The Logic of American Politics

The Logic of American Politics by Samuel Kernell and Gary C. Jacobson

Chapter Eleven: Voting, Campaigns, and Elections

Skillset: Scatterplot Charts

This Skillset will help you better understand the concept of scatterplots, which are a type of chart. You've probably seen these charts all over the place but didn't know they had such a fancy name. So what are they, and how do they differ from other charts?

Well, the good news is they're pretty similar in most respects to charts we've already discussed in Chapter 3's (Federalism) Skillset. If we look at the chart from page 438 of your text, we see that there's an x-axis that goes left to right and a y-axis that goes up and down, and you can find the value of individual points by tracing down to the x-axis and left to the y-axis. All pretty standard stuff. So what good is a scatterplot? Scatterplots are good when you've got a lot of datapoints (you'll sometimes hear them called a "cloud of points") but are especially good when you're trying to pin down a relationship between the things on your x- and y-axes. By plotting points, you often gain intuition about whether you're looking at a direct relationship, an inverse relationship, or no relationship (see chart).

Direct Relationships: Follow the Leader
Let's start off by going right to a direct relationship because that's actually what the figure from the book shows (until we start messing with it). If we've got a direct relationship, it means that as one of our values goes up, the other generally goes up, too. In the case of our figure, we see that as the Democrats increase their advantage of quality challengers over the Republicans (corresponding to larger values on the x-axis), they boost the percentage of House seats they win. Note that the direct relationship also implies that decreases in one value are associated with decreases in the other.

Inverse Relationships: What Goes Up Means Something Else Is Going Down
So what's an inverse relationship? The above headline says it all (which is why it's so very, very long). Basically, as one value goes up, we expect the other one to go down. If our figure presented an inverse relationship between candidate quality and change in House seat share, it would look something like this.

No Relationship: Strikeout
You don't see these sorts of figures very much in the textbooks because they indicate we haven't really figured out what's going on yet. In this case, if you had a limited change in challenger quality but a huge change in outcomes or a huge change in challenger quality but a limited change in outcomes, the charts would look something like this.

You Say Inverse, I Say Direct: Let's Call the Whole Thing Off?
So if all of what we've been talking about relies on judgments of how figures look, how do we prevent our analysis from evolving into arguments like "I'll know an inverse relationship when I see it?" Although we won't go into it here, folks called statisticians have developed ways to empirically determine (a) the angle of the line that "best fits" the shape of the scattered points and (b) exactly how good (or bad) that fit is. The simplest way they do this is through something called "ordinary least-squares regression," but even typing that made my fingers hurt. So we'll just pretend I didn't say anything and move on.

Comprehension Questions