The idiots at “Think Progress’ have the following ignorant post up:
As Press Secretary Robert Gibbs explained to Garrett, it is Chrysler — not the federal government — that is in charge of selecting which dealerships will be closed. Further, as Nate Silver explained in a post that was published just hours after the Examiner’s initial report yesterday, “There is just one problem with this theory. Nobody has bothered to look up data for the control group: the list of dealerships which aren’t being closed.”
Silver explained, “It turns out that all car dealers are, in fact, overwhelmingly more likely to donate to Republicans than to Democrats — not just those who are having their doors closed.” In all, Silver found that “88 percent of the contributions from car dealers went to Republican candidates and just 12 percent to Democratic candidates,” while, the list of Chrysler dealerships being closed “gave 92 percent of their money to Republicans — not really a significant difference.”
As I write this there are 258 comments over there. Not one of the references the hypergeometric probability distribution, which indicates that not one of their commenters knows what he or she is talking about. Short version: you have a urn full of black and white balls. You take a number of balls out, and don’t put them back in before taking other balls out. If you know the number of balls of each color in the urn, then you can calculate the probability that, by random chance, you will draw out ‘x’ white balls in ‘n’ draws from the urn.
There are 3000 Chrysler dealerships. 750 got told they’re getting closed. Using Nate Silver’s numbers, there are 2640 “Republican” dealerships, and 360 “non-Republican” ones. Of those dealerships, 690 R and 60 non-R dealerships were closed.
Using R, we can calculate the probability that, by random chance, 60 or fewer non-R dealerships would be closed out of 750
phyper (60, 360, 2640, 750)
Unfortunately for Nate, and for the TP big talkers, the result is 3.671535e-05. Or 9 in 250,000.
So yes, that is a significant difference.
Some of the posters over at Nate’s are claiming 3500 dealerships. Keeping all percentages the same, we get
phyper (70, 420, 3080, 875)
That takes the chance down to 8.738693e-06. Less than 9 in 1,000,000. IOW, fail.
Greg's Weblog 
May 29, 2009 at 12:54 am |
Nate Silvers numbers are just a quick check of donating R and D with 4 “auto dealer” and similar name tags.
People first complained that the dealership closings are 92% repub.
He said we should try to figure out what the dealerships overall donations are.
So he decided to do a quick and dirty and find overall donating from all dealers, just as a background comparison group. His numbers are not just Chrysler dealers.
His figure was close to 92%, it was 88%.
Add in the billion unknown variables on top of all this, is all we have is a story were people complained that 92% of donations from closed dealers were republican, despite there being no reason to believe any foul play.
Nates 88% is just a quick reference number that shows why 92% shouldn’t stand out much on it’s own, vs most other job types where that would be huge.
So far, there is no evidence at all that the 92% is high, or that is it low for that matter. It could just as easily be that 94% of Chrysler dealers lean republican…. have just as much evidence to that as 88%.
We also don’t even have a shred of evidence that the White House picked the dealers, and all reasonable assumptions would be to the contrary and Chrysler picked them.
June 15, 2009 at 10:51 pm |
Orin,
The problem with Nate’s reply is that the numbers he gave do not prove what he says they prove. And he knows that.
The fact that he went all snarky and smugly self-righteous, while making a post that every person who knows anything about stats knows is complete crap, marks Nate Silver as being a dishonest left-wing political hack.
Is Nate’s data fuzzy? Fine. Then he should have stated at the beginning of his post that he was engaging in gratuitous hand-waving, and couldn’t really say anything definite. If you see where he said that in his post, please do point it out.
What I read was Nate saying “these numbers clearly show the conservatives are wrong.” So don’t give me grief for treating his numbers as good, before showing that they don’t say what he says they say.
May 29, 2009 at 7:20 am |
[…] Greg Q had run the numbers once again, using Nate Silver’s: The idiots at “Think Progress’ have the following ignorant post up: As Press Secretary Robert Gibbs explained to Garrett, it is Chrysler — not the federal government — that is in charge of selecting which dealerships will be closed. Further, as Nate Silver explained in a post that was published just hours after the Examiner’s initial report yesterday, “There is just one problem with this theory. Nobody has bothered to look up data for the control group: the list of dealerships which aren’t being closed.” […]
May 29, 2009 at 9:09 am |
Greg, your problem is that this assumes that every dealer is either a republican or democratic donor, ignoring the probably that some (or most?) donors are apolitical. Please see my post on 538 on how this may impact the numbers.
June 15, 2009 at 10:58 pm |
You are correct that I assume that most auto dealers are campaign donaters.
You are incorrect in saying that we have to get to a 95% confidence level before we can say there might be something going on. A 95%+ confidence result would put the burden of proof on the Obama Administration to prove they hadn’t been playing games.
Anything outside of, oh, say 1 standard deviation makes it worth studying, and makes it questionable enough that Chrysler and the Obama Administration should be forced to report exactly what did happen.
May 29, 2009 at 1:02 pm |
Errors:
-Silver was using a general system and would not have an exact ratio. This is based on available donation from Huffington Post and not an exact number so his range of error comes from there.
-How do you define R and non-R. Many are including those who gave to Clinton or Edwards as R since they are closed and assumed “targets” of Obama. The Ideal study would be Obama donators closed versus open.
-Donations not party affiliation. These are based on donation history only. Some have even given to both parties and takes the judgment of the analyzer to decide affiliation.
Doug Ross who started this all even listed this as a potential “target” of Obama…• Jerome Fader: $6,500 to Democrats; $2,500 to Independent Joe Lieberman.
How do you assume this guy is a target of Obama?!?!
-Lastly there is already a admitted large number of Republicans working as car dealers, but one of the requirements in closing dealers was income of local residents. That would push the possible closing into more republican areas. This is why your random picking of red balls is not correct. This was not completely random, but was not based on party affiliation.
June 15, 2009 at 11:04 pm |
This is why your random picking of red balls is not correct. This was not completely random, but was not based on party affiliation.
Can you prove that claim? Can you provide the equation used by whoever picked the closed dealerships? Can you show that it was executed without any favor based upon the donations of the dealership owners?
No?
Then why are you putting your credibility on the line in a situation where there’s a fair deal of evidence that some political favoritism has been played?
May 29, 2009 at 1:39 pm |
[…] Greg’s Weblog: Why Can’t “Liberals” Do Basic Stats […]
May 29, 2009 at 3:49 pm |
These are not independent selections so the numbers don’t work quite so cleanly, I’m afraid. I don’t doubt that the probability is quite low. But the difficulties presented by this problem do not seem quite so simple, imo.
May 29, 2009 at 4:55 pm |
Two problems with your analysis. First, the 88% figure is for all car dealers, not just the Chrysler ones. It’s conceivable that Chrysler dealers differ from trhe rest in their campaign giving propensities. Second, and worse, is you can’t go from the 88% or 92% to 2640 and 690 resp. The former numbers are the Republican fractions of total compaign contributions and you cannot draw categorical information from that alone. For example, it’s conceivable that 92% of the dealers strongly favored Republican candidates even though only 88% of the total money went to Republicans.
June 15, 2009 at 11:06 pm |
Give me better numbers, and I’ll be happy to use them.
I just note, again, that Nate Silver used those numbers to “prove” that there wasn’t a problem, and that’s not what the numbers show.
May 29, 2009 at 5:04 pm |
Correction: I wrote “strongly favored” but whould have written just “favored.”
May 29, 2009 at 5:10 pm |
Greg,
For fun, can you turn the problem round? Right now you’re asking the question with the assumption that the a priori probability of picking a single white ball from the urn is 0.5, and computing the probability of picking few white balls from the urn.
Suppose we fix the probability of picking a given number white balls from the urn to be 0.5 (if feasible), but allow the a priori probability of picking a single white ball out of the urn to float. What would the probability of the biased pick be? 0.95? 0.995? Is an equally likely outcome probability even be feasible?
In other words, in a different but semi-analogous problem coin flips, I can presume that the flip is fair and then compute the probability that 9 out of 10 flips will be heads. In this case, the probability of one heads will be p = 0.5 and the probability of the result will be (n,k) p^9 (1-p)^(1) ~ 0.01. On the other hand, knowing that the flip isn’t fair, solve the equation (n,k) p^9 (1-p)^(1) = P, where P is the desired outcome probability. In this case, the maximum of P is about 0.39, for a value of p = 0.9. Note that I can’t even find an a priori value of p such that the outcome P = 0.5.
PS. For those with Matlab, here’s some code you can run. Just cut and paste the snippet below:
pp = 0:0.01:1;
nn = length(pp);
PP = zeros(1,nn);
for ii = 1:nn;
p = pp(ii);
PP(ii)=nchoosek(10,9)*p^9*(1-p)^1;
end
plot(pp,PP)
grid on
xlabel(‘A Priori Flip Probability’)
ylabel(‘Outcome Probability’)
title(‘Probability of nine out of ten heads given the coin flip probability’)
June 15, 2009 at 11:12 pm |
Noah,
I’m not sure I understand what you’re trying to do, so i can’t tell you how to do it. 🙂
May 29, 2009 at 5:26 pm |
Just a followup – I stated the premise wrong in my haste. I meant to say “… the a priori probability of picking a single white ball from the urn is 0.5 for an urn with equal numbers of white and black balls …” In other words, the ball selection is unbiased.
May 29, 2009 at 5:42 pm |
Thanks for looking at this Greg. I’m not quite sure about your math though. If 88% of the money goes to the GOP, that doesn’t mean 88% of dealerships gave money to the GOP. I think many of them don’t give any money. If the non-partisan group is big (I don’t have the number) there then only a few partisan dealers got shut down and it would be easier to explain the difference by chance.
To be really accurate, one would need to have data for each dealer. Then, I would group them as D,R, or I and use a chi-square test to see if the distribution is non-random. Or you could use a logistic regression with donations as the predictor. Not that I am volunteering to compile the data.
June 15, 2009 at 11:13 pm |
Terry,
My understanding of Nate’s claim was that 88% of the dealers gave to Republicans, not that 88% of the total donations went to Republicans.
May 29, 2009 at 10:39 pm |
You are way ahead of me on knowing math but I think you misunderstand the premises. There isn’t any random drawing. What the two sides found were lists of dealers who DID donate, chosen unscientifically. They both came out with about 8 to 1 Republican. That only gave the proportion of DONATING dealers GOP v Dem. Dealers who did not donate were not included in either sides’ figures.
A big majority of the dealers on both lists didn’t donate to either party. I ran random samples of both groups. I checked 19 of 789 closed dealerships and the scores were 4 (22.2%) donated GOP and 1 (5.7%) donated Dem. I know I ran a small sample but I’ve got the only one I’ve found on the net yet that was randomly chosen. If one were to use my percentages, I’d expect out of 789 closed dealerships we’d have 175 GOP donors and 45 who donated Dems.
By the way, I also took 32 scores randomly from the open dealer list of 2392. 4 (12.5%) donated GOP and 0 donated Democratic. I don’t know what you could make of that. That’s not much but its the best measure I’ve seen of the control group. If you disregarded weighting and combined both my samples, you’d get 8 to 1 GOP donations, about what the other guys found.
The conspiracy theorists are also way off over whose decision it was to close dealerships. Chrysler has had a plan, Project Genesis, in the works since at least as far back as February, 2008. Here’s a link: http://www.carseek.com/news/february2008/Chrysler-announces-Project-Genesis/
Since Chrysler has been planning this long before Obama was in office, and both the White House and Chrysler deny any White House role in selecting the dealerships to be closed, and the chairman of the new Chrysler Group was a member of G.W. Bush’s election organization and has consistently contributed to Republicans running for Congress and the White House, there is strong reason to believe Chrysler is the one picking the losers and winners.
On the other side, that the White House made the selections, is the word of one lawyer (bias? honesty?) for the closed dealerships who doesn’t even allege he was told by anyone that the White House directed the choices. The lawyer just said he got the “impression” while deposing a Chrysler exec that the company didn’t want the closures. That’s proved wrong by the link above. There’s also a member of the task force who is married to a Democratic fundraiser, but that’s not really evidence of anything, and doesn’t mean that the White House made the choices.
June 15, 2009 at 11:21 pm |
1: I’m sure that Chrysler has wanted to close a lot of dealerships for some time.
2: I’m not at all sure that the dealerships that were closed were picked solely by Chrysler, or that there was no political influence on the picks. The fact that all six of Mack McClarty’s dealerships avioded the axe, but that Republican Congressman’s dealerships didn’t, would right there make me at least somewhat suspicious.
3: You need to look at several hundred dealerships in order to get numbers big enough that you can extract reasonable inferences.
4: I’ll be very surprised if it ends up that < 25% of auto dealers were campaign donors.
May 30, 2009 at 2:13 am |
“There is just one problem with this theory. Nobody has bothered to look up data for the control group: the list of dealerships which aren’t being closed.”
OK that’s just plain stupid there. We looked up the data for all dealers and we looked up the data for the dealers that got closed. We only need to subtract the data for the latter from the former and we get the data for the dealers that weren’t closed. In a sane world no one would pay any further attention to someone who dropped such a logical clunker.
May 30, 2009 at 10:34 pm |
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