.

While we can use various research methods to provide answers to these questions, quantitative analysis can shed a unique light on them due to its grounding in probability theory and the generalizability that stems from it. Of course, like any research method, using statistics for inference particularly in the social sciences has its problems and limitations. Thus, we have to be very careful in not overstating conclusions and to always qualify our findings based on the specific way we have operationalized our variables (i.e., exactly how we have measured a concept), as well as depending on our sample size, the statistical assumptions we’ve made, the uncertainty we’re dealing with, etc., etc.

While most real-life research involves many variables at the same time, examining multivariate associations like that are beyond the scope of this book. Instead, in the remainder of this textbook I focus on bivariate associations — associations between two variables. Still, keep in mind that while this is a necessary first step when just entering the world of variable associations, this hardly ever (rather never) reflects reality in any way: the social world is too complex for there to only be one and only one cause to something we observe and that we’re trying to explain. I’ll remind you of this fact frequently as one of the biggest mistakes you could probably make with inference is to assume that the variable on which you have chosen to focus is the only one associated with (or worse, affecting) another variable of interest.

In short, from now on we work with two variables in order to understand how associations work in principle, not because inference based on two variables reflects reality (neither in general, nor in real-life research).

The chapter starts with introducing what we mean by associations between variables, and with distinguishing between statistical and causal associations. In a brief return to descriptive statistics, you’ll then learn how to describe bi-variate associations. At the end, I’ll bring you back to the theory (and practice) of statistical inference, specifically to hypotheses and hypotheses testing, as this is again what allows us to move from sample descriptions to generalizable conclusions about the population of interest. Finally, I provide a brief discussion of the inevitability of uncertainty through introducing you to the two types of errors of inference.