ONE IN 257 TRILLION? The state exit poll MOE's were too conservative.

[TruthIsAll]

It turns out that in my prior analysis, I have been conservative in calculating state exit poll margin of error.

Here's the simple formula I've been using all along:
MOE= 1/sqrt/(N), where N = sample size.

The simple MOE is slightly higher than the MOE calculated using the more accurate formula:
MOE = 1.96*sqrt(p*(1-p))/sqrt(N).

Here's an example of how the formula is used:
Assume a state has N exit poll respondents and the 2-party percentage is Kerry 52%/Bush 48%.

N = 1000
P = 0.52
1-P = 0.48

Using the simple (conservative) formula,
MOE = 1/sqrt(N) = 3.16%

Using the more accurate formula,
MOE = 1.96*sqrt(P*(1-P))/sqrt(N)= 3.10%

Applying the more accurate MOE to the final state 2-party vote percentages and Freeman's exit poll results, we find that SEVENTEEN (17) states deviated to Bush beyond the MOE. Using the prior, simple MOE formula, sixteen (16) deviated.

So, what's the big deal, you ask?
Once again, let's calculate the probabilities:

Using the simple, conservative formula:
1) 16 states deviated beyond the MOE

Probability =1 - BINOMDIST(15,50,0.025,TRUE)= 5.24025E-14
or 1 in 19,083,049,268,519 (1 in 19 TRILLION).

Using the more accurate formula:
2) 17 states deviated beyond the MOE

Probability =1-BINOMDIST(16,50,0.025,TRUE)= 3.88578E-15
or 1 in 257,348,550,135,457 (1 in 257 TRILLION)

But, I'm not done yet...

Another state fell within a hair of the MOE. If we included it, then 18 states would fall beyond the MOE. The probability of that occurrence is as close to ZERO as you can get.

It's less than 10E-30, which is STATISTICALLY IMPOSSIBLE.

[jab105]

1. Ah, but the Republicans accounted for all those statistics...

they interviewed more democrats than Republicans...you see...democrats are friendlier...and your statistics cant account for the fact that nice democrats give poll workers information a whole lot more often than Republicans...problem solved (or at least accounted for in a really back-assward make the polls fit the results sort of way:))

[Chi]

2. No...it was the rain!! I read it at Freeperville...

sarcasm off

[Disfronted]

3. it could be 1 in 500 gazillion - the issues haven't changed

Ok, I don't get your point. You've proven 2 things:

1) The exit polls did not match the reported results
2) This was not due to sampling error

Are the Republicans even denying this? Of course the exit polls were wrong. The real issue is the reason, be it:

1) An poorly-chosen sample
2) fraud

Republicans push the first explantion, Democrats the second, but neither one requires you to believe the exit polls are accurate.

You don't have to crunch numbers to figure out if 40/50 states lean one way versus the exit polls, it's not randomness - that is obvious. The real question is why the numbers don't match.

[TruthIsAll]

4. You appreciate the odds; many do not. That's the point. But you are right.

You know damn well why the numbers don't match.
Thousands of anomalies...99.9% favoring Bush.

It sure wasn't faulty polling.

[dzika]

5. TIA, I almost wish I didn't believe you...

...but I do. And it sucks.

[TruthIsAll]

6. OK, here is the full probability tree

Number	
states	
beyond	Probability
MOE	1 in
1	1.4
2	3
3	8
4	28
5	123
6	662
7	4,214
8	31,188
9	264,775
10	2,551,003
11	27,650,777
12	334,779,027
13	4,500,728,464
14	66,853,020,488
15	1,092,586,148,150
16	19,577,335,627,708
17	383,460,581,646,824
18	8,189,695,680,931,680
19	190,319,450,041,161,000
20	4,804,103,490,729,780,000
21	131,535,012,282,613,000,000
22	3,901,974,362,957,790,000,000
23	125,306,706,297,519,000,000,000
24	4,353,671,419,737,160,000,000,000
25	163,598,780,929,116,000,000,000,000
26	6,648,193,701,525,870,000,000,000,000
27	292,204,109,059,574,000,000,000,000,000
28	13,896,097,266,080,100,000,000,000,000,000
29	715,477,803,848,928,000,000,000,000,000,000
30	39,919,266,727,746,200,000,000,000,000,000,000
31	2,416,346,782,507,100,000,000,000,000,000,000,000
32	158,914,991,404,095,000,000,000,000,000,000,000,000
33	11,375,826,489,208,300,000,000,000,000,000,000,000,000
34	888,300,430,007,246,000,000,000,000,000,000,000,000,000
35	75,862,583,475,284,400,000,000,000,000,000,000,000,000,000
36	7,107,773,520,372,520,000,000,000,000,000,000,000,000,000,000
37	733,295,463,227,010,000,000,000,000,000,000,000,000,000,000,000
38	83,670,002,377,083,200,000,000,000,000,000,000,000,000,000,000,000
39	10,614,122,675,345,300,000,000,000,000,000,000,000,000,000,000,000,000
40	1,506,483,027,083,520,000,000,000,000,000,000,000,000,000,000,000,000,000
41	241,070,528,151,754,000,000,000,000,000,000,000,000,000,000,000,000,000,000
42	43,906,750,235,413,300,000,000,000,000,000,000,000,000,000,000,000,000,000,000
43	9,210,338,869,052,550,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
44	2,259,344,869,726,780,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
45	661,276,977,742,810,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
46	237,409,991,198,539,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
47	108,856,287,475,067,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
48	67,964,127,794,279,700,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
49	64,974,402,882,020,900,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
50	126,765,060,022,822,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

[TruthIsAll]

10. Here are the Seventeen (CT almost made it)

		Poll			Kerry	2party	Poll	Prob.	Dev/	Beyond
	St	Size	MOE	StDev	Vote	Poll	Dev	Dev	MOE	MOE?
1	NH	1849	2.27%	1.16%	50.69%	55.50	-4.81%	0.00%	-2.12	Yes
2	NY	1452	2.47%	1.26%	59.29%	63.97	-4.68%	0.01%	-1.89	Yes
3	SC	1735	2.34%	1.20%	41.36%	45.79	-4.42%	0.01%	-1.89	Yes
4	NC	2167	2.10%	1.07%	43.76%	47.31	-3.55%	0.05%	-1.69	Yes
5	VT	685	3.56%	1.81%	60.30%	65.69	-5.38%	0.15%	-1.51	Yes

6	PA	1930	2.22%	1.13%	51.26%	54.41	-3.15%	0.27%	-1.42	Yes
7	OH	1963	2.21%	1.13%	48.94%	52.06	-3.12%	0.28%	-1.41	Yes
8	MN	2178	2.09%	1.07%	51.76%	54.61	-2.85%	0.38%	-1.36	Yes
9	FL	2846	1.84%	0.94%	47.48%	49.93	-2.45%	0.44%	-1.34	Yes
10	DE	770	3.48%	1.78%	53.83%	58.44	-4.61%	0.47%	-1.32	Yes

11	MA	889	3.10%	1.58%	62.68%	66.46	-3.79%	0.84%	-1.22	Yes
12	AL	730	3.57%	1.82%	37.10%	41.08	-3.98%	1.45%	-1.11	Yes
13	RI	809	3.30%	1.69%	60.58%	64.24	-3.66%	1.49%	-1.11	Yes
14	NJ	1520	2.49%	1.27%	53.40%	56.13	-2.73%	1.61%	-1.09	Yes
15	AK	910	3.18%	1.62%	36.77%	40.14	-3.37%	1.91%	-1.06	Yes

16	UT	798	3.18%	1.62%	26.65%	29.93	-3.28%	2.16%	-1.03	Yes
17	NE	785	3.37%	1.72%	33.15%	36.54	-3.39%	2.43%	-1.01	Yes
18	CT	872	3.27%	1.67%	55.28%	58.47	-3.20%	2.76%	-0.98	
19	NV	2116	2.13%	1.09%	48.68%	50.66	-1.98%	3.44%	-0.93	
20	AR	1402	2.61%	1.33%	44.72%	46.93	-2.21%	4.89%	-0.84	

21	VA	1431	2.59%	1.32%	45.87%	47.96	-2.09%	5.65%	-0.81	
22	MS	798	3.44%	1.75%	40.44%	43.20	-2.76%	5.77%	-0.80	
23	NM	1951	2.22%	1.13%	49.60%	51.34	-1.74%	6.17%	-0.79	
24	LA	1669	2.38%	1.22%	42.67%	44.50	-1.83%	6.67%	-0.77	
25	IL	1392	2.60%	1.33%	55.22%	57.13	-1.92%	7.44%	-0.74	

26	CO	2515	1.95%	1.00%	47.63%	49.07	-1.44%	7.45%	-0.74	
27	AZ	1859	2.27%	1.16%	45.00%	46.60	-1.60%	8.39%	-0.70	
28	ID	559	3.91%	1.99%	30.68%	33.33	-2.66%	9.14%	-0.68	
29	WA	2123	2.12%	1.08%	53.65%	55.07	-1.42%	9.43%	-0.67	
30	GA	1536	2.48%	1.26%	41.65%	43.11	-1.46%	12.33%	-0.59	

31	DC	795	1.92%	0.98%	90.52%	91.63	-1.11%	12.86%	-0.58	
32	MO	2158	2.11%	1.07%	46.38%	47.48	-1.09%	15.42%	-0.52	
33	IA	2502	1.96%	1.00%	49.66%	50.67	-1.01%	15.62%	-0.52	
34	IN	926	3.17%	1.62%	39.58%	40.97	-1.39%	19.43%	-0.44	
35	MI	2452	1.98%	1.01%	51.73%	52.55	-0.83%	20.66%	-0.42	

36	CA	1919	2.22%	1.13%	55.04%	55.73	-0.69%	27.12%	-0.31	
37	KY	1034	3.00%	1.53%	39.99%	40.76	-0.76%	30.89%	-0.25	
38	MD	1000	3.07%	1.57%	56.57%	57.04	-0.47%	38.14%	-0.15	
39	OK	1539	2.38%	1.21%	34.43%	34.73	-0.30%	40.32%	-0.13	
40	ME	1968	2.20%	1.12%	54.58%	54.83	-0.25%	41.15%	-0.11	

41	WI	2223	2.08%	1.06%	50.19%	50.21	-0.02%	49.17%	-0.01	
42	MT	640	3.78%	1.93%	39.50%	39.28	0.22%	45.51%	0.06	
43	HI	499	4.38%	2.23%	54.40%	53.32	1.08%	31.38%	0.25	
44	OR	1064	3.00%	1.53%	52.11%	51.22	0.89%	28.17%	0.29	
45	SD	1495	2.45%	1.25%	39.09%	37.42	1.67%	9.11%	0.68	

46	WY	684	3.50%	1.78%	29.69%	32.07	2.38%	9.07%	0.68	
47	ND	649	3.63%	1.85%	36.09%	33.58	2.51%	8.76%	0.69	
48	KS	654	3.65%	1.86%	37.13%	34.60	2.53%	8.68%	0.69	
49	WV	1722	2.35%	1.20%	43.52%	45.19	1.67%	8.14%	0.71	
50	TX	1671	2.31%	1.18%	38.49%	36.84	1.65%	8.08%	0.71	
51	TN	1774	2.29%	1.17%	42.81%	41.15	1.66%	7.75%	0.73	
										
		73607	2.71%	1.38%	47.09%	48.84	-1.75%	10.27%	-0.62	

[davidgmills]

7. TIA

Today I wanted to show someone your chart comparing the 50 states and DC between 2000 and 2004 but I can't find it.

Could you post the site here please?

Thanks.

[TruthIsAll]

8. Here it is..

[davidgmills]

11. How many were beyond the Moe in 2000?

According to your chart it looks like at least six were, but they were evenly split between Bush and Gore 3-3.

Is that right?

[TruthIsAll]

12. Here are the numbers.

http://www.democraticunderground.com/discuss/duboard.php?az=show_topic&forum=203&topic_id=193452#193462

Yes, it was split 3/3 assuming a 3% MoE, but we don't really know the sample sizes.

39 were within 1%.

29 states shifted to Gore, 21 to Bush.

[msongs]

9. have you EVER gotten a response from an elected democrat???

ya know, a congress person, a dog catcher, anyone who is elected as a democrat??

Msongs
www.msongs.com/political-shirts.htm