Tue June 5, 2012
Great Time To Be A Political Stat Nerd
As a political scientist, I am sort of a “number cruncher” who likes to empirically test what we know about human behavior through statistical analysis. With the election results certified by the N.C. Secretary of State, I ran some statistical analyses on the county-wide results to see what, if anything, might explain things from the May primary.
One key question that interested me, along with many others, was “what might explain how a county voted for the constitutional amendment regarding marriage?” A number of guesses—partisan affiliation, race, the urban vs. rural divide—were contemplated during the run-up to the amendment vote.
Now that we have the final numbers, I ran a linear regression analysis on the county results. For the non-statistics nerds out there, an explanation of linear regression might be helpful:
Linear regression is a method of organizing data. Sometimes it is appropriate to show data as points on a graph, then try to draw a straight line through the data. Linear regression is an algorithm for drawing such a line. … R-Squared is a measure of how well the data points match the resulting line.
“a statistical technique used to make predictions based on available characteristics. In polling models, regression analysis will often try to predict the likelihood of support for a policy or candidate based on information about religiosity, socio-economic status, previous election results, etc. For example, to predict the level of support for a Democratic candidate across states, we might use variables like the religious identity of the state (the percentage of Catholics, for example), the amount of money spent by the candidate, the percent of the vote received by the Democratic in the previous election, the percent of the population that is African-American, the mean income, and the percentage of residents that live in cities.”
So, if you want to explain why something happened (say, why a county cast their vote for an amendment), think about what factors might influence that vote; and then hope your factors will add up to explain as much of the vote as possible (the R-Squared reference in the first description, which goes from 0.0 to 1.0—with 1.0 being everything is explained perfectly by the factors you have).
Now, if you take the percentage of votes cast for the amendment in all 100 counties in the state (what you are trying to explain) and line them up from least to the most support, you would see something that looks like Figure 1:
Now, the question is: what makes these dots go from 21 percent in Orange County to 89 percent in Graham County?
That’s what linear regression will hopefully let us know.
In running a linear regression model, you have to try and quantify (express in numbers) the various factors that you think would influence those dots in going from 21 percent to 89 percent.
Here are a couple of factors I thought might be influential:
- Was the county an urban or rural county?
- What was the racial make-up of a county? Would an increase in black registered voters in a county have an influence on the votes cast for the amendment?
- We know that polls showed Democrats moving against the amendment while Republicans were very much in favor of it (so the more GOP registered voters there are in a county, the more we would expect a vote for the amendment). What about independents (read, registered unaffiliated voters)—would a county that had higher percentages of unaffiliated registered voters have voted for or against the amendment?
- Would a county that saw increased votes either against Obama or against Romney in their party primary have any influence on whether that county voted for or against the amendment? Here my reasoning is that if Democrats or Republicans were not voting for their presumptive nominees, would that have any influence on the vote for or against the amendment?
In running the analysis, I used the percentage of the “for” vote in a county (for the stats geeks out there, the dependent variable).
For the various factors that might influence the “for” vote (read, independent variables), I used the following: whether a county was urban or not, the percentage of black registered voters, the percentage of registered Republican voters, the percentage of registered unaffiliated voters, and the percentages of “no preference” in the Democratic primary and the percentage vote for “anyone but Romney” in the county.
When all is said and done, here’s what I found: all of the variables were statistically significant—meaning that with 95 percent confidence, we could say the independent variables had an impact on the county’s vote for the amendment.
And, more interestingly, the adjusted R-Squared (which indicates how much of the county’s vote was explained by these factors) was 0.81—meaning that 81 percent of a county’s vote for the constitutional amendment could be explained by six factors (listed in order of influence):
- The more a county saw Democratic voters voting “no preference” against President Obama, the more likely it was to vote for the amendment (and this was the most influential variable of all);
- The county’s percentage of registered GOP voters—the more registered Republican voters a county had, the more likely it was to vote for the amendment;
- The percentage of unaffiliated registered voters—but interestingly, the more unaffiliated registered voters a county had, the less likely it was to vote for the amendment;
- the percentage black registered voter—the more registered black voters a county had, the more likely it was to vote for the amendment;
- whether a county was urban or not (meaning: all things being equal, when you go from a non-urban county to an urban county, the less the vote for the amendment); and,
- Those who voted for someone other than Romney on the GOP ballot—meaning that in counties that voted for someone other than Romney were more likely to vote for the amendment.
Two things really amazed me: one, that over 80 percent of a county’s vote could be explained using those six factors, and second, that the “no-preference” vote (meaning, Democrats voting no-preference against their unopposed president) had the most impact.
I’ll be doing more analysis (in particular, looking at the issue of black voting patterns in rural and urban areas), but many commentators said that the conservative rural side of North Carolina’s personality came roaring out for the amendment — and now we have a pretty good idea what makes up that side of the Tar Heel’s political soul.