Extrapolating 120 million votes from 13,360

[davidgmills]

I just sent my PhD father (biochemistry and forty years of teaching medical and graduate students) the USCountVotes article for his review.

He does not believe that pollsters can accurately extrapolate the votes of 120 million people from 13,660 voters, no matter how diligently one attempts to select these 13,660 as being representative of the total.

He doesn't agree with the one premise that USCountVotes and Mitofsky do agree on; i.e., premise No. 1, that the first possible cause, random statistical sampling error, can be ruled out.

There must be some literature that says 13,660 representative voters, properly selected, can accurately extrapolate the voting patterns of 120 million people. But, he doesn't believe such a thing has ever been proved, especially in America, with it's extremely heterogeneous and transitory population.

Any ideas as to where academic literature can be found to disprove his notion?

[Carolab]

1. I would refer the question to Stephen Freeman

or Kathy Dopp. I am sure they would have some suggestions.

[Bill Bored]

2. Comes down to margin of error.

There are 2 formulas for this, which are not that much different. One is 2 standard devs I think and the other??? I'll leave that to TIA to explain.

Then you have the potential for clustering, due to precincts being selected incorrectly. But the pollsters and USCountVotes have both ruled this out.

So they came up with within-precinct error to explain the discrepancy.

One question I have about the national poll is whether the sample sizes in each state were adjusted in proportion to their populations or was some other algorithm used?

And also, I'm not sure if the state polls, which had a much larger sample size than the 13,660, have been combined to arrive at a national popular vote total to compare to the 13,660. Again, TIA should know this but if it hasn't been done, it should be. The same question about state sample size would apply to this.

Does your dad believe the election wasn't stolen?

[TruthIsAll]

3. David, tell your father he is wrong.

Use 1.96 standard deviations for a 95% confidence level.

The margin of error formula for a sample size = n is
MoE = 1.96* Sqrt(p(1-p)/n)/2

where
p = winning vote percentage
1-p = losing vote percentage

As the spread widens, the MoE gets tighter.

For instance, assume p=.6, 1-p=.4:
.6 *.4 = .24
Sqrt (.24) = .4898

Compare to p=.5, 1-p=.5:
Sqrt (.5 *.5) = .5000

So the MoE is slightly lower for a 60-40% poll result then 50-50%.

Let's assume p= .5, 1-p=.5 (an even election)
n= 13047 = Pristine (Raw?) Nat. Exit poll respondents.

Sqrt (13047) = 114.2

MoE = 1.96 *.5 / Sqrt(13047) =.98 / 114.2 = 0.875%

The confidence level is 95%. That means that 19 times out of 20, the exit poll result will fall with +/- 0.875% of the true population mean.

So if Kerry has a 51-48% exit poll margin, the chances are greater than 95% that the exit poll would match the vote to within 0.875%.
That means there is a 95% probability that Kerry's true mean percentage was in the range {50.125-51.875}

The probability that Kerry would get 48% of the vote after winning the exit poll by 51-48% is:

p = 1 - NORMDIST(0.51,0.48,0.00875/1.96,TRUE)
p = 0.0000000000091

or 1 in 109,444,820,165

You:
One question I have about the national poll is whether the sample sizes in each state were adjusted in proportion to their populations or was some other algorithm used?

Me:
Don't know.

You:
And also, I'm not sure if the state polls, which had a much larger sample size than the 13,660, have been combined to arrive at a national popular vote total to compare to the 13,660.


Me:
The National Poll is a subsample (13000) of the state polls (70000+)

FL sample size was 2862 (MoE = 1.8%)
OH was approx 2200 (2.1% MoE)

[Bill Bored]

4. So has anyone looked at the aggregate of the 50 states + DC

to see it that matched the 13,660 results at roughly the same time of day (say 7:30 PM)?

[TruthIsAll]

6. State-weighted pre-election and exit polls vs. National (13047)....

Disregard the final 13660. That was contaminated to match the
vote.
Focus on the 13047, which Kerry won.

Compare Kerry's state weighted pre-election and exit poll  to
the National(50.5%, 50.4% to 50.8%).

The weighted national pre-election poll average (50.51%)
matched the exit poll average (50.37%). 
That's 1/7 of one percent.

Total percentages are based on the weighted average.
Kerry's actual 2-party vote: 48.76% = 59028/121056

Votes and percentages are 2-party based.
Vote percentages are shown for Kerry. 
Bush% = 100 - Kerry%.

Pre: final pre-election state poll average.
Exit: exit poll 2-party percentages based on data downloaded
by Simon at 12:22am Nov.3.

P/A = 100*Pre/Actual
E/A = 100*Exit/Actual

Prob: Probability of deviation
P/A Prob = pre-election poll to actual 
E/A Prob = exit poll to actual 

Based on the pre-election polls:  
41 out of 51 states (incl DC) deviated to Bush
Based on the exit polls:  
43 out of 51 deviated to Bush

								Pre/	Exit/	Prob	Prob	Favor	Favor
	Vote	Pre	Exit	Act	Pre	Exit	Act	Act	Act	P/A	E/A	Pre	Exit

Total	121056	50.37%	50.51%	48.76%	60979	61144	59028	103.3%	103.6%	14.1%	12.2%	41B	43B

				
AK	302	34.48%	40.14%	36.77%	104	121	111	94%	109%	6.3%	1.2%	K	B
AL	1870	40.63%	41.08%	37.10%	760	768	694	109%	111%	0.9%	0.4%	B	B
AR	1043	50.00%	46.60%	45.07%	522	486	470	111%	103%	0.1%	15.4%	B	B
AZ	1998	47.37%	46.93%	44.72%	946	938	894	106%	105%	3.9%	7.1%	B	B
CA	12255	53.85%	55.73%	55.04%	6599	6830	6745	98%	101%	21.3%	32.3%	K	B

CO	2103	49.47%	49.07%	47.63%	1040	1032	1002	104%	103%	11.0%	16.9%	B	B
CT	1551	55.32%	58.47%	55.27%	858	907	857	100%	106%	48.8%	1.6%	B	B
DC	224	87.64%	91.63%	90.52%	197	205	203	97%	101%	2.7%	22.9%	K	B
DE	372	54.22%	58.44%	53.83%	202	217	200	101%	109%	39.9%	0.1%	B	B
FL	7548	51.55%	49.93%	47.48%	3891	3769	3584	109%	105%	0.3%	5.1%	B	B

GA	3280	44.68%	43.11%	41.65%	1466	1414	1366	107%	104%	2.2%	16.5%	B	B
HI	426	50.00%	53.32%	54.40%	213	227	232	92%	98%	0.2%	23.5%	K	K
IA	1494	53.19%	50.67%	49.66%	795	757	742	107%	102%	0.9%	25.0%	B	B
ID	590	33.71%	33.33%	30.68%	199	197	181	110%	109%	2.2%	3.8%	B	B
IL	5239	56.25%	57.13%	55.21%	2947	2993	2892	102%	103%	24.3%	10.0%	B	B

IN	2448	40.21%	40.97%	39.58%	984	1003	969	102%	104%	33.7%	17.7%	B	B
KS	1171	38.14%	34.60%	37.13%	447	405	435	103%	93%	25.0%	4.6%	B	K
KY	1782	41.05%	40.76%	39.99%	732	726	713	103%	102%	24.0%	30.6%	B	B
LA	1922	45.45%	44.50%	42.67%	874	855	820	107%	104%	3.2%	11.2%	B	B
MA	2875	70.33%	66.46%	62.74%	2022	1911	1804	112%	106%	0.0%	0.7%	B	B

MD	2359	55.67%	57.04%	56.57%	1313	1346	1334	98%	101%	27.5%	37.6%	K	B
ME	727	56.18%	54.83%	54.58%	408	399	397	103%	100%	14.4%	43.4%	B	B
MI	4793	53.61%	52.55%	51.73%	2569	2519	2479	104%	102%	10.5%	29.1%	B	B
MN	2792	54.17%	54.61%	51.76%	1512	1525	1445	105%	106%	5.4%	2.9%	B	B
MO	2715	47.31%	47.47%	46.38%	1284	1289	1259	102%	102%	26.7%	23.3%	B	B

MS	1130	45.16%	43.20%	40.49%	511	488	458	112%	107%	0.1%	3.6%	B	B
MT	440	38.71%	39.28%	39.50%	170	173	174	98%	99%	70.1%	44.2%	K	K
NC	3487	48.45%	47.31%	43.76%	1690	1650	1526	111%	108%	0.1%	0.9%	B	B
ND	308	38.89%	33.58%	36.09%	120	103	111	108%	93%	3.1%	4.7%	B	K
NE	767	34.41%	36.54%	33.15%	264	280	254	104%	110%	20.1%	1.2%	B	B

NH	672	50.00%	55.49%	50.69%	336	373	341	99%	109%	32.3%	0.1%	K	B
NJ	3581	54.35%	56.13%	53.37%	1946	2010	1911	102%	105%	25.7%	3.3%	B	B
NM	748	50.00%	51.34%	49.60%	374	384	371	101%	104%	39.5%	12.3%	B	B
NV	816	50.00%	50.66%	48.68%	408	413	397	103%	104%	19.0%	9.4%	B	B
NY	7277	59.38%	63.97%	59.29%	4321	4655	4314	100%	108%	47.7%	0.1%	B	B

OH	5599	51.55%	52.06%	48.94%	2886	2915	2740	105%	106%	4.1%	1.9%	B	B
OK	1464	31.46%	34.73%	34.43%	461	508	504	91%	101%	2.4%	42.1%	K	B
OR	1810	53.19%	51.22%	52.11%	963	927	943	102%	98%	23.5%	27.8%	B	K
PA	5732	52.63%	54.41%	51.26%	3017	3119	2938	103%	106%	18.0%	1.8%	B	B
RI	429	60.87%	64.24%	60.58%	261	275	260	100%	106%	42.3%	0.7%	B	B

SC	1600	43.30%	45.78%	41.36%	693	732	662	105%	111%	9.9%	0.2%	B	B
SD	382	44.68%	37.42%	39.09%	171	143	149	114%	96%	0.0%	13.3%	B	K
TN	2421	48.98%	41.15%	42.81%	1186	996	1036	114%	96%	0.0%	13.4%	B	K
TX	7360	38.54%	36.84%	38.49%	2837	2711	2833	100%	96%	48.6%	13.5%	B	K
UT	905	25.81%	29.93%	26.65%	234	271	241	97%	112%	28.6%	1.4%	K	B

VA	3172	47.96%	47.96%	45.87%	1521	1521	1455	105%	105%	8.1%	8.1%	B	B
VT	305	56.99%	65.69%	60.30%	174	201	184	95%	109%	1.4%	0.0%	K	B
WA	2815	54.17%	55.07%	53.65%	1525	1550	1510	101%	103%	36.4%	17.2%	B	B
WI	2968	53.68%	50.21%	50.19%	1593	1490	1490	107%	100%	1.0%	49.4%	B	B
WV	750	48.42%	45.19%	43.52%	363	339	327	111%	104%	0.1%	13.2%	B	B
WY	238	30.85%	32.07%	29.69%	74	76	71	104%	108%	21.9%	5.6%	B	B
													
Avg	121056	48.57%	48.84%	47.09%	60979	61144	59028	103.4%	103.8%	16.3%	9.7%	B	B
Median		50.00%	49.07%	47.48%				102.7%	103.9%	4.6%	9.4%	B	B

[davidgmills]

7. Let me put the problem another way

Suppose you took a sample of 13,047 people from New York City and extrapolated from that sample what the US population would look like as a whole. Or did the same thing with 13,047 Mormons from Utah. You certainly would not get the same predictions.

I guess his point is that this is the same problem, only on a smaller scale, but it still may be significant enough to have serious questions about the prediction.

[TruthIsAll]

8. It's a NATIONAL sample, not a New York sample

"Suppose you took a sample of 13,047 people from New York City and extrapolated from that sample what the US population would look like as a whole. Or did the same thing with 13,047 Mormons from Utah. You certainly would not get the same predictions."

OF COURSE YOU WOULDN'T, UNLESS YOU ARE SAMPLING TO PREDICT THE NEW YORK VOTE.

"I guess his point is that this is the same problem, only on a smaller scale, but it still may be significant enough to have serious questions about the prediction".

THIS IS STATISTICS 101.
STAYING UP TOO LATE?

The National Exit Poll, just like the pre-election polls, samples selected precincts around the nation

THE WHOLE POINT IN POLLING IS TO ANALYZE A RANDOM SAMPLE OF PRE-DESIGNATED PRECINCTS WHICH REPRESENT THE POPULATION (STATE OR NATION) AS A WHOLE.

YOU CAN'T INTERVIEW EVERYONE.

ONE OTHER IMPORTANT STATISTICAL FACT:
A NON-BIASED RANDOM SAMPLE OF 1000 INDIVIDUALS HAS THE SAME MARGIN OF ERROR, WHETHER IT IS FOR A CITY OF 100,00, A STATE OF 5 MILLION OR A NATION OF 100 MILLION.

[davidgmills]

9. Precincts as representative of the whole

You say:

"THE WHOLE POINT IN POLLING IS TO ANALYZE A RANDOM SAMPLE OF PRE-DESIGNATED PRECINCTS WHICH REPRESENT THE POPULATION (STATE OR NATION) AS A WHOLE."


I would not presume to argue for him, but I think he would say: "Yes that is the point, but how can you be sure that your analysis of of a random sample of designated precints accurately represents the population as a whole." I think he would be saying that because of our diversity and mobility, the designated precincts would be subject to rapid change in demographics; therefore, you need to prove to me that these precincts are stagnant enough so that inevitable change does not invalidate the choices of selected precincts as being representative.

I guess what I would be looking for is literature suggesting that precincts are far more stagnant or stable over time than one might assume and that they can be used as accurate representations of the population as a whole.

[TruthIsAll]

11. Quick answer...

Historical demographic trends are well known to professional pollsters who have many years of experience and data to draw upon. That's why they get paid.

Polling is just not some arcane art. It's a discipline which has a solid scientific basis. The pollsters know what to look out for. They know what adjustments to make.

Statistical trends do not change dramatically from year to year. In any case the latest data is available. Computers and publicly available data make it easier than ever to analyze demographic trends. Statistical techniques applied to the demographics in polling have a mathematical foundationwhich goes back centuries.

[davidgmills]

14. And that is the data he would want to see I'm sure.

He would never take, on blind faith, someone's word for this.

To the naysayers who say "I don't believe in the accuracy of exit polls" there have to be scientific studies you can shove in their faces and say "here, take a look at this."

I told him about the accuracy of the German polls. His comment was that they are a much more homogeneous people and they may not be nearly as mobile.

I told him about the Ukraine. He said we should have stayed out of their elections. He thought it was a bad idea to use exit polling as a means to get a re-vote.

And of course he vividly remembers Truman/Dewey.

So, I am going to have to find the sources for the assumption that statistics do not change significantly from year to year in order to convince him.

[mgr]

16. So if Mitofski is the expert.

Why don't you take his word that the MOE for the national election results is 6.5%? Or is he no longer an expert? You can't argue out of both sides of your mouth.

I completely disagree with your third statement--in areas of moderate to fast growth it is near impossible to assess demographic trends as they are underway. Four years after the census and a population of 200,000 is now 250,000? The next census is not for another six years, by then the population will be what? Composed of whom? (what I have just described is Stockton CA). How does one address areas that plan for growth but it does not happen at the rate predicted(Merced CA)?

It is the history of the US population's ability to pick up and move that underlies his father's skepticism. You cannot discount that with a general statement that equates statistics with demography.

A stable precinct population may have predictive capabilities only when compared to other stable precincts. Those experiencing growth or contraction may not be subject to the same constraints.

Mike

[Name removed]

26. Deleted message

Message removed by moderator. Click here to review the message board rules.

[mgr]

15. I disagree

One can certainly extrapolate from carefully selected precincts and with subsequent weightings in either New York or Utah to characterize the national election outcome. The only problem might be the MOE.

Mike

[davidgmills]

10. I think a fairer statement would be

That he doesn't believe in the accuracy of exit polls. He doesn't believe you can get a representative sample from which one can accurately extrapolate.

[Sancho]

5. Hmmmmm.....New England Journal of Medicine is a start!

Just to keep things in Dad's experience...has there EVER been a medical trial less than 10,000 patients? We extrapolate from smaller samples to the entire population regularly. One study of a few hundred medical students to the entire US population on tran-fatty acids in NEJM a few years ago was the cause of all the butter and margarine in the US being accused of killing us.

[davidgmills]

12. I wouldn't go there

I am sure he could cite me dozens of studies where the extrapolation from a few people proved to be wrong when applied to a large population.

[mgr]

13. Very simple to evaluate

In a sample of 13,660 how many votes are represented by a individual vote in the sample (120,000,000/13660). Assume that maybe one or two samples are tabulated or recorded improperly, would the swing make you uncomfortable as to the reliability of the estimate?

This is the basis of my argument (and one that you agreed with in a separate post) is that an exit poll should sample 1% of the total electorate. The order of magnitude between the sample and the population is too vast to be reliable.

There will be nothing in the literature specific to your inquiry. Proper selection is part of the methodology, and if bias enters into the proper selection, the range of error increases.

It is basic to statistics that sampling error is thought to be incorporated into the standard deviation. You may want to show him NEP's January 19, 2005 report to see if you are getting his objection properly. He may not recall what MOE refers, since it is a concept limited in its use.

Mike

[liam_laddie]

17. sample size

Maybe I've got this wrong; I'm not a number-cruncher. The sample size nationwide was actually about 70,000; 0.057% of 122MM voters, about 3/5 of the "one percent sample" mentioned above. The "national" exit poll sample of 13,047 (two initial reports)
was derived from the 70,000, based on E/M's selection. Recall,
the NEP poll was conducted by TWO experienced research firms, in a joint venture. This would seem to result in an accurate selection procedure. Their experience would indicate that the 13k sample would accurately predict results within acceptable MOE. If election was corrupted, the results indicate that the thieves have cleverly determined just how much, and where, to alter the results to avoid detection. Or certainly make it difficult, what with their friends making DRE's and tabulators and wireless modems. FWIW, HTH.

[mgr]

18. I gave the calculation

Try it and see if a sampling error of one or two respondants makes you uncomfortable or not? Substitute 70,000, it still does not cut it, IMHO.

Mike

[mgr]

19. The national poll is nested in the state polls

13,047 (or 13,660) is the sample to evaluate, not the residual 53,000 which were likely applied to state's results, and not employed at all because of sampling discrepancies. I would not, given all the vagaries of sampling, like sampling on the scale of 1 to 20,000 for a heterogeneous population unless the MOE were 0.1% We have an MOE of 6.5% for the 13660 sample when weighted, and no calculated MOE for the 13047 sample when weighted (at least from NEP). The methodology published prior to the election was revised from the predicted 1.0% to 6.5% by NEP (Mitofski). A 6.5% MOE means a range of ~13,000,000. The 3,000,000 difference between Kerry and Bush is swallowed within it, if the predicted outcome and actual outcome are within the range of 6,500,000 votes.

Mike

[TruthIsAll]

20. And we won't swallow it. The MOE is 1.74% for a 3168 sample

Do you know how to calc the MoE?

Moe= 1.96* sqrt(p*(1-p)/n)
If P = .5,
MoE = 1.96* .5 /sqrt(n)

MOE = .98/sqrt(3168) = 1.74% * cluster factor?

For you, the cluster factor = 250%
For everyone else, it's from 0 to 30%
and the MoE = 1.74% - 2.30%.

For a 13047 sample, the MoE = .98/sqrt(13047) =0.857%.
Add 30%, the MoE = 1.13%

You are in a world of denial.

[WI Independent]

21. You didn't address his assertion...

He asserted that Mitofski stated the MOE was 6.5%.

If this is a true assertion then it's case closed IMO. Since Mitofski seems to be the one that set up the sampling clusters and weighting, I would have to assume either:

1) he knows what he's doing (including his MOE)
-or-
2) he doesn't (including his weighting)


I can't see accepting part of his work then off-handedly rejecting the other.

[Time for change]

24. The margin of error was nowhere near 6.5%

6.5% was the within precinct error -- which essentially means the within precinct discrepancy between the actual vote count and the exit poll. This was way outside of the margin of error, which means the probability of that happening by chance is miniscule -- as noted in the USCountVotes report.

[mgr]

30. No, it adumbrates upwards through out the sample weighting.

If there is no bias.

The MOE of 6.5% is the WPE error, which Mitofski argues is characteristic of a design bias, he suggests that he fails to adequately control for the variability within the exit poll takers methods (resulting in an undersampling of Bush supporters), and that this generates a bias that does not permit employing the central limit theorum that would allow one to combine the precincts into a larger population, and thus have a smaller MOE. It is a skew that likely does not allow the exit poll to fall within a goodness fit test parameter with the election results both at the state level and the national level.

Mike

[TruthIsAll]

25. Edison/Mitofsky stated that the MOE was 1.0% for his National

Exit poll. Its right there at the bottom of the page.

Mitofsky also stated the Reluctant Bush Responder as a possible reason for the discrepancy.

The MoE argument, and the cluster effect, have long been refuted.

Do you want to believe a 200% cluster effect?
They will make it 500% if that's what they need to say that the polling results are off.

And I suppose you want to believe the 43/37% split was due to sampling error.

THE FINAL EXIT POLL WAS MANIPULATED TO MATCH THE VOTE.

AS A DEMOCRAT, THAT SHOULD BOTHER YOU.

[mgr]

31. I believe this was in Mitofski's response to Freeman's first report, or

on Mystery Pollster. I cannot get it right now, and cannot afford to stay this late in the office. Tomorrow.

Mike

[mgr]

38. Here's a link

http://www.mysterypollster.com/main/2004/12/so_if_exit_poll.html
http://www.mysterypollster.com/main/2004/12/what_is_the_sam.html

I could recall a post somewhere summarizing Mitofski's private communitcation with Freeman, that addressed three things--cluster sampling, a 99.5 CI, and an MOE far greater than 1. If anyone has it, please provide.

However, the mystery pollster has a citation of 5 to 8%, which is sufficient to bury the margin with the MOE.

Mike

[davidgmills]

22. Order of magnitude

You say:

"The order of magnitude between the sample and the population is too vast to be reliable."

I think he would concur with this statement; but I don't believe Mitofsky or USCOuntVotes would agree with it.

As TIA points out, and I have heard it elsewhere, that if the sample is random or truly representative of a fraction of the whole, the total number of voters makes no difference whether the total voters number 100,000 or 100 million.

[mgr]

28. If the sample were random, and if there was no bias.

The sample is not random, but specific to precincts with preselected demographic criteria. The randomization is only within the precinct population. One compares the random sample within the non randomly selected precinct to determine how close you got to getting it right, and then a multiplier is introduced to match 100% turnout. Any errors at the sample level (only respondents) is multiplied up wards and increases the allometry of the sample error.

The control to this is the number of precincts sampled has to be large enough to prevent random drift from affecting the sampling. My experience is that this is around 20 or so samples.

The bias, which you have not revealed to him, but is addressed in the NEP report would make him even more skeptical. This indicates that the sampling was not representative of the whole, but skewed in a manner not consistent with patterns previously encountered.

With a 6.5% MOE (given in a response to the early draft of what is was Freeman's report by Mitofski)representing 13 million votes, translates into having mis-sampled how many voters out of the 13,000 or so?

Mike

[eomer]

36. You've made an implicit assumption that the "bias" is really a bias.

"The bias, which you have not revealed to him, but is addressed in the NEP report would make him even more skeptical. This indicates that the sampling was not representative of the whole, but skewed in a manner not consistent with patterns previously encountered."

The so-called bias is actually a discrepancy between the exit poll result and the official count result. The cause of the discrepancy is a subject of debate, not a fact that can just be revealed as you imply.

One possible explanation for the discrepancy is NEP's theory of the reluctant Bush responder (rBr), which they call a bias. NEP does not provide any evidence to support this conclusion.

The other possible explanation is that the exit poll is correct and the official result is wrong, due to errors, fraud or both. In other words, the exit poll has no bias - it is actually correct. USCountVotes does point to evidence to support this conclusion.

[mgr]

39. I think you underestimate what NEP demonstrates

Good luck explaining this to a PhD in Chem with 40 years teaching experience.

Mitofski discussed the reluctant Bush responder problem in early November as a hunch, because the pattern was too extreme for a Kerry victory. The report possesses the evaluation that supports that hunch, and makes it a plausible hypothesis--that poor training and preparation of the exit pollsters allowed for an unacceptable level of bias to enter into the calculations of voter preference at the precinct level, this bias is evident in under sampling of voters that preferred Bush.

You cannot argue that one is competent to conduct and design a sampling experiment, but not competent to evaluate it. I'm on record stating that I think NEP's work is crap, but that is because the bias is so great that you cannot postulate any changes within the sub populations that the polling was to supposed to characterize.

Mitofski's evaluation has the real possibility of MSM pulling the plug on any future exit polling, if it takes on the parameters of "junk science". Constant expansion of the numbers of precincts sampled over two elections, and the error bar increases? You still need time to perfect your methods? What are we paying you for?

I've looked at the USCVotes report. I've not reached any conclusions yet, but I think it makes a repeated presentational error--it addresses precinct WPE as percentages, but never directly gives how many precincts are included in each comparison group. This makes their case appear stronger than it may be, if what you are comparing is three precincts to seven hundred (which is approximately the case when you compare what they are evaluating to the evidence in the NEP report).

I also noted the use of an 'and' in characterizing NEP protocols when I suspect it should be an 'or', but I have not been able to evaluate how that difference in the logical connective affects their argument.

By the way, when is anyone going to evaluate the LA Times exit poll?

Mike

[liam_laddie]

41. past NEP results

Are you saying that the 2000 polls were wrong? Didn't Gore win the popular vote by a half-million? Didn't he "win" FL, had the SCOUS not stopped the FL recount? (there's judicial integrity
...read the tortured reasoning supporting that ONE vote which appointed * CinC)
I recall that post-election, the media sponsored recount, though not complete, concluded that Gore would prevail.

[mgr]

44. The NEP report only applies to 2004.

It establishes a problem with the 2004 election, but that problem may undermine the certainty one may have with the methods applied in 2000 (It has mine). There was not the bias issue in 2000. I don't recall anyone bothering with a fraud analysis of those results.

As a favor, I understand the semaphore is accepted practice, but I almost mistook chimp in charge for Cincinnati (!). Could you spell it out for us older farts on occasion (insert semaphore for smile).

Gore won in 2000. He ain't president, legal precedent was manufactured, and we have another problem now. We need reform on how federal elections may be challenged, and the timelines for those challenges. Ohio is obvious, but there may have been crap going on with the other battleground states. You cannot get to the problem with NEP or TIA, that is all I am saying.

Mike

[eomer]

45. What, that they establish rBr as a plausible hypothesis?

If you think that is a big deal then I assume you are equally impressed that USCountVotes establishes election fraud as a plausible hypothesis.

I won't argue whether rBr is a plausible hypothesis because I don't see any need to. Let's stipulate that it is for the sake of argument. The relevant argument is this: there are two hypotheses - one that rBr occurred and the other that election fraud occurred. (As you mention, these are not mutually exclusive - both may have occurred to some extent.)

We should not tolerate an election system that does not provide enough transparency and verifiability to distinguish which of these hypotheses is correct. After all, we are talking about a swing of about 5.5%. Surely we can do better than that.

The conclusion I am arguing for is that further investigation is warranted. The fact of the discrepancy should be sufficient to win this argument. A serious investigation with subpoena power and a credibly non-partisan approach should be started and continue until hard facts are uncovered to explain the discrepancy.

[mgr]

46. Fraud is not the question

With a swing of 5.5% you cannot detect fraud in the national election poll. What I have been arguing, but have held off on posting, is that one may be able to evaluate the exit poll results specific for the battleground states, through an ANOVA, as the bias issue may be not independent (equally distributed in all states), but may correlate to specific states and precincts. Reviewing the NEP, I get the inkling that high WPE would be greatest in Ohio. If there is a preponderance in Ohio, then maybe another state has fewer.

The reason I have held off is that the idea that the exit poll can detect fraud in the national election is pervasive, and to question TIA is tantamount to being called a "freeper".

My agenda is simple-- show that without a doubt, the national election results cannot be addressed through the NEP exit poll contra TIA, present a model for how one may reduce the MOE for battleground state exit polls that may allow for assessment whether fraud could occur, and try to keep Richard Pombo from being re-elected.

Mike

[eomer]

48. I'm aware of your position on that...

I just don't agree with you.

If the issue were using the exit poll as proof of fraud and as the final word on the subject then I would agree with you.

But the issue is only to say that there is a discrepancy that needs to be investigated.

Surely as a scientist you cannot argue against investigating?

[mgr]

50. I don't think we have all that much to disagree on then

I'm a touch cranky with absolutists, so it is sometimes hard to separate out the straddlers.

What is making me cranky is that this discussion has not moved forward since December, and we are running our own clock out. I've been troubled that no one with any stats experience seems to weigh in on how to move the issue forward on the state exit poll side, since the Washington recount showed that the red shift was probably an artifact of the sampling design.

We should have had it together when the precinct data was deposited.

I will try to generate a half coherent thread tomorrow, as to the formulation of the ANOVA and the F statistic tables. I am not comfortable that I can give the computation instruction with sufficient clarity at this time, I like having the time to stew over something. Constructive criticism will be welcome.

Mike

[TruthIsAll]

56. You do not WANT the discussion to move forward. That's why you are here.

You have not advanced the discussion one iota; you have only tried to smother it. To nip it in the bud, so to speak.

Well, its too late.

The horses have fled the corral.

[TruthIsAll]

27. Creating a new theory of statistical sampling, are you?

You are being supremely arrogant to ignore the well-known statistical relationship between survey sample-size, confidence intervals, standard deviation and margin of error.

So 13,000 polling respondents are not enough for you?. Are you creating your own revolutionary statistical theories, mgr? Do you claim to rebut the theorems built by mathematicians such as Laplace, Gauss, Bernoulli and Chebyshev over the last three centuries?

Do you claim to stand on the shoulders of these giants, like all mathematicians who have come after them, or are you so presumptuous as to demean their work for the ages? Just whose shoulders are you standing on here?

May I ask, mgr, what you know to be a typical pre-election national poll sample? Isn't it 1000-1500, with a 2.5-3.1% margin of error?

But now you are telling all professional pollsters that they are FOS and should follow your lead by polling 100,000 or more.

Are you asking them to foot the bill by an order of magnitude just so they can decrease the MoE? They know the MoE, because it is their business to know, that it is 3% for a 1000 sample-size, 1% for 10,000 and 0.3% for 100,000.

Do you really think they will follow your advice and poll 100,000 to cut the MoE to 0.3%? Isn't 13,000 respondents and 1.0% good enough for you? And yet you display the nerve and the arrogance to tell the world of professional polling that 13,000 is not enough?

How much is enough for you?

mgr, for one as erudite and intelligent as you otherwise appear to be, your postings on this topic are beyond comprehension.

Those who know how to apply basic Probability and Statistics 101 to problem solving find your misleading rantings more than just a distraction, they are fundamentally anathema to the belief that we build on the knowledge accumulated by those giants who have given us the tools we need to find the truth that exists today so that we can build a better world for tommorrow.

To put it simply mgr, your twisting of logic is not just unscientific, it's un-American.

[mgr]

43. My gods are Darwin, Fischer, Dobzhanski, Huxley, Mayr, and Simpson

Maybe Galton.

Someone at my work recently said "An idiot with a calculator may think he's an engineer, but have him design the bridge, and see. The only problem is that he may not know he is not until the bridge falls. By then he will have been promoted"

I find it laughable that you consider a sample of 13,660 adequate to characterize an election of over 100 million votes, when it is apparent that human foibles of whether a poll taker is young or old determines how many responses you receive.

The only figure we are addressing is Mitofski. I may, like Newton avowed, be a dwarf ("That we are only dwarfs standing on the shoulders of giants") but I am not challenging the core of statistical inference.

But neither are you a statistician nor have experience with experimental design to even carry my lunch. What I have said time and again, is the only manner in which one can get past the bias (real or artifactual) is with an ANOVA with an F test to permit aggregation of only the precincts with an acceptable MOE based on the F test. The larger the sample, the more outliers you can permit yourself to ignore because they are inconsistent with the overall trend, while having a sufficiently tight MOE.

If you have more precincts sampled, the abler you are to select a sufficient number to perform an ANOVA, and the tighter the variance, the tighter that 66% of your sample rests within one standard deviation to wards the mean/median/mode, and the tighter the MOE.

You keep ignoring preconditions that permit an analyst to continue or not with a statistical analysis and associated computations. You manipulate spreadsheets, but you are not involved in any critical or reasoned appraisal of what needs to be done to unbullock NEP's bias. You continually conduct calculations that are not proofs, but suppositions.

'Look what happens when I assume the MOE is 1%.' One repeats it enough times, and the unsophisticated may come to think it is how arguments are made--state the antecedent, and the consequent proves it. Isn't that teleology? Wasn't that the problem with Ockham's razor in its original formulation? Isn't that what gets us to where one favors design over randomness? Isn't it a logical fallacy, yet you seem to engage in it all the time.

You continually cite the scientific design of the exit poll written prior to the exit poll having been conducted, as if it applied a posteriori, all the while ignoring statements by the designer and his team that bias entered into the sampling, and the MOE should be much greater (on the order of 5% to 8%).

At this point you have nothing more to offer. You are in the way. Spare me the false indignation. You offend your gods more than I offend mine.

Mike

[TruthIsAll]

55. Once again, do you KNOW how to calculate the MoE?

The formula does not have Mitofsky's or anyone else's name attached to it, last time I looked.

The bottom line, mgr, is this: Those of us at DU and elsewhere use available data and apply standard, plain vanilla, statistical measures to come up with probabilities. It's not the rocket science you make it out to be. The mathematics is readily available in any text.

You INVENT your own suppositions, just like you have with your 6.5% MOE WHEN YOU HAVE BEEN TOLD TIME AND TIME AGAIN THAT IT IS NOT AN MOE. IT'S WITHIN-PRECINCT ERROR. YET YOU BLINDLY FORGE AHEAD WITHOUT ADMITTING THAT YOU ARE WRONG.

You seek to make simple things complex. You have some gonads to question the competence of ALL polling organizations by claiming that YOU alone will come up with the ultimate solution to the sampling problem which in fact was solved a long time ago. All you need is a day or so to get your thoughts together. Right.

Just what do you feed on?

You SOUND like you know what you're talking about, but you only use mathematical terminology to mislead and impress: ANOVA, SPATIAL CORRELATIONS, KURTOSIS?

Do you really think anyone here will believe that your 40 years as a chemist matches up against world class-mathematicians at uscountvotes.org and elsewhere? These are heads of departments at world-class universities who have put their reputations on the line.

Why don't you just stick to your expertise? In your case, a little knowledge is not dangerous, it's just laughable.

And please stop repeating the personal attacks: Just once, can you write a post without resorting to your mantra:

"tia claims to be a statistician"...
or
"tia claims to be a mathematician...
or
"tia claims to be a software engineer who shows his incompetence every time he posts his probability threads..."

Your personal attacks are getting old.

Do you dream about my postings every night? Why do they bother you so much?

My posts only assert what we all know at DU: Bush stole it. Again.
Do you disagree?

You believe there was fraud, right? Of course you do. You have said so.But you will also say, if you don't mind my putting words in your mouth, that although there are indications of fraud, this happens in every election, and there was not enough of it to steal the election.

So far, not one of your postings has been either comprehensible or believable. On the contrary, they appear to be rantings of quiet desperation.

[Time for change]

23. Pick up any scientific journal that deals with human subjects

and see how many studies have more than 13,000 subjects in them. That would be a very low percent.

I'm an epidemiologist, so my whole career has involved studies like this, and very few of them have included more than 13,000 subjects. Yet these studies are meant to apply to the general population as a whole. Studies like this are the reason why we know that cigarette smoking causes cancer and that medication to reduce blood pressure can prevent stroke or heart attacks.

This is basic statistics, and the great majority of what we know about health status and risk factors for disease in this country are based on studies of less than 13,000 subjects, with methodology a whole lot less precise than the Mitofski-Edison exit polls or the "US CountVotes" analysis of them.

Does your father have any experience with these kinds of studies?

[mgr]

29. Epidemiology often uses an explicit control group

My experience with the epidemiology literature is scant, and will defer to your experience, but the biggest problem in comparison of the two is that there is usually a control group for comparison in most cases, and the CI is 99%.

Mike

[Time for change]

33. Your point about control groups is irrelevant

Control groups are used in epidemiological studies when there is a need for comparison between two groups. For example, if you want to assess the association between cancer and smoking you need to compare smokers with non-smokers, which would be the control group. But if you simply want to assess the prevalence of a disease in a population, which would be comparable to assessing the percentage of voters who voted for a particular candidate, a control group is not relevant.

[mgr]

42. I agree

I was not certain as to what class of studies you made reference to.

I think there might be a problem in the comparison between the types of inquiry an epidemiological study makes and an exit poll does. But my mind is old and rustier than I would like. It may have to do with the determinism of the sampling.

I think you are right that both have their basis within a multivariate context, but I don't think you are being completely frank in that you do not consider how goodness of fit tests may fit into both practices. Sampling should give some sense of an expected frequency, and comparison between the two should be conducted. I do not know if a goodness of fit test between the exit poll and the results has been conducted (good old p hat and q hat).

I suspect that the average WPE reported in NEP reflects an internal attempt to do a goodness of fit test.

That said, your experience should give you pause that when a researcher reports bias in his experimental design to probably take him at his word. The experimental design requires precincts that have WPE less than 4 if they are to be aggregated into a larger population (a national or state sample), or that the WPE that varies in both directions is balanced (the error cancels itself out). If there is directional bias in excess of the design WPE, you cannot combine these samples into a larger population within the bias term being included--you cannot simply allow the central limit theorem to permit you the reward for controlling sample error or bias with a smaller MOE. It would be, in a word, unethical.

One method to do this is sum(MOE1/n1, MOEn/nn)/n which if the average WPE MOE is 6.5% makes all the aggregated samples MOE about 6.5%, and is consistent with what NEP reported on Mystery Pollster.

http://www.mysterypollster.com/main/2004/12/so_if_exit_poll.html

Mike

[TruthIsAll]

59. mgr, you really should try this SAMPLE on for SIZE...

Sample size calculator
http://www.raosoft.com/samplesize.html


The margin of error is the amount of error that you can tolerate. If 90% of respondents answer yes, while 10% answer no, you may be able to tolerate a larger amount of error than if the respondents are split 50-50 or 45-55.

Lower margin of error requires a larger sample size.
What margin of error can you accept?
5% is a common choice.
Why don't you try 1%, just like the National Exit Poll?
1%

The confidence level is the amount of uncertainty you can tolerate. Suppose that you have 20 yes-no questions in your survey. With a confidence level of 95%, you would expect that for one of the questions (1 in 20), the percentage of people who answer yes would be more than the margin of error away from the true answer. The true answer is the percentage you would get if you exhaustively interviewed everyone.

What confidence level do you need?
Typical choices are 90%, 95%, or 99%
You like 95%?
That's 2 standard deviations from the mean.
Can you live with that?
Ok, 95%

How many people are there to choose your random sample from? The sample size doesn't change much for populations larger than 20,000.
Higher confidence level requires a larger sample size.
What is the population size?
Oh, you don't think 20,000 is enough?
Ok, try 100,000,000 voters

For each question, what do you expect the results will be? If the sample is skewed highly to one end, the population probably is, too. If you don't know, use 50%. This gives you the largest sample size.
Almost there

What is the response distribution?
The most conservative choice is 50%
Assume 50%.
You're a conservative, anyway.

******* mgr, your recommended sample size is 9603******

This is the minimum recommended size of your survey. If you create a sample of this many people and get responses from everyone, you're more likely to get a correct answer than you would from a large sample where only a small percentage of the sample responds to your survey.

Alternate Scenarios
Are you a believer in sensitive anlysis?
You know, the kind I like to present?

With a sample size of 1000, 3168, 13047:
your margin of error would be 3.10%, 1.74%, 0.86%, respectively.

With a confidence level of 95%, 97%, 99%:
your sample size would need to be 9603, 11772, 16585, respectively.

As you're a beginner, mgr, I suggest you read Basic Statistics:
A Modern Approach and The Cartoon Guide to Statistics.

In terms of the numbers you selected above, the sample size n and margin of error E are given by x = Z(c/100)2r(100-r)

n = Nx/((N-1)E2 + x)
E = Sqrt<(N - n)x/n(N-1)>

where N is the population size, r is the fraction of responses that you are interested in, and Z(c/100) is the critical value for the confidence level c.

Happy MoEing.

[davidgmills]

32. Lots of experience

My father probably wrote nearly 100 published papers and critically reviewed many hundreds more for publication.

You do make an interesting point; i.e., why would the scientific community make all kinds of recommendations based on health risk analyses which were far less precise than the exit polls.

Maybe the difference is as mgr states that you have control groups. Or maybe that kind of precision is not necessary when making health risk recommendations. Does that make a difference or not?

I have cited or shown many studies in the past to my dad which he readily accepted. I do know he can pick apart many different kinds of scientific studies. Maybe he has a bias of his own that he just intrinsically believes that polls are not very accurate so what he perceives as flaws jump out at him.

[Time for change]

34. Yes, perhaps your dad has a bias about polls

If they are so illegitimate, why are so many millions of dollars spent on them by the people who are most interested in the outcome of elections?

With regard to the necessary precision, that varies with the study. In the case of the M-E poll, even Mitofsky admits that statistically the odds are astronomical against the possibility that random error accounted for the discrepancy between their exit polls and the election result.

[davidgmills]

35. Cognative Dissonance perhaps

My father like many Americans, would not want to face the implications of what the exit poll discrepancy means. I don't want to face it either. It means that we have had an electronically engineered bloodless (so far) coup.

I am a lawyer and the implications are very hard for someone who has taken an oath to support and defend the Constitution of the United States. I keep telling myself I must be wrong, but I know I am not.

[liam_laddie]

40. polls, surveys

Ask your dad, and yourself, why TV networks, major print
media, major market research firms, automakers...spend $$MILLIONS annually to use these techniques for "accurizing" business decisions, pitching advertisers, and so on. They use sampling, random in the sense that they select from the population, a "representative" sample chosen by past experience and recognized methods, to poll or question, and use these results with a relatively high degree of confidence.
And the sample sizes are generally much smaller than the 13K+
chosen for NEP's national sample. You're saying that these professionals are not to be trusted or believed? Tell that to
a few thousand CEO's...
BTW, re: your second paragraph...anyone who has participated
in this "bloodless coup" should be tried for treason and publically hung, IMHO. The death penalty SHOULD be used in these cases; and I'm not normally in favor of the "ultimate punishment."
And to take nothing away from your dad's background, but his
experience and career don't necessarily make him expert in
a non-related discipline. Unless exit-polling is a hobby, that is...

[davidgmills]

49. I am on the side that believes that the polls were accurate enough

to predict a fraudulent election. But I am not a mathmatician or scientist and people like mgr give me pause. I am not capable of judging his opinions and I am not really capable of judging my father's when it comes to science or math.

Still, I am like you and have a hard time believing that ceo's and other people whose livelihoods depend on polling and are willing to spend millions of dollars on it would do so if the accuracy of polling weren't proved. But it may be that in these commercial cases if the polls are off by 5% it really doesn't matter and that accuracy within 5% is good enough. So I don't find the financial argument all that persuasive at the level of accuracy we need to prove fraud.

I am encouraged by people like the epidemiologist who finds the exit polls accurate enough to convince him. In my father's case, I don't think he wants to find fraud so I think he works hard at finding fault with polling. I can assure you he knows absolutely nothing about computers and was more shocked by the Chuck Herrin article. The problem there was that Chuck does not write at all like an academic and dumbs down his article to Joe six pack level. To an academic, that is a no no and academics find this type of article difficult to accept. I need to get him the Johns Hopkins study if I want to convince him about the ease of computer electoral fraud.

[mgr]

52. As an attorney you are trained in logic

All of this centers on logic. Keep that at your center. As an attorney the key concept, from Scottish law, is the appeal to common sense. Science is organized common sense according to Thomas Huxley. Common sense is what underlies David Hume's radical empiricism and scientific materialism. Everything about the scientific method is built from this foundation. If something misaligns with your common sense, you have the right to reject it.

As I tried to explain before, the difference between legal proof and scientific proof is that circumstantial evidence to the scientist is not an acceptable criterion of proof, it is speculation. What you are describing are you attempts to persuade your father using circumstantial evidence, that in your opinion as an attorney is sufficiently damning, but being speculation he will not consider. (After all there is that story from Scottish jurisprudence regarding the corpus delicti)

Ask him to do as David Hume, take off the hat of the philosopher, and to then consider your argument. If Herrin shocked him, then give him what you consider the strongest evidence, given that you do not have a compass for evaluating scientific and mathematical explanations (in other words avoid these). Don't just reiterate with a more academic study, I think he got the gist.

I will tell you that the preponderance of circumstantial evidence is what makes me think fraud occurred. My scientific training and common sense balks at accepting the NEP exit polling though.

Good luck, Mike

[davidgmills]

58. Circumstantial evidence

Circumstantial evidence is not speculation. The evidence itself, say for example, a murder suspect fleeing town, is not speculation. It is the inference from the evidence which may be speculation. But that is part of logic. Do these two things, a murder, and a suspect leaving town, have a relationship or not? The more the circumstantial evidence points to one conclusion, the more likely the conclusion is correct.

Unfortunately in law, we don't have the certainty that science does. Until we get a fool proof lie detector, we won't. So proving election fraud in the courtroom takes much less precision than scientific proof. That is why I have said from the begining an exit poll is good enough proof to win an election controversy.

[mgr]

47. I think you may under estimate your father

It would not be the first time for it to happen to a son.

The fact that he has been open when you have approached him on the issue suggests that what you discuss he gives a fair shake.

His statement regarding the Ukraine is consonant with what others have averred on this site, that our government interceded in the election, not because of the exit poll, but of well documented fraud and suppression, as well as a geopolitical interest (compare it to our non-involvement in Zimbabwe's current election).

The bloodless coup occurred in 2000. If he's a Democrat and in academia, he's already sensitized, and may be better informed than you think. His standards for proof are going to be high, and let's face it, the exit poll conducted this year was inadequate to provide stringent proof alone.

Try some of the articles about what occurred in Ohio, and see what his response is to those.

Mike

[davidgmills]

51. A couple of responses

I knew my dad's position on exit polling long before I sent him the article. He doesn't like them. I suspected he would find fault with the article when I sent it. Still I wanted his input.

In 2000 he was quick to criticize people who could not properly mark a ballot. I am much more tolerant of inept behavior than he, and I am inclined to blame those who make voting difficult for the mentally challenged rather than blame the mentally challenged. He doesn't see any problem with a voting system that confuses the mentally less gifted; I do. I want to know who they want for President not whether they can read a butterfly ballot. Voting should be no more difficult than picking a person out of a lineup.

He naively, I think, believes that we can accurately count 120 million votes. I don't. We can't do a census accurately; why should we think we can do voting any more accurately? I also believe that when 1 billion dollars are spent by the two major political parties to get their man elected, the financial stakes are very high and the incentive for fraud is huge. I find no comparable incentive for exit poll fraud.

The issue for me has never been whether the exit polls are accurate enough to prove fraud. The issue for me has always been which one of these two systems, the exit polls or the actual tabulation, is likely to be the most accurate at determining the intent of the voters of America. As between the two, I think exit polling is much more likely to give an accurate measure of the intent of the voters.

You may find fault with the accuracy of the exit polls. We have picked their accuracy to death. Have we subjected the actual tabulations to the same scrutiny? No way. An exit poll is the only check on a fraudulent tabulation. It is not a perfect check, but when large discrepancies occur, investigation of the actual tabulations are warranted and those investigations never happened.

As for the coup of 2000, that did not bother me nearly as much as this one has. I didn't like what the Supreme Court did in 2000, but I accepted a legal solution to a legal quagmire. It did appear to have propriety and openness. The coup of 2004 had neither. It was just underhanded, dark and ugly.

[mgr]

53. In no way would I disagree

I do not know your father. But if he is a scientist, I would caution against describing his conception of what constitutes accurate as naive, ignorant possibly.

I am troubled that he accepted the media portrayal of what produced the high ballot spoilage in Florida to people not knowing how to mark their ballots. I thought that argument was preposterous on its face. I think how people responded to that account revealed much about their hidden assumptions regarding other's abilities and deficiencies. Those involved were elderly Jews, and we know what educational stratum of American culture they attain to, and if it is not the apex, then I do not know what I am talking about.

You and I have much to agree on, and that is how I would like it to remain. I take great stock in maintaining good relations between father and son, since I am the first male in my family out of memory that has fathered a child, that remained alive, or married for more than ten years after the child's birth, and stays involved in their child's life. I hope I can keep it that way.

Mike

[Time for change]

54. Cognative dissonance -- that is exactly right

I have been absolutely amazed that there is so much unwillingness in this country to recognize a stolen election when the evidence for it is overwhelming and staring them in the face.

Even for people who don't understand the statistical evidence, how can we accept the fact that our votes are counted with "proprietary" (i.e., secret) software programs?

But you are absolutely correct. Most people have a very difficult time believing something that they really don't want to believe.

But if we as a country don't wake up and admit the obvious we're doomed to repeat the lessons of all the other great fallen civilizations of history.

[berniew1]

37. Exit poll data isn't the only case; there is documentation of the major

problems that caused a huge swing, and statistical analyses by myself, Univ. of Calif.-Berkeley researchers, others, that found results consistent with each other and the Exit Poll data; the studies by the researchers at the Nashville conference were consistent with each other and other Univ. researchers studies and of similar magnitudes regarding the swing.

A combination of documenation and analysis by researchers at the Nashville Conference on 2004 Election Irregularities makes a strong case that Kerry won Ohio, and the national election:

http://www.flcv.com/ohiosum.html

Florida http://www.flcv.com/fla04EAS.html
http://www.flcv.com/fraudpat.html

Nationwide: http://www.flcv.com/summary.html

[Sancho]

57. Here's a power analysis as an example:

At http://www.raosoft.com/samplesize.html there is a sample size calculator typical for statistical power.

With a margin of error of .05 (typical), a confidence level of 95%, a population size of 120,000,000 and a 50/50 predicted distribution (democratic, republican), the suggested minimal sample size is....385. For 99% confidence you would need 664 in the sample.

Random samples are very powerful for simple dichotomous choices.

Think about it - if you had 120,000,000 coins and they were supposed to be fair, and you tossed 500 randomly chosen coins and got 290 heads and 210 tails, would you conclude the coins were fair or biased to the heads. There seems to be a big difference between 290 and 210, but that's 8% of 500.

Here, we have 13, 360 "randomly" or "representatively" chosen coins and Kerry won....hmmmmm.....