Early today, I wrote a diary about this subject that ultimately made the argument that Clinton does not do better in closed verses open primaries and in fact, according to the mean of both groups, does better in open primaries.  dbrown correctly argued in response that I had omitted the possibility of other variables that could affect the means and bias the data.  So, this is another attempt at the same argument - with a variety of controls in place.

Here's the data from the original post:

"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)."

Awesome; that's all we need, right?  Not exactly - this data is useful only if we can sufficiently prove that only variables are not being mistakenly forgotten.  So, we need to recycle the null hypothesis:

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 in two demographically similar areas that utilize the two different systems.

How might we prove that one?  Simple, we need to find two demographically similar areas (not necessarily states) with similar turnout voting at the exact same time under two systems: one open primary and one closed primary.  Super Tuesday is the best time frame to pull from to control for the fact that John Edwards is not longer in the race, minimize the chance of Obama momentum skewing the data and increase the possibility of sampling multiple areas.

Now, the moment of truth - which area did I chose? Drum roll...The Ozarks!  Luckily, the entire area voted during Feb. 5, shares a unique, interstate cultural unity and has two open primaries and one closed represented.  To ensure relatively even distribution between populations in the three states one major city is included in each grouping of counties: Joplin, MO; Fayetteville, AR and Greene County, OK (excluding Tulsa County).

So, to give you specific areas and some numbers:

Arkansas: Benton, Carroll, Crawford, Franklin, Madison and Washington Counties.  
Combined Democratic Vote: 41,308
Mean Clinton Percentage of Vote: 75.165% (normal only when divided into population size categories - small towns verses large towns)

Missouri: Barry, Christian, Lawrence, McDonald, Newton, Stone and Tanny Counties.
Combined Democratic Vote: 34,551
Mean Clinton Percentage of Vote: 63.375% (nearly normal - see statistics below)

Oklahoma: Adair, Craig, Cherokee, Delaware, Mayes, Nowata, Ottawa and Rogers counties.
Combined Democratic Vote: 37,621
Mean Clinton Percentage of Vote: 64.75% (nearly normal)

Actual Individual State States:

AR Stats:
No. of observations: 6
Minimum: 68
Maximum: 82
Range: 14
Mean: 75.167
Std. deviation: 6.4936 (Absolutely useless unless we want to discuss large cities verses small cities in the three states)

MO Stats:
No. of observations: 8
Minimum: 58
Maximum: 68
Range: 10
Mean: 63.375
Std. deviation: 3.2486 (Skewed slightly toward the left)

OK Stats:
No. of Observations: 8
Minimum: 60
Maximum: 69
Range: 9
Mean: 64.75
Std. deviation: 2.6049 (Skewed slightly toward the left)

MO and OK are our best sets of data despite being a little skewed, and as before, their means are far too close to have any level of significance.  Thus, there is insufficient evidence to reject the null hypothesis.

Speaking in the most general terms without statistics getting in the way, it appears that OK's closed primary slightly benefited Clinton verses MO's open primary.  However, while I controlled for a variety of factors, there's no realistic way to replicate exact demographics or populations without creating a hypothetical control state that was simultaneously running two systems at the same time with the two primaries running independently of each other.  Some might argue that Texas will be a good model to test, but I contend that since Texas allows early voting, it's not a truly reliable system to use.

Sorry again, Clinton supporters. I tried to find something, but I really didn't have a lot of hope since party crossover has never been successfully attributed to a candidate's loss.