Reasons to identify one variable as the response and another as the explanatory.
A variable is a quantity or characteristic that varies from one person to another, or more generally, from one unit of observation to another. There are two distinct types of variables: quantitative (numeric) and categorical (labels/words/etc.).
There’s another distinction to be made about variables, which is not about the type of the variable itself but the role the variable will play in the statistical methods we use to describe a situation of interest and the relationships among the variables involved. This distinction is between the response variable and the explanatory variables.
Think about how we describe human relationships. For example, consider two women: Eliana and Rabia. One possible relationship: Eliana is Rabia’s aunt. Another possible relationship: Rabia is Eliana’s niece. As you know, these two relationships are exactly the same thing, just expressed differently. Each of the expressions involves a reference person, that is, a person with respect to whom the relationship word (“aunt”, “niece”) is used.
Similarly, when we describe a relationship between two variables, it’s helpful to consider one variable to be the reference. We describe the pattern of the other variable with respect to the first variable. Now phrases like “one variable,” “other variable,” and “first variable” are ambiguous. It’s hard to keep track of which variable is which. So, to simplify things, we identify one of the variables as the response variable and the other as the explanatory variable. Then, when describing the relationship, it’s always a matter of describing the response variable with respect to the explanatory variable. So, if Response and Explanatory were the names of the two women, the relationship would always be stated as “Response is the ______ of Explanatory” or “As Explanatory changes by ____, Reponse changes by ____ .”
How to decide which variable should play the role of the response and which the explanatory? There’s no absolute rule; generally you can describe relationships either way, keeping in mind that the statement of the relationship (“aunt”, “niece”) will depend on which is which. Here are some rules of thumb.
Most statistics books have traditionally been written without making much use of the concepts of response and explanatory variables. Mathematicians, in particular, seem to like to talk about “bivariate relationships” and to use statistics, like the correlation coefficient, that are the same whichever order you put the variables in. But most two-variable statistics – for instance the slope of a regression line, or the difference between two proportions – depend on the order of the variables. As such, it’s helpful to be clear indicating the particular variable you want to predict or that’s being caused, or that you have a particular interest in.
And, when there are more than two variables, it’s particularly helpful to distinguish between the single response variable and the multiple explanatory variables (which are sometimes called covariates or confounders.)
There are two main types of variables: quantitative and categorical. Strickly as a matter of logic, there are four possible ways that these two types can be arranged as the response and explanatory variables. It’s important to know this, since the choice of an appropriate statistical technique should be shaped by the types of the response and explanatory variables.
|Response||Explanatory||Statistical technique||Little App|
Depending on where you are in you statistics course, you might have not yet encountered one of these techniques or the other.
We’re going to give you a few pairs of variables. For each pair, you are to:
View the data with Regression, using the Little_app_Regression. This will let you readily see which type each variable is. (The choice of one variable as response and one as explanatory isn’t critical here, since the reverse choice would generate the same plot but turned around the diagonal to reverse the axes.)
Use the Regression Little App to visualize the relationship. Characterize it as “strong”, “moderate”, “weak” or “none”. You don’t need to give a more detailed description. We just want you to decide whether you can see a clear relationship or not.
In order to give a detailed description of the relationship, or sometimes in order to detect any relationship at all, you need to calculate appropriate statistics on the data. For this, you have to pick the appropriate Little App, which often means that you need to designate one variable as the response and the other one as the explanatory variable. (You can refer to the table above.)
Open up the appropriate Little App from step (3) and turn on whatever statistics you need to describe the relationship. (In some Little Apps, this is on by default.) Give an appropriate English-language description of the relationship. Some of the terms you might use are “upward sloping,” “downward sloping”, “difference of means,” “difference of proportions,” “no relationship.”
Say whether the relationship (if any) shown by the statistics in the Little App is clearer than the relationship you discerned in step (2) from the point plot.
Consider causation. Sometimes causation is a matter of common sense (the rising sun causes the rooster to crow), and sometimes it can be subtle or is a matter of your beliefs about how things work in the world. No matter, it is always one of a small set of possibilities. The simplest to understand are these three:
More subtle, and harder to understand even for professionals, is this one:
Consider prediction. Prediction may or may not relate to causation. (Example: Someone’s post on a dating app may help predict what kind of person they are. But probably the kind of person they are is what causes the post to be what it is.) For the purposes of prediction, (1) the explanatory variable must be known before you find out the response variable. (Otherwise, why bother to predict the response variable? You know it.) And, generally, (2) the explanatory variable will be something that’s relatively easy to measure, while the response is harder to measure. (Example: antigens in blood are relatively easy to measure, while past exposure to a disease is not known.)
These variables are found in the data available through the Little App. For simplicity, we’re using only those categorical variables that have just two levels.
Little Apps, Data set:
Little Apps, Data set
mosaic, Data set
Version 0.3, 2020-09-15