# Binomial Analysis of Clinton vs. Obama Contest in New Hampshire

# Binomial Analysis of Clinton vs. Obama Contest in New Hampshire:

##### The Dichotomous Returns from Hand-Counted-Paper-Ballot Precincts and Diebold-Optical-Scan Precincts Are “Statistically Impossible"

*"The Excel spreadsheet shown below gives the binomial probability that the boundaries of the hand-counted paper ballot (HCPB) and Diebold optical scan precincts should have, by sheer accident, corresponded to parts of New Hampshire that had bizarrely dichotomized into 6% pro-Obama and 6% pro-Clinton enclaves, respectively. That probability (corresponding to 17 standard deviations, or “SDs”) turns out to be so infinitesimally small that I haven’t yet found a look-up table for it. Seventeen SDs is about as close to “statistical impossibility” as one ever gets to see."*

**See full commentary on hypothesis and method, below chart**

**COMMENTARY by David L. Griscom, EDA Co-Coordinator for Investigations**

January 20, 2008

January 20, 2008

As a Ph.D. research physicist for nearly 42 years, I am accustomed to gathering data and then deciding what these data mean. That is, I (and any physicist worth his salt) seek hypotheses suitable for explaining all existing data. Hypothesizing usually begins with an educated guess. But it can never end there. As soon as a guess is on the table, the challenge is to quantify its predictions. And to do that requires mathematics.

Since my retirement from the Naval Research Laboratory seven years ago this month, I have continued to carry out research and publish papers in peer-reviewed journals using data I had gathered at NRL but not yet published, data gathered as a visiting professor somewhere, or data gathered by colleagues still working in well equipped laboratories. It has really been impossible for me to give up the habit of being a physicist.

However, in recent years I have increasingly turned my attentions from physical phenomena to “political” phenomena, including the 9/11 attacks, insider manipulation of the financial markets, and insider-perpetrated election fraud. Once again, educated guesses have been my starting points, but I never stop there. Typically, I gather all data available from public sources and make sure that none of these data contradict the hypothesis I may be hatching. Then it comes time for the mathematics.

##### Binomial Analytic Method Evolved from Investigation of 2004 Presidential Election in Pima County, AZ

With my friend and colleague John Brakey, I have been on the trail of election fraud in Pima County, Arizona, ever since the 2004 election. This has culminated in the chapter I wrote for publication in a book being edited by Mark Crispin Miller entitled ** Loser Take All** (which will also feature chapters by many of my distinguished colleagues from Election Defense Alliance and elsewhere, all of whom exhibit research skills and methodology matching those of any good physicist).

In my paper, I exploit publicly-available data for the 2004 presidential vote at 63 precincts belonging to a single Tucson legislative district. My educated guess, or operating premise, was that on the average the Bush and Kerry vote shares for any given precinct should be closely the same for the three modes of voting used in 2004: **mail-in voting, at-the-precinct voting, and voting by provisional ballots**. I found this premise to be true within 95% statistical confidence (the math I brought to bear at that point) when comparing the mail-in voting to the provisional ballot voting.

I used data for provisional ballots that were accepted by the county registrar; therefore, the vote shares represented there had to have been honest since the registrar had to verify the name and signature on the affixed voter affidavits and check to see that those persons were voting in the correct precinct and had not voted by mail. Thus, to my surprise, I was force to conclude that the mail-in vote had not been stolen despite the ease with which this could have been done, given that these ballots are counted by Pima Election Department officials without witnesses.

But when I compared the at-the-precinct presidential vote shares to the now-shown-to-be-(mostly)-honest mail-in vote shares for these 63 precincts, I found a large shift favoring Bush that was outside of 95% statistical confidence. Still, the mathematics I was using then were crude – and I wanted to sharpen in my mind the concept that was to become my hypothesis. That is, there certainly must be random variations in people’s choices whether to vote by mail or in person at the precinct. And to prove fraud I must prove that differences in the public record substantially exceed the nominal limits of such random variations.

I realized that such situations are mathematically described by the **binomial distribution function**. So I searched for and found a handy calculator of this function on the Internet, and did the math. (N.B. This is the same function that gives you your chances of flipping heads *x* times in *n* tries.) In this way I proved that there was only **one chance in 15,773** that the at-the-precinct vote for the entire legislative district (56,930 Bush-plus-Kerry voters) was not flipped by 3.4% from Kerry to Bush (for a net vote shift of 6.8%).

##### How the 2004 Arizona Methodology Applies to the 2008 New Hampshire Primary

The New Hampshire primaries were held only two days after I turned in the final version of my chapter to the publisher of *Loser Take All*. And there staring me in the face were these Clinton-plus-Obama data: Clinton took 46.8% of the hand-counted paper-ballot (HCPB) vote but fully 52.7% of the Diebold optically-scanned vote. Obama was virtually the reverse, taking 53.2% of the HCPBs but only 47.3% of the Diebold vote! Now, just how probable is that? **Another job for the binomial distribution function calculator!**

I reason that the boundaries of the Diebold op-scan precincts and those of the HCPB precincts had been drawn up years ago, either arbitrarily or with an idea toward somehow giving an advantage to Democratic or Republican candidates (depending on which political party did the deciding). Such a demographic bias, if it even exists, should in my view have little impact on a Democratic primary contest between two Republican-lite candidates. It was **inconceivable to me that the distribution of HCPB and Diebold precincts was anything but random with respect to the Clinton-Obama contest.** But, hey, why listen to my opinion when the binomial distribution function speaks with far greater authority?

**The Excel spreadsheet shown above gives the binomial probability that the HCPB and Diebold precinct boundaries should have, by sheer accident, corresponded to parts of New Hampshire that had bizarrely dichotomized into 6% pro-Obama and 6% pro-Clinton enclaves, respectively.**

**That probability (corresponding to 17 Standard Deviations, or “SDs”)** turns out to be so **infinitesimally small** that I haven’t yet found a look-up table for it. Seventeen SDs is about as close to “statistical impossibility” as one ever gets to see.

In my humble opinion, this should be sufficient proof that insiders hacked the Diebold GEMS central tabulator for the New Hampshire Democratic primary op-scan ballots. As a corollary, in the event that a recount should show the paper ballots in the Diebold machines to match the GEMS count, then the binomial distribution function would assure us that the ballot boxes had been stuffed as well.