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THIS EXIT POLL SIMULATION TEST BLOWS AWAY THE NEDERLAND "PROOF"

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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Mar-12-05 11:52 AM
Original message
THIS EXIT POLL SIMULATION TEST BLOWS AWAY THE NEDERLAND "PROOF"
Edited on Sat Mar-12-05 12:51 PM by TruthIsAll
Let's simulate the NEP.

1) Assume our sample design consists of 131 precincts, and a
total 13047 respondents, just like the preliminary exit poll,
weighted for Kerry to win 51.75% share of the two-party vote.

2) Assume a precinct MOE of 10%, and calculate random numbers
within a +/- 10% range of the precinct result.

3) Sum up all the votes and calculate the percentages for each
of the four simulation trials.

4) Compare the average of the four trials to the exit poll. 
Kerry's 51.65% average compares very nicely to the 51.75%
prelim. exit poll.  

We have just illustrated the law of large numbers. It
disproves  the argument that the high individual precinct MOE
(10%) invalidates the use of the 1% MOE for the complete 13047
sample-size preliminary National Exit Poll.

SAMPLING ERRORS IN INDIVIDUAL PRECINCTS ARE TO BE EXPECTED.
THEY ARE "AVERAGED OUT" IN THE TOTAL SAMPLE.

THE LAW OF LARGE NUMBERS AND THE CENTRAL LIMIT THEOREM. 

The simulation result graphically illustrates the concept: 
The average of the simulation trials falls within a hair of
the exit poll.

										
		Exit Poll		Dem	Rep								
		Actual		      51.75%	48.25%								

		Random Test1		51.57%	48.84%								
		Random Test2		51.81%	48.60%								
		Random Test3		52.03%	48.37%								
		Random Test4		51.20%	49.21%								

		Average		      51.65%	48.75%								


			Prelim. Exit Poll        Test1	Test2		Test3		Test4	
Prect	Total	MOE	Dem	Rep		Dem	Rep	Dem	Rep	Dem	Rep	Dem	Rep
Total	13047	0.875%	6752	6295		6728	6372	6759	6341	6789	6311	6680	6420
			51.75%	48.25%		51.57%	48.84%	51.81%	48.60%	52.03%	48.37%	51.20%	49.21%
													
1	100	10%	80	20		86	14	76	24	85	15	75	25
2	100	10%	50	50		41	59	60	40	52	48	46	54
3	100	10%	65	35		59	41	67	33	75	25	55	45
4	100	10%	25	75		17	83	34	66	17	83	26	74
5	100	10%	50	50		42	58	44	56	51	49	56	44
6	100	10%	55	45		64	36	51	49	49	51	63	37
7	100	10%	60	40		68	32	50	50	63	37	63	37
8	100	10%	90	10		91	9	81	19	84	16	100	0
9	100	10%	55	45		51	49	60	40	51	49	55	45
10	100	10%	70	30		75	25	74	26	78	22	69	31
11	100	10%	55	45		64	36	63	37	45	55	50	50
12	100	10%	65	35		62	38	57	43	61	39	64	36
13	100	10%	60	40		51	49	56	44	64	36	53	47
14	100	10%	90	10		83	17	90	10	87	13	85	15
15	100	10%	50	50		42	58	41	59	49	51	48	52
16	100	10%	40	60		39	61	37	63	30	70	33	67
17	100	10%	60	40		57	43	56	44	55	45	62	38
18	100	10%	25	75		35	65	22	78	17	83	28	72
19	100	10%	55	45		57	43	65	35	63	37	64	36
20	100	10%	60	40		60	40	67	33	65	35	62	38
21	100	10%	50	50		55	45	60	40	52	48	50	50
22	100	10%	45	55		52	48	51	49	43	57	40	60
23	100	10%	50	50		54	46	41	59	56	44	50	50
24	100	10%	80	20		90	10	74	26	86	14	76	24
25	100	10%	50	50		43	57	58	42	47	53	57	43
26	100	10%	20	80		10	90	26	74	27	73	16	84
27	100	10%	50	50		52	48	51	49	46	54	50	50
28	100	10%	30	70		35	65	38	62	29	71	37	63
29	100	10%	50	50		46	54	44	56	49	51	51	49
30	100	10%	60	40		68	32	70	30	62	38	64	36
31	100	10%	50	50		59	41	40	60	58	42	42	58
32	100	10%	30	70		38	62	40	60	20	80	39	61
33	100	10%	50	50		51	49	52	48	53	47	41	59
34	100	10%	30	70		24	76	39	61	28	72	25	75
35	100	10%	50	50		54	46	49	51	46	54	46	54
36	100	10%	50	50		46	54	49	51	53	47	41	59
37	100	10%	70	30		76	24	64	36	66	34	73	27
38	100	10%	50	50		48	52	47	53	58	42	44	56
39	100	10%	50	50		57	43	49	51	42	58	46	54
40	100	10%	80	20		75	25	81	19	81	19	80	20
41	100	10%	50	50		41	59	41	59	60	40	41	59
42	100	10%	80	20		71	29	78	22	78	22	72	28
43	100	10%	50	50		41	59	56	44	48	52	45	55
44	100	10%	50	50		53	47	59	41	59	41	56	44
45	100	10%	70	30		67	33	76	24	68	32	67	33
46	100	10%	50	50		45	55	44	56	48	52	43	57
47	100	10%	50	50		44	56	40	60	40	60	44	56
48	100	10%	40	60		45	55	35	65	39	61	49	51
49	100	10%	50	50		47	53	50	50	45	55	41	59
50	100	10%	20	80		13	87	30	70	23	77	19	81
51	100	10%	50	50		47	53	60	40	49	51	58	42
52	100	10%	90	10		89	11	87	13	89	11	90	10
53	100	10%	50	50		50	50	47	53	60	40	47	53
54	100	10%	50	50		59	41	53	47	44	56	54	46
55	100	10%	30	70		36	64	23	77	38	62	39	61
56	100	10%	50	50		51	49	44	56	43	57	59	41
57	100	10%	80	20		76	24	82	18	85	15	75	25
58	100	10%	70	30		67	33	68	32	76	24	64	36
59	100	10%	80	20		71	29	82	18	74	26	76	24
60	100	10%	50	50		40	60	45	55	42	58	46	54
61	100	10%	20	80		27	73	22	78	17	83	27	73
62	100	10%	30	70		36	64	28	72	32	68	27	73
63	100	10%	50	50		50	50	48	52	50	50	53	47
64	100	10%	50	50		51	49	57	43	40	60	44	56
65	100	10%	60	40		69	31	59	41	50	50	70	30
66	100	10%	50	50		50	50	41	59	49	51	59	41
67	100	10%	60	40		59	41	57	43	53	47	68	32
68	100	10%	50	50		45	55	51	49	54	46	42	58
69	100	10%	40	60		30	70	33	67	48	52	45	55
70	100	10%	50	50		52	48	59	41	58	42	40	60
71	100	10%	50	50		57	43	60	40	59	41	52	48
72	100	10%	60	40		68	32	52	48	56	44	53	47
73	100	10%	50	50		52	48	59	41	57	43	53	47
74	100	10%	30	70		25	75	22	78	38	62	22	78
75	100	10%	50	50		45	55	50	50	45	55	57	43
76	100	10%	70	30		69	31	75	25	73	27	63	37
77	100	10%	50	50		41	59	49	51	43	57	44	56
78	100	10%	40	60		47	53	30	70	50	50	46	54
79	100	10%	50	50		48	52	59	41	49	51	46	54
80	100	10%	70	30		60	40	64	36	77	23	74	26
81	100	10%	50	50		46	54	59	41	46	54	58	42
82	100	10%	80	20		81	19	72	28	73	27	76	24
83	100	10%	70	30		76	24	64	36	74	26	62	38
84	100	10%	50	50		40	60	52	48	49	51	53	47
85	100	10%	40	60		48	52	32	68	42	58	35	65
86	100	10%	50	50		45	55	40	60	59	41	56	44
87	100	10%	30	70		34	66	27	73	27	73	20	80
88	100	10%	50	50		41	59	56	44	57	43	58	42
89	100	10%	40	60		42	58	34	66	43	57	42	58
90	100	10%	50	50		58	42	42	58	53	47	43	57
91	100	10%	30	70		35	65	26	74	25	75	34	66
92	100	10%	50	50		58	42	43	57	59	41	58	42
93	100	10%	40	60		37	63	46	54	47	53	42	58
94	100	10%	50	50		53	47	40	60	54	46	41	59
95	100	10%	30	70		37	63	36	64	37	63	39	61
96	100	10%	50	50		55	45	44	56	40	60	41	59
97	100	10%	80	20		71	29	88	12	71	29	70	30
98	100	10%	50	50		51	49	53	47	58	42	60	40
99	100	10%	50	50		60	40	59	41	51	49	53	47
100	100	10%	55	45		65	35	59	41	54	46	50	50
101	100	10%	45	55		37	63	38	62	36	64	35	65
102	100	10%	60	40		55	45	70	30	58	42	51	49
103	100	10%	30	70		38	62	23	77	26	74	29	71
104	100	10%	35	65		36	64	39	61	26	74	45	55
105	100	10%	70	30		80	20	61	39	69	31	65	35
106	100	10%	45	55		37	63	55	45	43	57	49	51
107	100	10%	55	45		54	46	57	43	62	38	47	53
108	100	10%	55	45		50	50	50	50	50	50	49	51
109	100	10%	50	50		59	41	49	51	60	40	42	58
110	100	10%	45	55		44	56	35	65	36	64	49	51
111	100	10%	45	55		37	63	43	57	46	54	41	59
112	100	10%	65	35		71	29	60	40	73	27	73	27
113	100	10%	70	30		60	40	80	20	74	26	71	29
114	100	10%	55	45		54	46	53	47	57	43	58	42
115	100	10%	40	60		38	62	49	51	42	58	49	51
116	100	10%	45	55		40	60	50	50	52	48	37	63
117	100	10%	40	60		41	59	49	51	39	61	47	53
118	100	10%	45	55		44	56	40	60	44	56	39	61
119	100	10%	60	40		54	46	60	40	70	30	56	44
120	100	10%	55	45		60	40	48	52	61	39	63	37
121	100	10%	40	60		46	54	45	55	31	69	38	62
122	100	10%	45	55		36	64	52	48	37	63	43	57
123	100	10%	55	45		46	54	57	43	51	49	54	46
124	100	10%	40	60		43	57	47	53	40	60	46	54
125	100	10%	45	55		50	50	46	54	43	57	43	57
126	100	10%	55	45		45	55	55	45	61	39	62	38
127	100	10%	50	50		58	42	55	45	51	49	56	44
128	100	10%	60	40		63	37	59	41	61	39	55	45
129	100	10%	45	55		44	56	53	47	40	60	36	64
130	100	10%	40	60		35	65	39	61	45	55	44	56
131	47	10%	27	20		29	71	21	79	37	63	22	78
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The Doctor. Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Mar-12-05 11:57 AM
Response to Original message
1. As always... Thank you TIA.
Your number crunching shames my lazy ass.
I love watching how numbers play, I just never set aside the 'crunch time'.

We all owe you a lot for keeping on top of this.


So, If these numbers say what we think - you shown how much MORE improbable divergence from MOE is as you increase the scope.

Please tell me you are in touch with Conyer's good offices.

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The Doctor. Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Mar-12-05 11:58 AM
Response to Reply #1
2. PS: I missed the Nederland study... got a link? nt
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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Mar-12-05 12:36 PM
Response to Reply #2
5. I would not call it a "study".
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Name removed Donating Member (0 posts) Send PM | Profile | Ignore Sat Mar-12-05 08:31 PM
Response to Reply #5
8. Deleted message
Message removed by moderator. Click here to review the message board rules.
 
Nederland Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 10:56 AM
Response to Reply #8
17. It has nothing to do with university degrees
It has to do with facts. The fact is that TIA is not calculating the MOE correctly. See post #10.
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The Doctor. Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Mar-13-05 03:07 AM
Response to Reply #5
9. Oh, just took a look.
He simply trying to deal in absolutes.

Yes, lightning can strike the same man twice on the night he wins the lottery after his wife marries a penguin.

And that you say that that is nearly impossible doesn't make it impossible.

Nice of him to waste our time telling us.
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Nederland Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 11:22 AM
Response to Reply #9
21. Its not you I'm arguing with
Edited on Mon Mar-14-05 11:22 AM by Nederland
Its TIA. TIA continues to ignore the effect of cluster which everyone--even Steve Freeman--agrees is relevant. I thought that if I spelled out a simple example of how clustering can produce a result that is outside the MOE even TIA would get it, but s/he is a lost cause.
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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Mar-12-05 12:57 PM
Response to Reply #1
6. Note: Individual precinct MOE = 10% = 1/sqrt(N), where N=100.
Edited on Sat Mar-12-05 12:58 PM by TruthIsAll
The total sample MOE = 0.875% = 1/sqrt(13047).

The final average result falls well within the 1.0% MOE.
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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Mar-12-05 01:24 PM
Response to Reply #1
7. SIMULATION #2 . SLIGHT ERROR IN SIM #1 (PRECINCT #131 TOTALS)
Edited on Sat Mar-12-05 01:52 PM by TruthIsAll
													
		Exit Poll		Dem	Rep								
		Actual		      51.75%	48.25%								

		Random Test1		51.48%	48.52%								
		Random Test2		51.03%	48.97%								
		Random Test3		51.42%	48.58%								
		Random Test4		51.95%	48.05%								

		Average		       51.47%	48.53%								


			Exit Poll 		Test1		Test2		Test3		Test4	
Prec	Total	MOE	Dem	Rep		Dem	Rep	Dem	Rep	Dem	Rep	Dem	Rep
Total	13047	0.875%	6752	6295		6716	6331	6658	6389	6709	6338	6778	6269
			51.75%	48.25%		51.48%	48.52%	51.03%	48.97%	51.42%	48.58%	51.95%	48.05%
													
1	100	10%	75	25		72	28	76	24	78	22	65	35
2	100	10%	50	50		59	41	42	58	55	45	57	43
3	100	10%	55	45		55	45	59	41	61	39	61	39
4	100	10%	25	75		33	67	16	84	20	80	19	81
5	100	10%	50	50		44	56	41	59	56	44	49	51

6	100	10%	55	45		59	41	45	55	62	38	49	51
7	100	10%	65	35		72	28	56	44	61	39	57	43
8	100	10%	85	15		83	17	82	18	94	6	86	14
9	100	10%	60	40		57	43	65	35	69	31	56	44
10	100	10%	70	30		78	22	79	21	72	28	62	38

11	100	10%	55	45		63	37	57	43	65	35	59	41
12	100	10%	60	40		66	34	55	45	67	33	65	35
13	100	10%	60	40		64	36	59	41	53	47	64	36
14	100	10%	90	10		84	16	94	6	89	11	92	8
15	100	10%	55	45		64	36	47	53	46	54	63	37

16	100	10%	50	50		57	43	46	54	57	43	57	43
17	100	10%	60	40		55	45	57	43	52	48	53	47
18	100	10%	25	75		17	83	28	72	15	85	30	70
19	100	10%	55	45		61	39	64	36	54	46	59	41
20	100	10%	60	40		50	50	65	35	60	40	56	44

21	100	10%	50	50		42	58	59	41	50	50	41	59
22	100	10%	45	55		55	45	50	50	55	45	46	54
23	100	10%	50	50		48	52	43	57	58	42	51	49
24	100	10%	80	20		82	18	76	24	83	17	76	24
25	100	10%	50	50		53	47	60	40	54	46	48	52

26	100	10%	20	80		17	83	15	85	19	81	27	73
27	100	10%	50	50		43	57	47	53	44	56	53	47
28	100	10%	30	70		33	67	37	63	24	76	30	70
29	100	10%	50	50		41	59	46	54	50	50	55	45
30	100	10%	60	40		64	36	59	41	50	50	69	31

31	100	10%	50	50		47	53	59	41	50	50	54	46
32	100	10%	30	70		27	73	28	72	29	71	28	72
33	100	10%	50	50		46	54	59	41	53	47	40	60
34	100	10%	30	70		27	73	36	64	35	65	26	74
35	100	10%	50	50		41	59	41	59	51	49	57	43

36	100	10%	50	50		51	49	46	54	46	54	50	50
37	100	10%	70	30		66	34	68	32	71	29	63	37
38	100	10%	50	50		48	52	43	57	52	48	47	53
39	100	10%	50	50		50	50	47	53	54	46	45	55
40	100	10%	80	20		70	30	82	18	74	26	85	15

41	100	10%	50	50		60	40	55	45	46	54	51	49
42	100	10%	80	20		77	23	71	29	75	25	85	15
43	100	10%	50	50		59	41	53	47	55	45	50	50
44	100	10%	50	50		44	56	54	46	47	53	44	56
45	100	10%	70	30		63	37	62	38	68	32	73	27

46	100	10%	50	50		47	53	42	58	51	49	43	57
47	100	10%	50	50		57	43	43	57	49	51	43	57
48	100	10%	40	60		45	55	30	70	43	57	48	52
49	100	10%	50	50		45	55	41	59	59	41	43	57
50	100	10%	20	80		16	84	18	82	30	70	30	70

51	100	10%	50	50		49	51	40	60	48	52	45	55
52	100	10%	90	10		96	4	88	12	98	2	92	8
53	100	10%	50	50		53	47	51	49	49	51	54	46
54	100	10%	50	50		55	45	53	47	45	55	55	45
55	100	10%	30	70		40	60	34	66	21	79	36	64

56	100	10%	50	50		60	40	51	49	44	56	43	57
57	100	10%	80	20		74	26	77	23	71	29	85	15
58	100	10%	70	30		77	23	75	25	64	36	75	25
59	100	10%	80	20		88	12	88	12	74	26	72	28
60	100	10%	50	50		52	48	44	56	60	40	53	47

61	100	10%	20	80		12	88	11	89	24	76	12	88
62	100	10%	30	70		20	80	32	68	40	60	40	60
63	100	10%	50	50		48	52	43	57	49	51	60	40
64	100	10%	50	50		54	46	40	60	42	58	42	58
65	100	10%	60	40		66	34	70	30	54	46	66	34

66	100	10%	50	50		41	59	46	54	46	54	55	45
67	100	10%	60	40		66	34	62	38	60	40	64	36
68	100	10%	50	50		43	57	55	45	53	47	59	41
69	100	10%	40	60		48	52	36	64	34	66	38	62
70	100	10%	50	50		56	44	49	51	44	56	40	60

71	100	10%	50	50		46	54	49	51	45	55	59	41
72	100	10%	60	40		50	50	59	41	65	35	58	42
73	100	10%	50	50		48	52	43	57	47	53	50	50
74	100	10%	30	70		37	63	27	73	25	75	21	79
75	100	10%	50	50		51	49	43	57	41	59	57	43

76	100	10%	70	30		62	38	66	34	65	35	64	36
77	100	10%	50	50		44	56	40	60	51	49	52	48
78	100	10%	40	60		48	52	40	60	30	70	36	64
79	100	10%	50	50		49	51	59	41	46	54	48	52
80	100	10%	70	30		62	38	65	35	65	35	65	35

81	100	10%	50	50		46	54	41	59	59	41	55	45
82	100	10%	80	20		85	15	77	23	70	30	87	13
83	100	10%	70	30		60	40	77	23	67	33	72	28
84	100	10%	50	50		41	59	47	53	47	53	47	53
85	100	10%	40	60		44	56	41	59	43	57	40	60

86	100	10%	50	50		43	57	60	40	41	59	53	47
87	100	10%	30	70		30	70	32	68	29	71	25	75
88	100	10%	50	50		47	53	46	54	51	49	46	54
89	100	10%	40	60		41	59	30	70	33	67	32	68
90	100	10%	50	50		44	56	50	50	40	60	56	44

91	100	10%	30	70		32	68	36	64	33	67	30	70
92	100	10%	50	50		55	45	60	40	47	53	57	43
93	100	10%	40	60		49	51	44	56	41	59	39	61
94	100	10%	50	50		54	46	51	49	58	42	49	51
95	100	10%	30	70		40	60	32	68	21	79	28	72

96	100	10%	50	50		53	47	47	53	52	48	40	60
97	100	10%	80	20		86	14	73	27	73	27	83	17
98	100	10%	50	50		40	60	42	58	55	45	50	50
99	100	10%	50	50		40	60	40	60	55	45	43	57
100	100	10%	55	45		65	35	55	45	57	43	65	35

101	100	10%	45	55		38	62	51	49	41	59	43	57
102	100	10%	60	40		70	30	52	48	53	47	57	43
103	100	10%	30	70		21	79	25	75	37	63	29	71
104	100	10%	35	65		25	75	37	63	31	69	37	63
105	100	10%	70	30		60	40	68	32	74	26	76	24

106	100	10%	45	55		55	45	50	50	44	56	48	52
107	100	10%	55	45		54	46	49	51	51	49	47	53
108	100	10%	55	45		54	46	59	41	49	51	51	49
109	100	10%	50	50		55	45	58	42	47	53	60	40
110	100	10%	45	55		49	51	50	50	43	57	35	65

111	100	10%	45	55		48	52	48	52	44	56	50	50
112	100	10%	65	35		58	42	64	36	66	34	69	31
113	100	10%	70	30		78	22	79	21	77	23	71	29
114	100	10%	55	45		47	53	47	53	54	46	61	39
115	100	10%	40	60		31	69	35	65	44	56	46	54

116	100	10%	45	55		55	45	49	51	36	64	40	60
117	100	10%	40	60		33	67	46	54	32	68	45	55
118	100	10%	45	55		47	53	36	64	53	47	52	48
119	100	10%	60	40		57	43	68	32	67	33	52	48
120	100	10%	55	45		53	47	46	54	59	41	53	47

121	100	10%	50	50		48	52	42	58	49	51	48	52
122	100	10%	45	55		45	55	49	51	35	65	46	54
123	100	10%	55	45		47	53	55	45	51	49	55	45
124	100	10%	40	60		50	50	46	54	45	55	42	58
125	100	10%	45	55		55	45	48	52	55	45	55	45

126	100	10%	55	45		49	51	57	43	62	38	64	36
127	100	10%	50	50		48	52	56	44	57	43	42	58
128	100	10%	50	50		46	54	51	49	58	42	58	42
129	100	10%	45	55		36	64	49	51	50	50	37	63
130	100	10%	40	60		32	68	44	56	33	67	32	68
131	47	10%	27	20		25	22	24	23	29	18	24	23
													

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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 09:46 PM
Response to Reply #7
35. Here are the first 10 of 200 more simulation trials
Edited on Mon Mar-14-05 09:46 PM by TruthIsAll
Exit Poll	Dem	Rep							
Actual		51.75%	48.25%							
Kerry Exit Poll simulation - 200 trials

	
										
	Avg	51.79%								
	Max	53.18%								
	Min	50.20%								
	Med	51.78%								

Kerry										
Trial	1	2	3	4	5	6	7	8	9	10
Votes	6790	6790	6771	6834	6673	6751	6697	6684	6692	6756
Pct	52.04%	52.04%	51.90%	52.38%	51.15%	51.74%	51.33%	51.23%	51.29%	51.78%

Precinct										
1	79	81	73	65	78	70	83	74	71	85
2	57	57	51	57	44	46	52	40	55	43
3	50	62	58	49	56	55	59	50	51	53
4	33	17	25	33	25	23	15	21	35	20
5	42	53	56	55	48	60	50	54	47	57

6	52	59	60	64	60	65	46	55	50	46
7	55	57	67	67	69	64	71	71	59	63
8	80	78	91	95	89	85	88	79	88	92
9	57	60	58	50	57	62	64	64	55	55
10	76	60	68	75	80	70	79	62	71	70

11	65	60	61	50	46	58	45	54	51	47
12	50	55	55	69	54	63	61	59	59	56
13	50	51	70	58	67	67	50	68	51	70
14	97	84	86	97	99	93	92	83	89	87
15	47	56	50	51	54	60	45	58	48	45

16	53	57	53	42	46	55	53	45	40	59
17	62	70	51	64	53	56	60	51	55	52
18	35	35	18	17	19	33	33	19	26	18
19	51	52	60	60	49	61	65	45	52	49
20	51	50	58	69	57	51	68	63	54	57

21	50	47	42	53	59	42	42	46	53	49
22	51	52	35	42	38	45	50	54	35	40
23	42	45	42	50	46	57	53	52	49	60
24	90	76	89	83	75	84	70	77	76	78
25	43	52	52	51	49	48	40	48	44	56

26	28	13	18	17	14	19	13	21	21	19
27	56	41	46	60	51	44	40	51	59	56
28	38	30	34	38	29	27	37	31	22	40
29	48	57	47	46	45	58	42	40	41	42
30	62	68	59	57	64	68	62	69	57	62

31	58	44	56	50	50	53	53	47	58	59
32	29	28	30	40	25	22	31	35	26	34
33	55	48	44	49	60	46	41	53	45	56
34	30	38	22	22	25	29	27	37	33	37
35	50	41	52	42	60	42	50	54	55	40

36	53	57	60	45	54	59	41	54	43	40
37	79	61	65	71	73	63	72	77	77	65
38	40	46	46	56	56	60	50	42	45	51
39	55	53	53	45	46	51	54	46	53	57
40	82	88	85	90	80	85	81	76	71	80

41	58	43	46	54	43	59	43	44	58	42
42	76	89	81	82	89	90	78	77	80	74
43	58	52	50	42	48	55	42	48	54	48
44	57	42	57	49	53	52	42	59	58	55
45	62	76	74	80	62	66	65	67	79	79

46	43	43	42	55	56	49	48	40	55	46
47	49	52	51	55	44	44	52	58	43	50
48	47	41	49	32	39	30	49	48	43	44
49	48	42	60	59	48	59	51	42	60	41
50	10	13	26	19	30	18	22	20	19	25

51	42	41	45	50	47	56	57	46	54	58
52	96	80	90	97	98	91	87	81	91	94
53	40	57	44	56	48	57	42	60	52	55
54	59	42	48	59	40	45	52	51	59	52
55	21	21	28	33	37	40	23	37	29	20

56	55	50	56	46	52	54	50	57	50	51
57	73	71	86	81	86	76	90	81	72	77
58	77	80	60	72	60	63	63	68	76	74
59	88	86	83	90	87	86	73	76	79	82
60	51	54	42	57	44	48	56	45	47	45

61	11	23	28	24	13	15	18	29	18	21
62	39	37	29	39	21	30	29	32	24	22
63	47	59	52	45	46	41	55	54	54	57
64	54	58	40	41	46	52	58	43	53	46
65	64	70	56	64	56	55	66	57	70	63

66	50	50	46	43	56	46	54	51	55	49
67	50	53	59	60	55	59	57	64	56	54
68	47	57	57	40	42	42	45	49	40	60
69	42	43	38	35	31	32	38	42	40	47
70	56	60	60	56	59	46	54	56	48	49

71	54	57	60	45	53	46	55	60	48	59
72	62	69	52	63	57	63	50	57	55	51
73	53	54	55	41	45	53	44	42	41	55
74	20	36	40	26	40	34	36	27	26	29
75	54	59	53	60	48	41	51	53	45	58

76	78	80	77	61	69	67	63	74	78	77
77	56	59	42	53	41	56	56	46	50	47
78	35	31	37	40	47	48	35	49	33	44
79	47	46	47	57	44	42	47	50	51	44
80	68	71	68	73	64	62	67	73	67	78

81	43	45	59	46	56	60	49	49	58	47
82	79	75	73	78	79	89	77	86	76	73
83	64	71	67	61	75	70	63	60	77	65
84	58	55	53	53	47	60	56	44	52	48
85	47	36	49	33	35	36	36	44	47	44

86	46	45	44	47	60	41	56	47	42	54
87	21	22	25	22	28	32	37	30	35	32
88	52	51	47	54	54	47	48	49	44	43
89	50	34	42	40	38	47	45	42	30	38
90	54	50	45	44	54	43	50	59	43	46

91	27	21	27	28	40	25	36	28	30	32
92	58	47	47	41	57	56	45	53	47	60
93	49	38	46	44	35	47	36	40	44	31
94	49	40	59	46	41	59	46	48	40	48
95	38	26	25	20	20	36	28	38	23	23

96	50	55	42	53	40	53	41	52	57	56
97	75	89	90	71	78	84	86	70	70	82
98	47	49	40	59	48	47	43	48	55	60
99	48	60	52	49	47	45	55	55	53	48
100	52	62	64	47	58	51	65	45	54	62

101	49	38	43	43	53	49	49	37	43	45
102	58	70	51	66	64	51	67	70	66	62
103	22	21	20	39	27	21	25	35	32	21
104	39	45	28	44	35	29	35	34	25	44
105	74	61	79	75	67	66	63	77	68	71

106	41	43	50	48	41	55	46	39	54	55
107	63	62	65	46	60	47	46	64	46	57
108	55	58	48	63	61	51	52	61	49	48
109	40	56	46	58	46	56	60	52	56	44
110	48	54	53	42	37	35	44	49	54	41

111	46	53	45	42	47	38	37	43	55	52
112	61	71	70	72	65	65	73	59	63	70
113	64	68	61	60	75	72	63	63	60	76
114	50	48	61	64	50	46	53	50	54	52
115	32	33	45	49	48	50	41	32	49	39

116	40	38	35	48	48	44	50	48	39	37
117	39	30	32	42	32	38	41	32	37	38
118	54	45	52	55	44	44	38	44	53	45
119	64	70	50	58	50	53	67	54	50	60
120	47	61	56	62	54	50	57	64	57	58

121	54	55	51	48	41	55	60	45	47	54
122	52	39	49	52	47	46	45	49	49	44
123	57	45	45	47	48	51	57	49	63	64
124	41	48	50	34	33	33	47	50	40	35
125	44	35	47	38	40	48	39	35	50	38

126	55	64	62	58	61	57	60	47	62	51
127	42	50	60	43	57	48	51	40	44	44
128	52	57	59	58	44	48	46	41	59	46
129	49	48	43	38	55	48	38	38	51	44
130	43	30	30	46	43	38	33	30	39	36
131	30	37	29	32	17	24	25	28	21	26
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berniew1 Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Mar-12-05 12:12 PM
Response to Original message
3. The law of large numbers applies here as long as there was no systematic b
bias in the exit poll methodology. There is experience with how to do this and someone was paid a lot of money to make it so.

I think the systematic bias that exist was strongly against Kerry and reality should have been more on the Kerry side than the exit poll data shows. There was well documented systematic dirty tricks, manipulation, malfeasance, suppression to prevent eligible minorities and students from voting; and in a fair election where such groups had been allowed to vote Kerry would have won big. But these not only weren't in the official vote count but also weren't in the exit poll data. This represents a big bias against Kerry in the exit poll data, since its clear that millions of eligible voters were turned away for illegitimate reasons or not allowed to vote because of registration system problems/bias.
http://www.flcv.com/summary.html
http://www.flcv.com/studentv.html


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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Mar-12-05 12:34 PM
Response to Reply #3
4. The purpose of the post was to illustrate the fallacy of the
Edited on Sat Mar-12-05 01:04 PM by TruthIsAll
bogus argument that the precinct 10% MOE invalidates Mitofsky's stated 1% MOE for the full 13047 sample.

IT'S THE LAW OF LARGE NUMBERS.
IT'S THE CENTRAL LIMIT THEOREM.

KISS.

BTW, your work on documenting fraud stands alone.
It's the ultimate proof.

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Awsi Dooger Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Mar-13-05 05:05 AM
Response to Original message
10. You are (predictably) overstating exit poll accuracy to ludicruous extreme
Once again, don't take it from me. Here are related paragrpahs from Mark Blumenthal, the Mystery Pollster, the guy who squashed Steven Freeman and caused him to redo his simpleton analysis. This is the link: http://www.mysterypollster.com/main/2004/12/what_is_the...

Sampling Error in Exit Polling

"Unfortunately, calculating the margin of error gets a lot more complicated for an exit poll. The reason is that exit polls use cluster sampling. Since it is wildly impractical to station interviewers at every polling place (the U.S. has roughly 225,000 voting precincts), exit pollsters sample in two stages: They first randomly select precincts within a state, then randomly intercept voters as they exit the selected polling places. Unfortunately, this clustering of interviews within precincts adds variability and error. Generally speaking, the additional error is a function of the number of clusters and the variability across clusters of the thing being measured. Error will INCREASE in a cluster sample (as compared to error for simple random sampling) as...

1)The number of clusters decreases relative to the number of interviews or

2) The thing being measured differs across clusters (or precincts)

(12/14: Clarification added in italics above. Another way of saying it: Error will increase as the average number of interviews per cluster increases).

Here is the way the NEP methodology statement describes the potential for error from clustering:

If a characteristic is found in roughly the same proportions in all precincts the sampling error will be lower. If the characteristic is concentrated in a few precincts the sampling error will be larger. Gender would be a good example of a characteristic with a lower sampling error. Characteristics for minority racial groups will have larger sampling errors.

Another problem is that calculating this additional error is anything but straightforward. To estimate the additional error produced by clustering, statisticians calculate something called a design effect. The calculation is hard for two reasons: First, it can differ greatly from question to question within the same sample. Second, in order to calculate the design error, you need to know how much the thing being measured varies between clusters. Thus, as this website by the British market research MORI explains, it is virtually impossible to say what between-cluster variability is likely to be until one has actually conducted the study and collected the results (emphasis added). Another academic web site explains that an estimate of the design effect calculated before data is collected must be based on past survey experience as statistical literature provides little guidance

A few weeks ago, I posted my reaction to a paper by Steven Freeman widely circulated on the Internet. Freeman did his own calculations of the significance of exit polls data that ignored the greater rate of error for cluster samples. To make this point, I cited an article that had calculated the design effect for the 1996 exit polls by two analysts associated with VNS (the forerunner to NEP). They had estimated that the clustering translates into a 30% increase in the sampling error as compared to simple random sampling. It was the only discussion of the design effect applied to exit polls that I could find in a very quick review of the limited academic literature available to me.

Freeman has recently updated his paper with calculations that rely on this 30% estimate. However, following my post I received an email from Nick Panagakis informing me that the 30% estimate was out of date (Panagakis is the president of a Market Shares Corporation, a polling firm that has conducted exit polls in Wisconsin and other Midwestern states). Panagakis had checked with Warren Mitofsky, director of the NEP exit poll, and learned that the updated design effect used in 2004 assumed a 50% to 80% increase in error over simple random sampling (with the range depending on the number of precincts sampled in a given state). Blogger Rick Brady (Stones Cry Out) has subsequently confirmed that information in an email exchange with Mitofsky that he posted on his website.

Thus, the calculations in Freemans revised paper continue to understate the sampling error for the 2004 exit polls (more on this in a post to follow).

All of this brings us to the sampling error table that the NEP included in their statement of methodology, which I have copied below (click the image to see a full size version). These are the estimates of sampling error provided to the networks on Election Day for a range of percentages at various samples sizes. They appear to represent an increase in sampling error of at least 50% over simple random sampling. NEP intended the table as a rough guide to the appropriate sampling error for the data they have publicly released, with the additional warning that highly clustered characteristics (such as racial groups) may have even higher error.

The table ( available at the link pasted above) assumes a 95% confidence level. However, Nick Panagakis brought another important point to my attention. NEP requires a much higher level of confidence to project winners on Election Night. The reasoning is simple: At a 95% confidence level, one poll in twenty will produce a result outside the margin of error. Since they do exit polls in 50 states plus DC, they could miss a call in 2-3 states by chance alone. To reduce that possibility, NEP uses a 99.5% confidence level in determining the statistical significance of its projections (something I was able to confirm with Joe Lenski of Edison Research, who co-directed the NEP exit polls with Warren Mitofsky). More on the implications of that in my next post."
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Mairead Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Mar-13-05 09:02 AM
Response to Reply #10
11. There is no support for your assertions
The '30% is out of date' meme has nothing behind it. It's handwaving, a product of needing the declared results to be true. Just like Mitofsky's 'explanation' that GOPers disproportionately refused to respond, which turned out to be contradicted by his own data. To believe the 'out of date' nonsense, you'd have to believe that people have changed their basic behavior patterns in just a few years. Nobody has offered any evidence to support that notion. It's all handwaved.

If I were going to bet, I'd bet there's something hokey about Blumenthal. At his site, he consistently used phrasing that implicitly supported the idea that the election was legitimate and the discrepancies mere functional errors. That's not the act of an impartial observer. Whether that means he's a dupe, a dope, or part of the problem I wouldn't try to guess without more information.

And to claim that Blumenthal 'squashed' Freemans 'simpleton' analysis reveals your biases very clearly. It's on a par with believing everything's okay because the cops only shot the innocent person 31 times, not 126 times as the victim's friends first claimed.

The shift from Freeman's original 250M:1 odds to his later 600K:1 odds came about because he bent over backwards to be conservative. The granularity of sampling affects the amount of random error present in the results. Precinct-level granularity has more error than person-level. To reduce that error, Mitofsky used stratification techniques. Freeman's analysis originally included that error reduction. His later paper did not.
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Nederland Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 11:19 AM
Response to Reply #11
20. Question
You argue that the there is no evidence to demonstrate that '30% is out of date'. Do this mean you accept the 30% number?
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Mairead Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 12:16 PM
Response to Reply #20
28. No, it means I don't impeach it without further information
Uncritically accepting large error values helps hide fraud, and those sample sizes intuitively seem quite large to be requiring 'even' 30% slop. Most national surveys with individual granularity have on the order of 4% slop with around two thousand samples. But I can't find my one stats text from grad school that covered the relevant techniques and numbers for dealing with clumping.
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Mistwell Donating Member (553 posts) Send PM | Profile | Ignore Mon Mar-14-05 08:23 PM
Response to Reply #11
34. Um, except there are studies that do support it
"Just like Mitofsky's 'explanation' that GOPers disproportionately refused to respond, which turned out to be contradicted by his own data. To believe the 'out of date' nonsense, you'd have to believe that people have changed their basic behavior patterns in just a few years. Nobody has offered any evidence to support that notion. It's all handwaved. "

How do you explain this?

http://www.duke.edu/~mms16/non_response2000.pdf
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Mairead Donating Member (1000+ posts) Send PM | Profile | Ignore Tue Mar-15-05 06:48 AM
Response to Reply #34
40. "How do you explain this?"
I'm surprised you would even bring it up. Or didn't you read it?

The '04 claim is that Democratic voters responded more often than Bush voters.

A claim in that study is that Buchanan voters responded more often than Bush voters!

In other words, no matter who Bush's opponent is, voters for that person are assumed to have responded more readily than did Bush voters, thus 'explaining' the unexpected Bush advantage that shows up again and again.

I'll leave you to work out the implications of that.
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Mistwell Donating Member (553 posts) Send PM | Profile | Ignore Tue Mar-15-05 10:27 PM
Response to Reply #40
44. That is not the conclusion of the study
You are kidding, right? One tiny example in a 25 page study, and you make an outrageous claim about "the claim in that study" being about Buchanan voters. No dice Mairead. You clearly didn't read the entire paper if you think that was the subject matter.

In case you missed this part of the conclusion: "Our results also lead us to conclude that exit polls are likely to over-represent the opinions of younger and non-white voters. Because non-white voters tend to vote for Democrat candidates, over-representation of this social class will skew an exit polls results in that direction."
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Mairead Donating Member (1000+ posts) Send PM | Profile | Ignore Wed Mar-16-05 08:28 AM
Response to Reply #44
49. I don't care--it's a lousy study
Edited on Wed Mar-16-05 09:14 AM by Mairead
When people uncritically accept junk, they produce junk.


(edit: Just to give another reason why it's crap: unintended bias can only creep in when 'invisible' factors intrude. Age and 'race' are not invisible.)
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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Mar-13-05 10:08 AM
Response to Reply #10
12. Mark Blumenthal? Like Mitofsky, that other "Democratic pollster"?
Edited on Sun Mar-13-05 10:38 AM by TruthIsAll
MP, to his credit, allows those who totally refute his arguments to post on his site.

His five main points (Should I say biases?) have been the following:

1. Exit Poll Cluster 30-80% effect - never mentioned by Mitofsky in the NEP.

2. Reluctant Bush Responder - decimated by uscountvotes.org reply to Mitofsky's 77-page paper.

3. Probability calculations - at least MP did not avoid the issue when he became aware of them. But he apparently had no clue on my use of the normal and binomial distributions for calculating probabilities since he needed and asked for outside help. That was an indication to me that his mathematical background was limited, to say the least.

He has not refuted the probabilities - but instead has focused on increasing the 95% confidence level and Exit polling margin of error in order to lower the number of states exceeding the MOE in favor of Bush(17) - and by so doing to lower the probability of fraud. Quite a sleight-of-hand. It fooled many people, but not those of us who could see right through the disingenuous ploy. A tight MOE is anathema to the naysayers.

4- The 95/99.7% confidence levels (C.L):
Once again MP has revealed, as you do now, a profound lack of understanding of how they are used. The 95% confidence level is the standard measure for computing probabilities based on the polling margin of error, and which assume a 95% C.L. (or 1.96 standard deviations from the sample mean). Check your statistics text.

MP was obviously confused by the networks use of a 99.7% C.L. (almost three standard deviations from the sample mean) for CALLING THE WINNER OF AN ELECTION IN PROGRESS. This has NOTHING to do with calculating the probability that a POPULATION mean will lie outside the MOE of the polling SAMPLE MEAN. It was a classic red-herring.

The networks want to be absolutely sure they don't screw up, so they use a 3-sigma C.L. before sticking their necks out to call the winner of an election.

5- Polling MOE
The MOE in a standard pre-election state poll is typically 4% (based on a 600 sample-size).
The MOE is usually near 3.0% for a national pre-election poll (1000 sample-size).
The MOE was 1.84% for the Florida Exit poll (2846 sample-size).
The MOE was 1.0% according to Mitofsky for the Preliminary National Exit poll (13047 sample-size).

Using the formula, MOE = 0.875% = 1/sqrt(13047), based on a 13,047 sample size. In the NEP notes, Mitofsky said nothing about a cluster effect when he declared a 1.0% MOE. Perhaps he already applied a 15% C.E. to the 0.875% formula MOE, raising it to 1.0%.

Or maybe he just rounded up to the nearest 1%, as he does for all of his exit poll stats. An interesting question would be: Why not provide just 1 decimal place to the weights so that those who wish to can more accurately do the calculations?

Could it be to fudge the results in order to prevent us
(F)rom (U)nderstanding (D)eviations (G)enerated (E)lectronically?


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Nederland Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 11:10 AM
Response to Reply #12
19. Question
Do you acknowledge that there is any effect on the MOE due to clustering?
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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 11:36 AM
Response to Reply #19
24. What's the matter, 10% precinct MOE is not big enough for you?
Edited on Mon Mar-14-05 11:47 AM by TruthIsAll
Keep trying.

Or do you dare apply THE CLUSTER to the FULL NATIONAL SAMPLE?
Mitofsky says NADA about Cluster in his notes claiming a 1.0% MOE for THE NATIONAL EXIT POLL 13047 SAMPLE.

IF HE DOESN'T, WHY SHOULD YOU?

BUT OK, IF YOU INSIST, I WILL APPLY A CLUSTER FACTOR OF 30% TO THE MOE.

CLUSTER MOE = 1.30/SQRT(13047) = 0.875% * 1.30 = 1.1375%

SO THERE YOU GO, THE CLUSTER FACTOR ADDS 0.1375% TO MITOFSKY'S STATED 1.0% MOE. BIG DEAL.

NEDERLAND,
HURRY UP, STUDY HARD AND GET YOUR BA IN PHILOSOPHY.

AND PLEASE, TAKE SOME MATH COURSES.
YOU NEED THEM.


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Nederland Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 11:40 AM
Response to Reply #24
25. Question
Can I take that response as meaning:

"Yes, I believe that clustering has an effect on the MOE"?
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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 01:55 PM
Response to Reply #25
30. No, there are two MOE's. The National and the Precinct.
Edited on Mon Mar-14-05 01:56 PM by TruthIsAll
The National MOE is 1.0%.
THERE IS NO SUCH THING AS A NATIONAL CLUSTER EFFECT, IS THERE?

But let's assume a cluster effect for individual exit poll precincts.

Do you know what it is? 15%, 30%, 100%?

If you had just a modicum of mathematical maturity, you would learn something from the simulation I just ran, in which I assumed a 10% precinct MOE.

The simulation produced a national average which fell within 0.25% of the actual 13074 PRELIMINARY poll sample, well within the 1.0% MOE.

But you do not acknowledge the simulation, because it totally refutes your feeble "proof".

JUST LIKE YOU NEVER RESPONDED TO MY POST REGARDING THE FACT THAT THE FINAL EXIT POLL WEIGHTINGS OVERSTATED THE BUSH 2000 VOTE BY 2 MILLION (4%), WHILE THE PRELIMINARY EXIT POLL WAS OFF BY ONLY .50 MILLION (1%)

WHAT ABOUT IT?
WILL YOU ANSWER THAT ONE?
WE ARE ALL STILL WAITING.



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jkd Donating Member (151 posts) Send PM | Profile | Ignore Wed Mar-16-05 12:02 AM
Response to Reply #30
45. There are state MOE's and national MOE"s.
Edited on Wed Mar-16-05 12:21 AM by jkd
According to Mitofsky they averaged about 4% for the states. The national poll had a MOE of about 3%. When only 250 of 225,000 precincts are polled in a national sample, there is definitely a cluster effect.
http://exit-poll.net/faq.html#a15 .
http://www.exit-poll.net/election-night/MethodsStatemen...

The 1% MOE that TIA keeps bringing up is over-all poll disparity after the final weightings are completed. Prior to the election the MOE for the national sample was established at 3%. At each stage of the exit poll reporting on election day that figure was at one percent. It didnt change with each additional report. Thats the final MOE. http://www.washingtonpost.com/wp - srv/politics/elections/2004/graphics/exitPolls_national.html.

These reports were never intended for public consumption and the percentage was simply the MOE desired for the poll after the final weightings.

If 250 precincts with an average MOE of 10% were used nationally for a simple random sample, they wouldnt have been able to predict the 1964, Johnson/Goldwater race, never mind this one.

The national sample is stratified and multi-staged, as are the state samples. They are not simple random samples. The unadjusted MOE for the national was not 1%. It was +/-3%.
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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Wed Mar-16-05 01:04 AM
Response to Reply #45
47. Then the final weightings were completed by 12:22am after 13047 responded
Edited on Wed Mar-16-05 01:04 AM by TruthIsAll
in the preliminary exit poll because that was when the 1.0% MOE appeared in the notes at the bottom of the exit poll summary stats on the WP/NEP site.

"The 1% MOE that TIA keeps bringing up is over-all poll disparity after the final weightings are completed".

Poll disparity? Why not just call it margin of error?

Thank you very much for confirming what we already know.
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anaxarchos Donating Member (963 posts) Send PM | Profile | Ignore Mon Mar-14-05 12:16 AM
Response to Reply #10
14. This is a debate from the beginning of December...
Edited on Mon Mar-14-05 12:17 AM by anaxarchos
Rick Brady, who is not just a "blogger", but a right-wing blogger, boasted that Freeman would be "chased off the Internet" as a result of this design effect. We both know that is not what happened. What is the purpose of dredging up this cold case file now?

<edit "know" to "now"... freudian>
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Mairead Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 12:24 PM
Response to Reply #14
29. "Rick Brady, who is not just a "blogger", but a right-wing blogger"
And a deeply, religiously-based rightwing blogger, too.

He persisted in claiming that Freeman should be sacked for fraud because he didn't use a particular two-tailed test. He didn't seem to grasp, or possibly to care, that if you're interested in valence as well as magnitude, a one-tailed test is more appropriate.
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smartvoter Donating Member (1000+ posts) Send PM | Profile | Ignore Wed Mar-16-05 12:52 AM
Response to Reply #10
46. What's interesting about this is that Republican pollsters (e.g., Morris)
incorrectly (and unfortunately) assumed that the public would be educated on the accuracy of exit polling and started to take strikes at polling samples. It seems that everyone thinks they are accurate except when the result is against the official result in our own country.
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cry baby Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Mar-13-05 09:09 PM
Response to Original message
13. kick
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intensitymedia Donating Member (101 posts) Send PM | Profile | Ignore Mon Mar-14-05 01:26 AM
Response to Original message
15. brilliant but explain it in a high concept phrase n/t
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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 09:56 AM
Response to Reply #15
16. This mathematical formulation must be converted to a Sound Bite
Edited on Mon Mar-14-05 10:21 AM by TruthIsAll
Given: N pre-selected precincts P(i), i= 1,N
Each precinct is selected based on the HISTORICAL TREND OF UNBIASED, PRISTINE EXIT POLL SAMPLES and is weighted accordingly:

R(i)+ D(i) = 1
where
R(i) = expected Republican vote percentage
D(i) = expected Democratic vote percentage

Let X(i) = number of respondents in precinct P(i)
Then ND(i) = number of expected Democratic votes in precinct P(i):
ND(i)= D(i)* X(i)

S = TOTAL number of NATIONAL respondents:
S = SUM(X(i)), i= 1, N

Then the total number of EXPECTED Democratic votes in the National sample is given by:
TD = SUM (ND(i)), where i = 1, N
and
the Expected Democratic National vote percentage is:
DP = TD/S

The Margin of Error for precinct P(i) is given by:
MoE(i)= 1.96* SQRT((D(i)*(1-D(i))/(X(i)))

The Margin of Error (MoE) for the National total is given by:
MoE = 1.96 * SQRT( (DP*(1-DP))/S)

Then the EXPECTED Democratic National vote percentage DP will fall within the range {DP-MoE, DP +MoE} 95% of the time.


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Nederland Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 11:06 AM
Response to Original message
18. Ho Hum
Edited on Mon Mar-14-05 11:06 AM by Nederland
Once again you miss the point. All of your calculations assume that the sample is representative. You can't prove that it is without referencing the recorded vote. How many people have to explain this to you before you "get it"?
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Name removed Donating Member (0 posts) Send PM | Profile | Ignore Mon Mar-14-05 11:26 AM
Response to Reply #18
22. Deleted message
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Nederland Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 11:31 AM
Response to Reply #22
23. Ok everyone
Please read the above post and tell me: do you think TIA understands the effect of clustering and how it can skew samples, or do you think that s/he is ignoring the question?

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Name removed Donating Member (0 posts) Send PM | Profile | Ignore Mon Mar-14-05 11:50 AM
Response to Reply #23
26. Deleted message
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Nederland Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 12:08 PM
Response to Reply #26
27. Get your facts straight
I got my BA in 1989.

Question: Is your caps lock stuck?
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Name removed Donating Member (0 posts) Send PM | Profile | Ignore Mon Mar-14-05 02:39 PM
Response to Reply #27
31. Deleted message
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Nederland Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 05:03 PM
Response to Reply #31
32. All of them
Actually I've taken all of them. I was a double major in CS and I've been working as a software Engineer for 16 years. Currently I'm a Java developer who spends far too much time on DU. As to your claim that I am among dwindling company, that is only true on this particular DU forum. That is because many of people that disagree with you have given up on you. Out side of this forum, however, I have far more company than you. This does not mean that you are wrong, but merely have your work cut out for you. In any case, I'm glad to see that you've finally acknowledged the effect clustering has on the MOE. That gives me hope that you are not too stubborn to admit your mistakes. Perhaps soon you will also recognize the necessity of weighting samples to make up for response rates.

Best of luck.
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Carolab Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 06:43 PM
Response to Reply #32
33. Your arguments are weak. So you are checking out. Plain to see.
Nice work, TIA.
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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 09:54 PM
Response to Reply #32
36. They agree with you outside of this forum? Which forum might that be?
Edited on Mon Mar-14-05 09:56 PM by TruthIsAll
And you say you have given up on me?

No, you have just given up.
You can argue just so long without the facts.

Let's face it.
You quit.
Because you had nothing left to say.
No more wiggle room on your chess board.

You could never spin that bogus 2000 voter demographic in the FINAL National exit poll.

You just plain ran out of straw men and red herrings.
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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Mar-14-05 10:18 PM
Response to Reply #32
37. Don't put words in my mouth. I never said I believed the cluster effect
Edited on Mon Mar-14-05 10:19 PM by TruthIsAll
I merely illustrated that even IF there was such an effect, it could occur only at the PRECINCT LEVEL, and would be of no consequence whatsoever in the NATIONAL total (13047). Like everything else in life, it would even itself out, as you took more and more samples.

That is what I proved in my exit poll simulation. Funny, you never said a word about that.

The Law of Large Numbers and The Central Limit Theorem.
You can bet Mitofsky is quite aware of them.
Are you?

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intensitymedia Donating Member (101 posts) Send PM | Profile | Ignore Mon Mar-14-05 10:56 PM
Response to Reply #37
38. CHECKMATE! Congratulations TIA, another boneheaded reactionary bites the
dust ...

peace - but never give up the struggle

che

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anaxarchos Donating Member (963 posts) Send PM | Profile | Ignore Tue Mar-15-05 12:08 AM
Response to Reply #38
39. Kick.............. n/t
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Zeebo Donating Member (78 posts) Send PM | Profile | Ignore Wed Mar-16-05 09:46 AM
Response to Reply #32
50. Nederland, Mistwell, Mgr have valid points and
I, like many, post much less than I read. I still read posts in this forum, but have drifted away from exit poll theory posts. But, I'm absolutely convinced that the concerns and issues brought up by Nederland, Mistwell, and Mgr would garner more support in the whole of DU than the opposing view.

Most have decided this debate has reached the end of it's useful life. One can only read so many posts that cover the same ground over and over.

And the argument by those opposing these posters that they use republican talking points and by inference are freepers is laughable. They take the time to argue, very convincingly mind you, that the "exit poll" theory as proof of fraud is without merit.

So, like so many others, I'm off to other post topics and forums. But Nederland and others, remember you have a ton of "silent" support.

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Name removed Donating Member (0 posts) Send PM | Profile | Ignore Thu Mar-17-05 09:31 PM
Response to Reply #50
51. Deleted message
Message removed by moderator. Click here to review the message board rules.
 
mgr Donating Member (616 posts) Send PM | Profile | Ignore Tue Mar-15-05 01:08 PM
Response to Original message
41. Not a good example for showing central limit theorum

1. The distribution of the 130 samples (I am ignoring 131 for simplicity) appears skewed and kurtotic (probably platykurtic). You have in your example a very uneven curve with slight upticks towards the tails. What this means is that the median and mode do not coincide with the mean, and there are suggestions that you included three distinct sub populations into the parametric curve.

2. It appears that your CL is 100%, as no random sample exceeds the MOE.

3. For these reasons, any random number generated and aggregated for a mean (I did not check to see if you obtained a mean or an average) will result in a value somewhere between the mean and the mode. There will not be any 'drift'.

Mike
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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Tue Mar-15-05 01:53 PM
Response to Reply #41
42. You are reaching, mgr ...
Edited on Tue Mar-15-05 02:13 PM by TruthIsAll
The random numbers were uniformly distributed within a +/- 10% range of the Kerry mean precinct percentage.

If I had chosen a 50-sample size and doubled the number of precincts, the precinct MOE would then equal 14%. I bet the results would not differ greatly if I used a +/- 14% range. In fact, I will run the numbers later.

You are reaching when you say that I have included 3 distinct sub- populations. I just picked the numbers out of my head to come up with the 51.75% Kerry national average as a starting point to illustrate the simulation.

Of course the median and mode do not exactly coincide with the mean.
They never do. Only you would expect that, mgr.

The whole point of the exercise, which you apparently miss, is that a 10% MOE for each of 131 individual precincts does not mean that the consolidated nationwide 1.0% MOE is impossible.

The simulation showed that not only is it possible, but a 1.0% MOE is to be expected, provided that a sufficient number of precincts/respondents are sampled. And 13,047 is more than sufficient.

Kurtotic, Platykurtic - it's all pure B.S.

Use of this statistical terminology does not mean that your argument is credible. You are fooling no one.

Obviously, the simulation puts to lie your fat MOE argument.
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mgr Donating Member (616 posts) Send PM | Profile | Ignore Tue Mar-15-05 04:22 PM
Response to Reply #42
43. Beg to differ, the two arguments are here--
My previous post is not an argument, but an observation as to why you obtained the pattern that you did; and that it has nothing directly to do with Central Limit Theorem.

All the "statistical terminology" I used is descriptive.

Here is the argument, and thanks for the intro:

As to the big fat MOE argument, the assumption that allows the combination of smaller samples into a larger aggregate is that the within population variance for each sample population is greater than the between population variance of the sample and the aggregate. Those two sub populations (humps near the tails) I pointed to, might under an ANOVA, not be from the same statistical population.

The second assumption is that the variables affecting the variance within one sub population are independent from those affecting the variance in another population. If they are not independent, or are insignificant one may use the aggregate population's SD, but if not, then the population would be biased or skewed into one direction, and your MOE can only be calculated (if one is foolish enough to persist) by (MOE/pop 1+MOE/pop 2,+.....MOE n/pop n), which within this context comes to 4%.

Now, lets build this back wards--we know that NEP reports bias within its sample design--they did not adequately control for variability within the exit pollers, such that there was an apparent under sampling of Bush support in a sufficient number of precincts. We don't know which precincts, but the 767:341:354 WPE ratio cited suggests that this is a significant factor.

If bias is in the design, and unbiased design is what dictates the National Exit Poll MOE of 1%, then aggregation of precincts to create the national poll can only be represented by their aggregate MOE.

Now an argument can be made that for the national poll, only precincts within the 341 population were used. This would be reasonable, if the stated purpose of the exit poll was a national poll, but it is not. If anything such sorting would be to use the extremes for the national poll, and used the 341 with balanced use of the other two extremes to characterize state exit polls, leaving the residual for the national poll.

The other problem is we do not know how these precincts are spatially arranged. Their spatial arrangement may permit unbulloching the bias, but would elevate MOE.

The other problem (back of envelope calculation):

If we assume with Minivis' Ohio Exit Poll Thread that it is three precincts for each congressional district (435), then 155 precincts are left for a national exit poll. This would require a response rate of 88% if only a 100 voters of each precinct was approached to approach the total of 13,000 responses. Or, a response rate of 44% if 200 voters were approached. Does anyone begin to see a problem?

I have suggested that the national exit poll was a culling of single responses into a preweighted pattern, rather than sampling at precincts, and then aggregated into a larger sample population. It is how one with any statistical background would expect a statistician to proceed, and it explains the later additions as a response when the weightings had to be altered. This probable explanation possesses greater weight when the above is considered.

Now, can we get on to the more plausible investigations of how this election was stolen? Or do you have another take on how you can spin our wheels?

Mike

Mike




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TruthIsAll Donating Member (1000+ posts) Send PM | Profile | Ignore Wed Mar-16-05 01:48 AM
Response to Reply #43
48. Another simulation: Twice the precincts,w/ 50 respondents per (14% MOE)
Edited on Wed Mar-16-05 01:57 AM by TruthIsAll
mgr, as promised: another simulation. 

But this time a 14% MOE, twice the number of precincts as
before with half (50) the number of respondents per precinct.

In other words the same 13047 total respondents.

The individual precinct MOE is now a whopping 14%.

And we still come in just .03% from the 51.75% Kerry national
average.



Exit Poll		   Dem	Rep							
Actual		51.75%	48.25%							
Kerry Exit Poll simulation - 200 trials (+/-14% precinct
MOE)										
262 precincts; 50 poll/precinct										
	Avg	51.78%								
	Max	53.62%								
	Min	50.37%								
	Med	51.76%								

										
Trial	1	2	3	4	5	6	7	8	9	10
Votes	6700	6795	6752	6750	6677	6738	6767	6778	6780	6778
Kerry	51.35%	52.08%	51.75%	51.74%	51.18%	51.64%	51.87%	51.95%	51.97%	51.95%
Precinct										
1	37	44	42	34	31	36	31	31	34	34
2	19	20	19	29	20	21	22	27	22	24
3	34	27	26	22	25	23	24	30	30	32
4	12	18	13	14	14	16	9	18	10	10
5	22	30	20	19	32	29	22	32	28	22
6	24	34	25	27	29	26	25	25	21	32
7	33	32	33	27	34	32	31	28	27	31
8	43	49	43	37	39	38	36	49	43	48
9	23	23	33	36	26	24	31	28	35	36
10	41	36	37	42	41	31	42	28	40	29
11	31	33	30	31	29	25	30	31	25	30
12	36	26	32	29	27	37	32	30	36	28
13	34	37	27	32	28	31	23	33	33	37
14	43	47	51	41	51	44	45	47	47	39
15	31	27	34	21	33	28	23	30	29	25
16	25	26	29	19	28	25	26	25	31	28
17	33	24	26	34	27	26	24	30	24	23
18	16	18	6	14	12	6	18	16	18	12
19	22	31	28	21	30	32	28	24	31	26
20	32	23	27	33	37	27	35	33	32	37
21	19	23	26	18	23	31	31	24	23	28
22	21	23	25	28	24	22	19	29	16	27
23	19	21	26	22	24	21	28	26	21	28
24	47	35	44	40	41	43	41	38	36	38
25	19	30	30	32	22	31	26	19	24	19
26	13	3	5	14	7	15	5	16	14	6
27	25	25	32	23	22	20	27	26	20	24
28	9	13	19	13	8	16	14	16	10	19
29	28	31	18	26	19	28	19	22	28	25
30	23	32	25	29	24	28	27	26	31	29
31	21	29	23	19	18	21	27	32	20	21
32	20	15	11	9	13	18	22	22	22	17
33	19	21	28	27	30	26	21	20	27	22
34	22	20	9	14	17	10	18	8	19	14
35	18	20	32	25	25	22	30	30	32	18
36	23	32	32	20	28	26	21	20	32	27
37	40	41	31	36	36	40	35	35	40	39
38	29	24	23	30	32	20	22	24	30	22
39	31	25	19	28	21	24	31	30	29	29
40	38	46	44	45	33	42	37	39	37	43
41	23	29	22	32	18	27	27	22	22	28
42	41	43	35	39	39	36	34	37	41	37
43	26	26	30	30	27	22	21	32	25	25
44	32	22	28	29	23	26	27	21	26	24
45	35	31	29	42	37	32	30	34	28	28
46	21	28	32	29	25	26	25	31	19	28
47	24	22	19	22	25	31	31	22	25	22
48	13	13	23	19	25	26	27	25	27	23
49	22	27	24	31	29	20	30	29	30	18
50	9	14	3	10	3	12	8	4	17	11
51	18	20	30	18	31	26	22	23	21	30
52	48	50	44	44	40	40	46	41	52	49
53	22	18	27	29	31	19	26	23	27	20
54	29	27	18	21	30	26	32	31	21	19
55	20	8	14	20	17	20	14	18	14	19
56	21	28	24	22	23	21	27	28	30	30
57	38	40	47	35	38	34	37	47	41	37
58	28	41	28	39	32	42	33	33	37	42
59	43	47	44	33	43	45	46	33	38	35
60	23	29	21	22	26	31	27	31	28	28
61	10	14	7	10	16	15	9	7	13	6
62	22	22	15	22	15	19	8	16	22	14
63	19	30	27	25	19	25	25	26	20	18
64	26	31	27	20	28	32	25	25	19	21
65	28	37	28	32	35	35	24	23	23	33
66	26	25	20	22	22	29	32	30	30	18
67	36	29	30	36	32	35	32	32	23	25
68	32	19	22	27	26	27	32	22	26	22
69	18	16	15	22	19	23	19	26	17	13
70	21	28	24	31	22	26	20	20	18	18
71	21	23	24	24	28	28	29	23	32	24
72	28	33	33	35	24	31	27	36	25	33
73	30	31	23	31	19	28	27	24	22	31
74	18	12	17	18	11	20	13	15	19	20
75	25	18	20	30	20	32	19	30	22	25
76	33	38	34	42	36	33	31	40	37	40
77	21	24	29	22	32	21	30	32	31	30
78	27	26	18	17	13	13	14	20	25	20
79	20	31	31	23	22	18	26	26	28	32
80	38	36	41	31	33	31	31	33	41	34
81	18	25	20	28	27	31	24	23	30	30
82	39	44	47	44	47	35	33	36	36	46
83	36	34	32	31	40	41	28	41	29	38
84	32	32	20	30	22	29	29	27	19	30
85	27	22	27	14	25	17	13	23	14	23
86	30	24	23	21	25	23	25	25	22	24
87	14	11	8	20	9	10	21	17	16	22
88	28	22	29	25	30	19	19	23	32	24
89	15	22	22	22	21	23	23	23	23	21
90	18	28	28	28	20	19	23	20	19	29
91	20	12	15	8	17	9	16	10	18	16
92	24	30	24	31	18	31	28	26	20	27
93	13	17	27	13	23	25	23	13	25	20
94	30	19	32	24	25	27	18	21	30	18
95	10	11	8	14	18	19	8	17	9	18
96	20	20	28	22	29	29	27	27	27	27
97	33	39	45	44	46	47	44	40	38	34
98	18	24	21	22	29	18	31	28	28	22
99	21	20	24	18	20	32	29	27	24	20
100	25	25	23	23	32	31	27	27	21	23
101	27	23	20	18	17	23	21	24	21	16
102	35	32	24	37	23	33	33	31	32	26
103	16	15	22	10	17	16	21	15	14	9
104	13	24	20	14	20	17	13	12	24	12
105	41	38	38	31	29	35	29	40	39	28
106	22	17	25	17	21	16	22	19	29	24
107	26	23	34	21	29	23	32	26	31	31
108	24	32	26	29	27	31	34	25	23	25
109	24	27	30	22	31	27	28	22	26	27
110	25	19	16	18	24	24	23	23	26	18
111	17	24	20	19	27	23	28	21	22	16
112	32	37	31	31	32	34	31	28	34	33
113	33	32	33	32	28	36	34	39	38	38
114	23	28	23	21	34	33	28	33	29	25
115	27	21	16	14	21	16	15	27	27	26
116	29	28	26	26	29	24	23	19	20	21
117	19	13	16	22	24	16	27	27	14	22
118	23	29	20	17	18	22	26	24	20	16
119	25	34	30	27	28	23	37	26	27	34
120	30	25	30	30	31	22	25	28	24	24
121	20	27	19	21	20	20	19	30	29	28
122	21	23	21	27	29	21	23	19	17	29
123	25	22	29	28	22	22	22	34	21	24
124	15	24	25	26	19	20	25	25	14	25
125	22	20	26	27	29	19	28	23	16	19
126	28	31	30	31	34	28	32	23	25	21
127	18	21	27	31	23	22	24	32	18	27
128	30	32	21	32	27	25	20	25	22	18
129	17	24	21	23	16	21	25	20	18	22
130	13	19	14	17	16	15	18	25	26	26
131	8	12	9	18	7	14	13	18	19	9
132	40	38	44	31	38	35	39	35	41	42
133	24	25	22	27	19	23	19	28	25	31
134	25	25	25	23	23	30	34	25	34	30
135	12	8	14	18	13	7	13	18	15	11
136	27	24	28	23	28	20	24	31	32	20
137	26	22	27	25	28	21	24	21	30	21
138	37	32	38	33	29	38	39	26	35	33
139	43	48	44	46	47	41	48	45	45	46
140	31	29	34	24	29	24	33	23	29	23
141	39	34	33	39	42	41	40	31	40	42
142	30	34	26	31	23	25	21	31	34	32
143	27	34	33	35	25	37	27	31	36	33
144	28	37	25	25	37	31	35	34	34	29
145	38	38	42	48	41	42	43	49	48	40
146	27	23	23	24	24	30	31	29	34	31
147	28	21	32	19	21	29	21	27	22	20
148	31	31	26	33	26	34	33	31	37	27
149	14	9	15	12	17	6	13	7	11	17
150	23	23	30	30	23	26	27	28	29	25
151	31	29	34	30	37	29	36	37	37	24
152	27	29	23	28	22	30	27	23	20	22
153	20	18	24	18	23	25	22	17	22	24
154	32	30	31	27	20	27	31	28	31	29
155	37	46	46	44	36	44	42	36	33	33
156	23	28	25	28	19	25	30	32	28	25
157	5	7	16	17	6	10	16	5	6	9
158	19	23	31	22	32	28	31	20	21	26
159	13	22	19	13	13	8	20	21	20	21
160	26	18	27	21	20	30	21	20	21	32
161	28	37	30	36	24	37	35	34	36	36
162	27	18	30	25	25	25	25	21	25	32
163	12	14	15	12	13	9	8	19	8	19
164	18	22	29	28	21	28	32	27	27	31
165	11	11	19	9	19	13	9	9	13	22
166	23	29	25	25	32	21	20	27	25	27
167	20	29	18	25	19	32	18	19	27	20
168	33	33	30	35	33	33	42	28	31	34
169	23	30	25	28	25	31	32	20	28	21
170	22	30	26	18	28	26	18	29	28	18
171	44	36	45	43	33	41	38	35	33	41
172	20	20	28	26	28	30	25	21	20	21
173	43	41	38	43	46	40	37	40	40	38
174	23	24	22	28	23	30	29	19	32	20
175	32	25	28	29	29	30	32	32	20	32
176	36	39	33	41	34	32	33	38	42	34
177	23	20	32	28	24	27	18	19	19	28
178	22	29	18	30	25	21	24	31	25	30
179	23	14	16	17	16	22	27	22	24	25
180	25	20	25	25	29	24	31	32	22	23
181	11	3	16	10	15	16	3	13	13	5
182	31	25	27	24	21	20	31	27	18	27
183	49	40	38	46	44	48	47	50	47	41
184	30	27	26	22	19	31	18	19	26	31
185	30	18	25	18	18	21	18	22	26	27
186	19	12	22	13	18	18	22	17	19	21
187	18	30	20	20	30	30	23	18	29	25
188	33	41	37	42	35	36	36	40	34	47
189	38	30	41	31	32	33	42	42	28	42
190	37	35	41	36	47	36	36	39	45	34
191	23	25	23	20	25	24	29	25	28	26
192	16	12	10	3	16	10	15	5	15	8
193	8	17	15	8	10	20	12	14	11	11
194	22	25	22	20	18	21	19	24	19	20
195	23	23	30	18	28	27	25	32	24	25
196	36	31	27	35	26	27	32	37	26	26
197	24	21	25	26	29	25	22	28	19	25
198	37	36	23	30	27	31	26	37	29	27
199	32	24	29	24	25	27	24	30	25	31
200	27	17	15	21	16	13	27	19	27	14
201	21	18	31	32	21	26	21	22	18	32
202	29	21	29	20	29	30	20	32	32	19
203	25	26	25	24	31	29	23	27	31	32
204	25	25	28	18	31	25	18	22	21	29
205	19	16	21	21	17	12	19	9	10	18
206	29	26	28	31	18	19	20	18	22	25
207	32	28	35	42	35	34	33	34	32	41
208	24	25	18	30	18	30	23	30	22	27
209	13	22	15	24	24	23	23	21	14	16
210	30	18	26	28	19	21	30	23	19	28
211	38	40	37	38	28	31	42	30	30	38
212	21	31	19	27	26	27	28	19	27	22
213	34	37	47	45	44	47	36	33	42	33
214	41	36	31	38	30	41	36	39	33	30
215	28	20	18	27	32	22	27	26	22	21
216	18	27	19	13	15	23	24	13	23	20
217	28	22	19	21	21	19	27	22	24	27
218	8	15	21	16	15	9	18	20	22	21
219	27	24	21	23	20	20	19	18	32	23
220	21	22	15	27	23	14	27	14	18	14
221	18	25	22	31	21	21	26	19	21	29
222	20	20	19	18	19	13	12	14	20	18
223	30	30	23	24	30	28	21	26	29	20
224	25	13	18	19	13	24	15	18	20	23
225	28	18	31	29	29	21	29	26	19	31
226	16	8	9	18	10	22	14	19	8	18
227	19	26	29	21	31	19	20	30	28	30
228	47	38	43	46	41	40	38	33	33	38
229	23	30	20	29	21	20	20	26	24	26
230	20	20	29	29	31	22	18	32	24	23
231	32	27	27	25	26	22	34	27	24	31
232	27	28	24	16	27	17	27	22	26	19
233	25	27	23	30	35	31	25	29	31	33
234	13	21	8	11	22	11	15	18	18	8
235	13	22	22	12	19	16	23	20	16	20
236	42	41	35	33	33	36	30	31	28	42
237	19	28	23	17	28	18	29	21	22	26
238	22	31	23	29	32	27	32	22	26	34
239	29	29	30	22	24	24	24	27	31	22
240	28	30	20	23	32	25	31	18	20	20
241	16	22	16	20	29	28	27	22	28	17
242	26	22	22	20	17	22	22	18	18	28
243	39	28	35	28	28	39	36	36	38	26
244	42	42	34	42	38	30	31	28	34	31
245	22	26	33	32	21	27	29	23	31	31
246	26	14	24	27	24	24	19	13	21	18
247	29	19	21	28	17	26	26	28	20	21
248	25	26	21	22	15	16	14	14	16	26
249	16	18	29	17	19	19	23	22	23	28
250	29	37	30	32	23	31	27	32	36	37
251	22	28	30	34	27	30	23	21	28	23
252	32	23	24	31	22	32	18	29	26	19
253	25	26	23	16	19	27	28	29	19	16
254	31	29	28	29	25	22	26	23	26	34
255	26	15	17	27	18	16	22	14	15	27
256	17	19	22	22	27	27	21	29	23	29
257	22	29	25	22	31	25	26	32	27	32
258	18	22	21	25	19	20	32	32	22	20
259	28	31	32	31	25	23	25	30	30	19
260	24	21	18	20	21	21	20	23	29	21
261	18	18	14	13	24	15	19	22	22	26
262	16	14	16	8	12	17	7	14	9	20
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