If 2016 UEP were random as it should be for unbiased exit polls, the chance of "red shift" for every state would be 50% or 0.5. The odds of negative red shift in 24 out of 26 such state UEP results would then be 1 in 13,110, or the odds of getting 24 heads in 26 coin tosses, as shown in cell 5J.
The usual attempted explanation for these consistent and statistically impossible biased UEP discrepancies in U.S. elections is exit polling "response bias." In 2004 this was dubbed the "reluctant Bush responder" hypothesis and disproven using the exit pollsters own data. In 2016 a similar, "shy Trump" voters, explanation has been proffered for the widespread statistically significant and one-sided deviations of official vote counts from pre-election polls and again disproven by the data.
Similarly, the notion that an unforeseen surge in Trump voters that was not taken into account by pre-election polls or the exit pollsters in assigning weights necessary to derive state level exit poll results from precinct exit poll samples, was the problem, is not consistent with UEP data from the 2016 primary elections that shows a statistically impossible bias against Sanders in the Democratic primary but no consistent UEP bias in the Republican primary(another pattern that cries out for investigation). If anything one would expect that surges in Trump voters that were unforeseen by the exit pollsters would be a greater problem in the primary when Trump was initially still viewed as a marginal candidate, and the most committed Trump voters were voting. There is also the question of why U.S. exit pollsters would repeatedly get the weights wrong for Republican candidates, no matter the candidate, in every U.S. presidential election since 1988, and the unresolved question noted above as to why the "Trump surge" or "Trump Shyness" phenomena would be, as with the equivalent Bush trends in past exit poll discrepancies, highly significant particularly in battleground and deep red states and not consistent across states. Perhaps an argument could be made for greater turnout efforts in battleground states, but why would this occur in deep red states where Trump was most likely going to win anyway? And if Trump supporters were generally hyper-motivated, or covert, why were there not similar "Trump surges" or "Trump Shyness" in UEP response in other states like New York where one would expect the social stigma of identifying as a Trump supporter would be greater?
Finally, the voting integrity community has been repeatedly asking for precinct UEPs and official counts so that analysis that would be unaffected by precinct weights could be conducted, and these requests, including my own request for UEP and precinct vote count from the 2016 election, have been ignored or denied. The reason offered for this is that such information is (in violation of the American Association for Public Opinion Research (AAPOR) code of ethics disclosure standards that specify that the geographic location of the population sampled should be disclosed) claimed as proprietary private information despite its obvious vital public importance. This is the case even though the UEP and official vote count margins are all that is needed, and could be provided without disclosing the exact locations of exit polled precincts.
In the one case, for the Ohio 2004 presidential election, where such information was obtained inadvertently and indirectly, precinct level analysis revealed highly significant precinct level UEP discrepancies, confirming that the statistically significant UEP discrepancies revealed by state level analysis were not simply a result of inaccurate precinct weighting. Moreover, follow-up direct investigation of polling books and central tabulators from the 2004 election in Miami County, Ohio revealed widespread discrepancies in number of votes cast and central tabulator miscounting acknowledged by the Republican County Election Board Director. This demonstrates that statistically significant discrepancies between UEPs and VCs in U.S. elections have been tied to proven election irregularities, implying that these should be investigated as the U.S. State Department recommends when UEP discrepancies with official vote counts appear in foreign elections.
Figure 1: 2016 Presidential Election "Red Shift" or Exit Poll Margins minus Vote Count Margins
b) Clinton Presidential Exit Poll Discrepancies
Though "red shift" is a measure of overall candidate VC versus UEP margin of victory, it is difficult to analyze statistically as candidate voting shares are not independent of each other. In a two way race vote shares would be exact complements and "red shift" would be exactly twice the size of each candidate's VC versus UEP deviation. With third party candidates in the race, the vote share relationship between the two major party candidates will not be exactly determinate. Standard statistical analysis of the difference of two independent proportions is thus not applicable.
The easiest way to get around this problem is to perform separate single proportion analysis of each major candidate's VC versus UEP vote share. The analysis is a standard single proportion deviation analysis of official vote count share deviation from UEP share. The only adjustment is a 30% "clustered sampling" increase in the random standard deviation estimate due to the fact that though exit poll samples are approximately random samples of precincts responses are geographically clustered as they come from precincts selected by pollsters to be representative of the state (see p. 9, footnote 22 of this).
Figure 2 below shows the results of this analysis for Clinton UEP minus VC shares. Column D shows VC minus UEP percentage for Clinton so that a positive percentage indicates that Clinton's vote count was less than her UEP share. Column G is the sample standard deviation (SD) estimated to be 30% larger than the standard random sample standard deviation after the cluster sampling adjustment. Column H gives the "Z-Score," or number of SD's, of the UEP -- VC deviation. Column I gives one-tailed P-Values (on either side of the distribution) for each state assuming a standard normal population with a mean equal to the UEP for Clinton and SD estimated in Column G. Under these standard sampling assumptions, these are the likelihood of the VC being this different from the UEP assuming random sampling error. P-values less than 5% are considered statistically significant as they indicate a 5% or less random chance that the VC share would be this different from the UEP share. Column J presents the same information (one divided by P-Value) in terms of the odds of VC share occurring given the UEP share. Columns K and L give the lower and upper bounds of the 95% confidence interval, or the range of VC values that have a 95% probability of occurring, given the Clinton UEP result. Since this is a two-tailed confidence internal, only VCs with P-values of 2.5% or less will be outside of this confidence interval.
As can be seen in Figure 2, statistically significant VC discrepancies with Clinton UEP shares (with odds less than 1 out of 30) occurred in OH, MO, UT, PA, NJ, ME, and NC. The analysis thus shows that Clinton suffered statistically significant VC reduction relative to UEP share in a small number of battle ground states (OH, MO, PA, and NC), the deep-red state of UT, and NJ, a state with a Republican Governor and Trump ally (recall per discussion above that UEPs for FL and MI are likely to be partially adjusted and thus not true UEPs). OH in particular has a long history dating back at least to 2004 of faulty official vote count reporting, for example the documented inconsistencies and miscounting in Miami county noted above, and many other incidents. Note that Figure 2 shows some evidence of statistically significant (below 5% P-value) Democratic UEP -- VC discrepancy for Clinton in the deep blue states of NY and WA, but as can be seen from the odds in Column J, the level of significance is much smaller than the pervasive discrepancies against Clinton in multiple states noted above.
The statistically important point is that the VC shift against Clinton was not pervasive but concentrated in key suspect states, suggesting that these "errors" were not random but a result of how the VC was counted, not counted, or miscounted. This is borne out by the fact that overall Clinton's vote share was smaller than her EP in just 12 out of 24 states, as shown in Cell 5M using a calculation like that in Figure 1 in cell 5J.
Figure 2: 2016 Presidential Election Clinton Exit Poll minus Vote Count Margins
Figure 3 below illustrates the Clinton UEP PA analysis conveyed in Figure 2, line 8. The normal distribution bell curve is centered around Clinton's PA 50.5% UEP share and has a 1.3% SD (or approximate "width") as calculated in Figure 2. Based on this SD, the 95% Confidence Interval (CI) displayed in the graph ranges from 48% to 53% as shown in Figure 2. This implies that there was a 95% chance that Clinton's PA VC would fall within this range due to statistical sampling error. The blue area over the CI under the bell curve distribution contains 95% of the total area under the bell curve. As shown in Figure 3 Clinton's reported PA VC of 47.6% is below the lower end of the CI, showing a statistically significant VC discrepancy with her UEP that would be expected to occur by chance only 1.1282% of the time, or less than a 1 in 88 chance (data for the illustration was from an earlier PA VC giving roughly 1 in 60 odds).
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