10.1: Independent and Dependent Variables

You’ve undoubtedly seen countless studies that claim to reveal important truths about the world, such as that smoking can cause lung cancer, greenhouse gas emissions can cause higher global temperatures, or orgasms can cure hiccups. Much of the time, scientists try to find a causal factor that links one variable to another: they suspect that the value of a variable A (often called the independent variable, or “i.v.” for short) is a reason, or cause, of a certain value in another variable B (the dependent variable, or “d.v.”).

Just to avoid misunderstandings, when we claim that A causes B, we don’t normally mean that it exclusively causes it, or even that it reliably causes it. There are lots of contributing factors to lung cancer besides smoking, after all; and tons of smokers never develop cancer. We simply mean that A is a contributing factor to B, and that the value of the A variable exerts some, but not total, influence over the value of the B variable.

Importantly, we’re using the word variable here in a different, but related way than we used it in chapters 3, 8, and 9. As we did in chapter 6, we use “variable” here to mean a specific aspect of the objects of a study that can differ, or “vary.” The objects in our study (often people, but sometimes companies, organizations, environments, nations, etc.) each have a value for the variable. Thus if you think of a “per-capita income” variable, you might think of an entire array of floats, each of which represented the average income-per-resident of a single nation.

The variables in question can be from any of the scales of measure from chapter 6. Take the smoking example, with patients as the object of study. We might say that independent variable A is categorical, with values SMOKER and NON-SMOKER. The dependent variable B is also categorical: CANCER and NO-CANCER. The key question is: do people with A = SMOKER also have B = CANCER more often (a higher percentage of the time) than people with A = NON-SMOKER do?

In the greenhouse gas emissions example, our objects of study might be years. Our variables are both numeric, with A (a measure of yearly greenhouse gas emissions, measured in gigatonnes CO₂) on the ratio scale, and B (average worldwide temperature increase/decrease) on an interval scale. Here, the question would be: do years in which A is relatively high typically also have B relatively high? Put another way: do years in which earthlings have released more gas into the atmosphere tend to correspond with years in which the global temperature increased?

And of course, we might have one categorical variable and one numeric. Perhaps our objects of study are American adults, and while our categorical A variable has values DEMOCRAT, REPUBLICAN, OTHER, and INDEPENDENT, our numerical B is yearly income. Our question would be: do adherents of one political party tend to be more wealthy than those of another?

Or, flipping sides, the independent variable A could be numeric while the dependent variable B is categorical. Our objects of study might be high school seniors applying to UMW. Let A be the number of different colleges a student applied to, and B a categorical variable with values ADMITTED-TO-UMW and NOT-ADMITTED-TO-UMW.

The question of interest is here is: do students who apply to more colleges tend to get in to UMW more often?