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Goodman Regression
One of the Oldest Techniques used in Redistricting and Voting Rights Litigations
It is very simple to run a Goodman regression procedure. Only two variables at the precinct level are needed: one is the fraction of voters who are from a minority group (e.g., Blacks), and the other is the fraction of votes that are cast for the minority candidate.
Our web app allows you to run Goodman Regression as soon as you submit a csv file containing the above two variables. Furthermore, we have visual tools for you to make sense of the results and avoid making wrong inference at the district level. These tools are available on the menu bar of this web page. You need to register as a member first in order to use these tools.
Take a look at the following three graphs based on the data from the 2008 U.S. Presidential election concerning Terrebonne Parish, Louisiana.
Figure 1
Scatterplot
Each dot is a precinct with fractions of Black voters and votes for Obama.
Note that the color-bar indicates the number of voters in each precinct, from less than 200 (deep blue) to more than 1000 (orange).
The more the Black voters, the higher the level of votes cast for Obama.
Figure 2
Goodman Regression Line
The best fitting line is entered into the graph to show the positive relationship.
Goodman regression examines how the regression line intercepts with the two vertical edges.
The left intercept shows the non-Black support for Obama while the right shows the Black support for him.
Figure 3
Tomography Plot
Each precinct becomes a line in this chart, unlike the previous charts showing dots.
Horizontal lines are close to the bottom showing the less than 25% support for Obama from the non-Black group.
The slanted lines toward the right show that the Black support for Obama were mostly above 60%.
Let's look at the results of Goodman Regression for this election, generated by our free web app.
Here is the original data uploaded to the Goodman Regression page as a csv file:
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Here is the output after uploading the above data as a csv file:
As shown in the above PDF file generated by www.easystates.com, the Black support for Obama was estimated by Goodman Regression as high as 1.025, or 102.5%, which is certainly unrealistic. Thus, it is a major shortcoming of Goodman Regression that it sometimes produces unrealistic results of racially polarized voting. In addition to this problem, Goodman Regression is known as vulnerable to the "the aggregation bias" problem. Basically, it assumes that voters, regardless which precinct they are from, have the same level of probability of voting for the minority candidate, given their own race.
The more advanced techniques that overcome the problems such as aggregation bias are also available on www.easystates.com. Explore our menu for Ecological Infernce (ei) tools.