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This is partly to illustrate why when doing analysis of absolute vote counts, logarithms should be taken.

This is the plot of the number of votes received by Clinton and Obama by precinct

And this is the plot of the same data on a log/log scale

I think it is immediately apparent that the log/log plot is better. The line is the result of the following regression:

lm(formula = log(Obama..d) ~ log(Clinton..d), data = NHDemVote,
    subset = Obama..d * Clinton..d > 0)

      Min        1Q    Median        3Q       Max
-1.898487 -0.252916 -0.003111  0.249842  1.066195

                Estimate Std. Error t value Pr(>|t|)
(Intercept)      0.69014    0.10753   6.418 5.41e-10 *
log(Clinton..d)  0.87164    0.01939  44.955  < 2e-16 *
Signif. codes:  0 `*' 0.001 `*' 0.01 `' 0.05 `.' 0.1 ` ' 1

Residual standard error: 0.3756 on 298 degrees of freedom
Multiple R-Squared: 0.8715,     Adjusted R-squared: 0.8711
F-statistic:  2021 on 1 and 298 DF,  p-value: < 2.2e-16

We have met the enemy, and he is us — Pogo
by Carrie (migeru at eurotrib dot com) on Sun Jan 13th, 2008 at 08:46:31 PM EST
So what these graphs are telling us is that Precinct size has no correlation with a tendency to differentially support either Obama or Clinton?  Thus the fact that machine counts are primarily in larger precincts does not explain why they should favour Clinton over Obama with the reverse happening in predominantly smaller hand counted precincts????

If so this would blow the urban vs. rural hypothesis for explaining Clinton's better performance in machine counted votes.

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by Frank Schnittger (mail Frankschnittger at hot male dotty communists) on Mon Jan 14th, 2008 at 09:30:48 AM EST
[ Parent ]
A few thoughts on the urban vs rural thing that suggest to me the argument doesn't even make sense on the grounds many out there argue it:

I believe some of the other models attempted to address it, showing precinct size did not explain things.  And think about it:  What black candidate has ever done better in rural precincts compared with urban ones (with the possible exception of Alan Keyes in his loss to Obama in 2004)?

And why, knowing the demographics Clinton and Obama play well with, would we bet that bigger, wealthier precincts (thought to have machines) would support Clinton?

Be nice to America. Or we'll bring democracy to your country.

by Drew J Jones (pedobear@pennstatefootball.com) on Mon Jan 14th, 2008 at 10:15:59 AM EST
[ Parent ]
Actually, the model here has a slope of 0.87 +/- 0.02, or 7/8. Which means for every 8% fractional increase in Clinton's vote count (say, from 100 votes to 108) one would expect a 7% increase in Obama's vote count (say, from 100 votes to 107). And you start at the lower end with 1 vote for Clinton and 2 for Obama. So, for instance, at 100 Clinton votes you predict 112 Obama votes, but at 1000 Clinton Clinton votes you predict 843 Obama votes.

If you use Obama's vote percentage as a predictor of Clinton's vote percentage you get a regression line that's much closer to 1:1 - this is because it is different to minimize the variation in Clinton's vote given Obama's than Obama's given Clinton. The correlation is 93% (explained to be that high because precinct size correlates with both vote counts) and that should be the geometric mean of the two regression slopes.

In fact, linear regression is not the proper tool here as we're not really trying to use one of them as predictor for the other but rather find a relationship between the two that treats them on an equal footing. Principal component analysis would be much better.

In any case, there seems to be a very slight slope here, favouring Clinton in large precincts.

I think I'm going to replace that chart with one in which Machine vs. Hand counting is represented by different colours.

We have met the enemy, and he is us — Pogo

by Carrie (migeru at eurotrib dot com) on Mon Jan 14th, 2008 at 11:39:19 AM EST
[ Parent ]
Could you do a Clinton vote minus Obama vote (in percentage) regression weighted by total vote in the precint?

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Mon Jan 14th, 2008 at 12:17:07 PM EST
[ Parent ]
As a different test, will you do what was suggested by stormy's link, a cross-check with Dean/Kerry etc. results from 2004? (I could do that, but only tomorrow.)

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Mon Jan 14th, 2008 at 12:19:46 PM EST
[ Parent ]
After the EDA people decided that their voting method assignment was outdated and the one I had been using was up to date, I decided to replace my charts with ones showing the machine counts in red and the hand counts in black. You can see voting method and precinct size correlate very, very well. There are very few "medium-sized" precincts.

Here's a chart of vote percentages:

We have met the enemy, and he is us — Pogo

by Carrie (migeru at eurotrib dot com) on Tue Jan 15th, 2008 at 02:37:00 PM EST
[ Parent ]


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