As some of you might know, I've been crunching numbers and by chance saw some interesting things in the tendencies of voting electorate - not surprisingly, most people either found this uninteresting or simply don't like math.  Frankly, me either, but I was friends with a Director of Institutional Research awhile back who convinced me you can enjoy it if the results mean something to you.  That inspired me to continue working with this data.

A question I see raised a lot is that of Obamacans: Republicans and independents registering as Democrats to vote for Obama.  Is there any significance?  Well, being a fan of statistics, I'm going to search for a statistical significance.  My null hypothesis (for those other nerds out there) is that there is no significance in the 2008 Democratic primaries that can be attributed to party crossover.

But how can we know?  Simple, we need to look at open verses closed primaries (I can't work with caucus data because they're inherently skewed and fail to provide numbers verses percentages) in which Clinton and Obama are in direct competition (to try to avoid any significant Edwards, Biden, Dodd or Richardson data mixing in).  That leaves us with Super Tuesday, the Potomac Primary and the others that have come since Edwards dropped out.  The Null Hypothesis in this case is that there will be no significant difference between open and closed primaries in which Clinton and Obama go head to head as evidenced by mean Clinton vote percentages.

OK, so here are our states arranged by open and closed primaries with open primaries listed first (Clinton percentage is given afterward in brackets):

Open Primaries (Super Tuesday Forward):

• Alabama [47.1%]
  
• Arkansas [69.7%]
  
• California (independents vote for whoever) [51.9%]
  
• Georgia [31.3%]
  
• Illinois (is weird but effectively open) [32.9%]
  
• Massachusetts [56.2%]
  
• Missouri [48%]
  
• New Jersey (primaries are closed to opposite parties; independent free for all) [53.8%]
  
• Tennessee [53.85%]
  
• Utah (independent free for all) [39.2%]
  
• Virginia [36.7%]
  
• Wisconsin [40.7%]

Closed Primaries:

• Arizona [50.5%]
  
• Connecticut [46.6%]
  
• Delaware [42.3%]
  
• DC [24.0%]
  
• Louisiana [35.6%]
  
• Maryland [36.7%]
  
• New York [57.4%]
  
• Oklahoma [54.8%]

Ok, now to calculate the means and SDs of each group.

Open:
No. of observations: 12
Minimum: 31.3
Maximum: 69.7
Range: 38.4
Mean: 46.779
Std. deviation: 11.158 (Skewed toward Arkansas)

Closed:
No. of observations: 8
Minimum: 24
Maximum: 57.4
Range: 33.4
Mean: 43.488
Std. deviation: 11.147 (Skewed toward DC)

Ok, they're not nearly normal (they're actually skewed in opposite directions), but it's fairly obvious that there isn't a huge difference.  If we were to pretend that these represented nearly normal distributions and ran an analysis of variance (ANOVA) we would get as a final score: .7685.  (Findings are generally considered significant when the score is lower than .05).

There is not enough evidence to reject the null hypothesis. Now, as dbrown points out below, there is an omitted variable bias which I will get at tomorrow (and include this entry with the updated one). Basically, the problem is that I'm comparing states with no control. I probably won't be able to fix that, but I'm going to think through how to get at it tonight. Suggestions would be appreciated.

Sorry fellow Clinton supporters, it looks like it makes no difference and that she's doing better in open primaries.  Caucuses might still be a valid battle to fight, but unfortunately, this is not the line of argument we want anymore.  I'll do an analysis of Obama's momentum tomorrow to see if we can find anything there.