Winnebago County Walker Recall: A Probability Analysis of Differences between Optical Scan and Touch Screen Vote Counts
Richard Charnin
Aug. 14, 2012
Assume that the votes cast on Optical scanners and Touch screens are given for a location (ward, precinct). All things being equal, the vote shares should be nearly identical. But if they are not equal, is the difference significant? And if the difference is significant, what is the probability that it would be due to chance?
Note that this is not an exit poll analysis. The probabilities are based on actual recorded votes.
The probability of the discrepancy is a function of the following:
1)number of optical scanners and touch screens
2)vote share percentages on each type of machine.
If the optical scan ballots are hand-counted, we can calculate the number of touch screen votes and vote shares by subtraction. We can then determine if the difference in vote shares between the touch screens and optical scanner is significant.
This spreadsheet is a probability calculator for the discrepancy between optiscan and touchscreen vote shares in a given ward/precinct.
The Z-score is based on the bell-curve (normal distribution). Z determines the probability of the difference between the touch screen and optical scan vote shares. If
Z = 1.65, the probability is 95.2% that the difference between touch screen and optical scan vote shares was not due to chance. Election Fraud is likely.
Z = 1.96, the probability is 97.5%
Z = 2.33, the probability is 99.0%
Assume that in a given location, we have:
nv = total number of votes
ns = number of optical scan ballots
ps = Walker’s vote share on optical scanners
Then we can easily determine
nt = number of touch screen votes = nv – ns
pt = Walker’s vote share on the touch screens
We can then calculate the probability of the difference in vote shares between the optical scanners and touchscreens:
1) Difference in vote shares: Diff = pt-ps
2) Standard error: Std = sqrt [ps*(1-ps)/ns + pt*(1-pt)/nt]
3) Z-score = ABS(Diff) / Std
4) Probability (Diff) = 2-2*NORMSDIST(Z)
The following table is based on the Winnebago County spreadsheet in the 2012 Wisconsin Recall True Vote Model. It shows that the large discrepancies between Opscan and TSX shares in the following locations could not have all been due to chance.
Walker 2-party %
Location.....Opscan...TSX.....Diff..ZS..Prob
Menasha(3,5,6).65.64% 60.23% -5.41% 1.89 5.82%
Neenah.........63.14% 73.21% 10.08% 1.67 9.45%
Poygan.........62.81% 72.66% 9.85% 2.68 0.74%
Rushford.......58.48% 65.92% 7.44% 2.10 3.59%
Utica..........66.67% 75.17% 8.51% 2.08 3.78%
Neenah(13-16)..60.32% 53.68% -6.63% 1.74 8.20%
Neenah(17-20)..51.31% 64.10% 12.79% 2.77 0.57%
Oshkosh(5).....42.73% 32.98% -9.75% 1.85 6.46%
Oshkosh(15)....50.76% 40.00% -10.76% 2.89 0.38%
Oshkosh(17)....40.48% 47.66% 7.18% 1.91 5.66%
Oshkosh(28A)...44.96% 52.58% 7.61% 1.88 5.98%
Oshkosh(29A)...60.63% 73.68% 13.06% 2.24 2.48%
Poygan Village Votes Pct
2-Party Total
Vote Count.... 662 100%
Optiscan...... 406 61.33%
TSX DRE....... 256 38.67%
Walker
Total Votes... 441 66.62%
Optiscan...... 255 62.81%
DRE TSX....... 186 72.66%
Z-Score....... 2.68
Probability... 0.74% (of 9.85% vote share discrepancy between Optiscan and DRE)
Take the Election Fraud Quiz.
