I thought I would start with a state where I didn't expect to see very much. I was wrong. Let's journey through New Hampshire together, shall we?
New Hampshire is proud to be "first-in-the-nation" when it comes to primaries. Candidates who win New Hampshire have an excellent chance to win the nomination. Based on the 2010 census, there are over 1.3 million people in New Hampshire. According to the Secretary of State's website, over 300,000 people voted in this year's primary. Contrast that with neighboring Maine, whose GOP turnout so far (according to their own website) is under 6,000.
Among the candidates still running for the nomination, recall that Mr. Romney won New Hampshire decisively with 39%. Dr. Paul was 2nd with 23%, and Mr. Santorum edged out Mr. Gingrich with just under 10%.
My focus is to determine if there is a relationship between precinct size and percent of vote for that precinct. Let's first look at the distribution of all 303 precincts in terms of voter turnout.
Notice that a single precinct, because of the nature of primaries (as opposed to caucuses), can handle hundreds to thousands of voters. However, we can see that almost half of the precincts had fewer than 500 voters.
Next, I decided to take a look at some of the raw data. This graph shows the precinct-level data for Dr. Paul and Mr. Romney (I looked at the other candidates but they had uninteresting results and made the picture too messy), where each candidate's support (vertical axis) in that precinct is measured as the percentage of that precinct's total vote. I plotted that against precinct size (horizontal axis).
The straight lines represent the best linear fit of the data for each candidate (using method of least squares). I will be the first to admit that the data do not appear to be all that linear, but it's a start. If we had expected Dr. Paul to do just as well in larger precincts as he did in smaller precincts, then we certainly WOULD NOT be seeing this type of graph.
To better understand this, I decided to plot the difference between the Romney percentage of the vote and the Paul percentage of the vote (vertical axis) against precinct size (horizontal axis).
Although there is quite a lot of "noise" in the smaller precincts, there is a definite trend in Mr. Romney's favor as precinct size increases. Based on a linear relationship between these 2 variables, the correlation is 0.44 (p-value < 0.0001).
So what's the big deal, right? Maybe there are demographic differences between large and small precincts. This is certainly a possibility, and it's a question that we can directly address. I attempted to identify precincts which could be grouped based on geographic location. The largest set of precincts I found were the 12 precincts representing the 12 wards of Manchester in Hillsborough County. When you look at just these 12 precincts, one would hypothesize that the difference between Romney votes and Paul votes would not vary much based on precinct size because these 12 precincts are demographically homogeneous. I was unable to find a map showing how the different wards for Manchester are divided up, but I would assume that Ward 1 is close to Ward 2, Ward 5 is close to Ward 6, etc. Here are the 12 ward numbers, sorted by precinct size from smallest to largest: 5, 3, 11, 4, 7, 9, 10, 12, 2, 6, 8 and 1. In other words, precinct size DOES NOT appear to depend on geographic location in Manchester. Maybe someone in Manchester could better identify if demographic differences exist in the various wards of Manchester. Anyway, here's what the graph for Manchester looks like.
This is very alarming. Here is a county where Mr. Romney beat Dr. Paul by more than 18%. Manchester, which is in that same county, is the largest city in the state of New Hampshire. Inexplicably, Dr. Paul won 2 of the 3 smallest precincts in Manchester, but Mr. Romney doubled Dr. Paul's vote totals in the 3 largest precincts in Manchester.
Am I missing something?