Are these Florida Precinct Reports a smoking gun or not? Part #2

[adolfo]

I’m continuing this thread because the other one has grown too large.

The original thread was about “twin” anomalies discovered within the precinct and voter statistics reports of Florida. For those not familiar with the issue please visit the link below for more info.

http://www.democraticunderground.com/discuss/duboard.php?az=show_mesg&forum=203&topic_id=353198&mesg_id=353198

Personally, I think the anomaly is significant since it *strongly* indicates automatic vote manipulation.

The main question was “Is the anomaly random?” After reading all the arguments I’ve found TruthIsAll’s analyses the most credible and thorough. He not only tried multiple scenarios but also explained his equations in detail (See below).

------------------------------------------------------------------------------------------------------
TruthIsAll’s Analyses
------------------------------------------------------------------------------------------------------
Vote Register
High 400 1200
Low 100 200
PCT Diff
AVG 253 690 46.2 31.4
MAX 400 1200 192.0 173.6
MIN 100 200 8.5 0.0
Diff 300 1000 183.5 173.6

Sim Matches:4 (1 in 950)
Probability (>=14): 1 in 13263


Prct Vote Reg Pct Diff
79 270 1051 25.7 0.0 1 Match
2060 357 845 42.2 0.0 1 Match
2576 371 730 50.8 0.0 1 Match
3553 262 668 39.2 0.0 1 Match



Prct Vote Reg Pct Diff MATCH
1 232 921 25.2
2 127 779 16.3 8.9
3 283 375 75.5 59.2
4 160 896 17.9 57.6
5 391 371 105.4 87.5
6 205 611 33.6 71.8
7 281 743 37.8 4.2
8 256 467 54.8 17.0
9 267 1028 26.0 28.8
10 219 426 51.4 25.4
11 246 282 87.2 35.8
12 325 1183 27.5 59.7
13 281 851 33.0 5.5
14 348 739 47.1 14.1
15 170 766 22.2 24.9
16 325 495 65.7 43.5
17 125 683 18.3 47.4
18 312 942 33.1 14.8
19 306 242 126.4 93.3
20 264 1081 24.4 102.0
21 132 1177 11.2 13.2
22 264 1142 23.1 11.9
23 353 992 35.6 12.5
24 120 597 20.1 15.5
25 222 1116 19.9 0.2
26 124 1145 10.8 9.1
27 377 836 45.1 34.3
28 366 986 37.1 8.0
29 366 1145 32.0 5.1
30 127 378 33.6 1.6
31 169 467 36.2 2.6
32 360 551 65.3 29.1
33 237 559 42.4 22.9
34 101 1016 9.9 32.5
35 206 286 72.0 62.1
36 277 528 52.5 19.5
37 249 662 37.6 14.9
38 281 901 31.2 6.4
39 123 645 19.1 12.1
40 352 381 92.4 73.3
41 342 917 37.3 55.1
42 348 984 35.4 1.9
43 400 269 148.7 113.3
44 248 849 29.2 119.5
45 163 439 37.1 7.9
46 223 1078 20.7 16.4
47 264 1002 26.3 5.6
48 232 438 53.0 26.7
49 276 1085 25.4 27.6
50 275 1148 24.0 1.4
51 373 876 42.6 18.6
52 246 945 26.0 16.6
53 349 268 130.2 104.2
54 195 902 21.6 108.6
55 327 917 35.7 14.1
56 191 1056 18.1 17.6
57 204 724 28.2 10.1
58 303 844 35.9 7.7
59 357 242 147.5 111.6
60 265 357 74.2 73.3
61 275 1175 23.4 50.8
62 389 470 82.8 59.4
63 302 577 52.3 30.5
64 117 1033 11.3 41.0
65 337 328 102.7 91.4
66 386 705 54.8 47.9
67 187 486 38.5 16.3
68 344 724 47.5 9.0
69 120 1057 11.4 36.1
70 342 1114 30.7 19.3
71 230 1024 22.5 8.2
72 381 611 62.4 39.9
73 299 557 53.7 8.7
74 388 872 44.5 9.2
75 362 336 107.7 63.2
76 168 321 52.3 55.4
77 197 308 64.0 11.7
78 307 1193 25.7 38.3
79 270 1051 25.7 0.0 1 Match
-------------------------------------------------------------------------------------------

This second post is an attempt to gain more opinions from everyone. Do YOU think it is a smoking gun? Please back up your claims with something solid if you want to provide an argument. It is up to the reader to decide.

The odds are greater against finding more “twins”. Private research in this area will continue and I encourage anyone interested to get involved.

[lenidog]

1. We have to switch tracks

We can calculate odds and statistics till hell freezes over and thaws out and the American people wont care. For them its a done deal. What we have to do is get out there and find a real smoking gun. People, files, software something tangible that either shows or can tell us that yes the election was rigged and here is the stuff or this is how we did it. That will be our smoking gun.

[berniew1]

2. The case is growing rapidly; apparently some haven't seen the evergrowing

evidence.

Here is a combination of evidence from the Nashville Conference:

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


There is likely no one big smoking gun; but there is a very large amount of fraud, irregularities, manipulation, illegal dirty tricks, etc. that are known and documented and the case is growing rapidly. More audits of more precincts in more counties are being done and they are finding significant problems. Things are starting to get investigated and the news is picking up some of it. Its hard to know which straw will be the one to break the "camels" back.

[Iceburg]

3. A gun at best ... definitely not smoking. Here's what I think is missing

Again, I repeat I am NOT an expert in probability theory... just a semi-sentient being. And as you well know I am firmly planted in the This-Election-Was-Stolen" camp. That said, here's what I think is missing in the probability estimate...

Firstly, (and perhaps most importantly) within any given county the pct numbers are not statistically independent. Thus, their associated attributes (precinct name/label, votes/registration etc) are not statistically independent. (Assignment of precinct numbers based on sorted lists discussed in an early post)

2ndly, the distribution of the ratio votes/regsitered may not be statistically normal (Dade,the county I looked at was not.)

3rdly, (non-randomness aside)I believe one would have to treat each county sequence separately since their respective distributions/ranges vary from county to county.
For example, a strong democratic county with 1000 precincts and total range from 40.0% to 95%, may have an IQR of only 15%, with its 25th and 75th percentile at 60% to 75% respectively. In this case 50% or 500 numbers lie in a very narrow band between 60.0 and 75.0 ( or 150 distinct possibilities). In this example, finding a match within the IQR will not have the same probability as finding a match outside the IQR.
-----------------------
To the nathsayers of statistical analysis....
The laws of probabilty WILL play an important role in establishing that fraud did take place. Face it, America sentences people to die based on probability theory (DNA analysis) and the work of the WWII code breakers (agin all statisical analysis) was one of the most important factors in the defeat of Hitler.

Adolfo, don't get discouraged ... every analomaly we find needs to be vetted thoroughly. In the end, some will diamonds, others just simple lumps of coal. A lesson from Edison: Thomas Edison is reputed to have tried 10,000 experiments before he found a filament for the light bulb. When asked how it felt to have failed 10,000 times, he replied "I didn't fail," said the inventor. "I found 10,000 ways NOT to make a light bulb."

[mgr]

5. All was addressed in previous thread

1.) The assortment of precinct letters and numbers probably are such that they are adjacent, in a linear fashion. However, since there is dissent, it needs proving one way or the other.

2.) This refers to what I called "spatial autocorrelation"

3.) This is a more specialized argument of the one qhg... made that TIA's analysis did not take into account a normal distribution, but threated the tails with equal weight as the center of the normal distribution. What you are arguing is that voter behavior is constrained by the county, I would suggest to the state, but still the same issue remains. Many more percentages will exist closer to the mean/median/mode than will be out at the extremes--in other words there should be more 50-70% range precincts, than 70-100%. However, the numbers of discrete percentages is greater in the 70-100% bracket than the 50-70%. Now if Adolfo were addressing adjacents in the tail of the distribution, he might be on to something, but he is not. (One may also see the issue with TIA's analysis)

The entire argument does not even consider spatial ramifications. Assuming a square grid, there are four edges and four corners to be considered adjacent. Adolfo will need a hell of a lot more matches, probably sufficient to exhaust the set of a particular percentage so that all are adjacent, for the pattern to be meaningful of human agency. And it still may be a random outcome.

What is it they say, the ignorant are nothing to worry about, its those with a little bit of knowledge that are dangerous. I think the problem here is that people with a smattering of probability theory from grade school, and without the experience of applying it to the real world, are making decisions and comparisons when they really ought not to. There are reasons why one should consult experts.

Math and science should never be subject to relativism. There are universal and objective criteria applicable to both, and that criteria underlies what is known as methodology. What TIA does, and many on this site emulate (Adolfo with this thread) is a failure to follow accepted protocols that when violated bring the very enterprise of science into question, and is the foundation from which of my dissent emanates.

Mike

[mgr]

4. I find this shift to a new thread troubling

There are several things wrong with making the shift

1. You do not critically evaluate why the other positions presented are unacceptable. The fact that you ask whether this pattern is significant suggests that you are already of the mind that it is so, and rejecting the other positions out of hand is ascientific, and contrary to formulating the appropriate null hypothesis. Two of us made very different arguments as to why the pattern was not compelling as to fraud.

2. The cogent mathematical criticism of TIA's position by qwg..... is marred by posts deleted by the moderator in the old thread, but enough remains to suggest that his position and argument was the robuster. The fact that he does not like TIA's approach, and questions his competence should not affect how one weighs his position one way or another. I have just as strong reservations regarding a software engineer posing as a mathematician, who then poses as a statistician. I am just not as rude.

3. Making such a shift stifles discussion. This is something similar to a practice I encounter in work, if the facts are uncomfortable, shop for someone's opinion that is ignorant of the specifics. Starting a new thread is just that. And, by dissenting, might I be subject to the same censorship as qhg...?

Mike

[TruthIsAll]

6. And what are you posing as, mgr?

An unbiased observer?

[Name removed]

8. Deleted message

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

[Name removed]

12. Deleted message

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

[adolfo]

7. Dissent Is Good

1. First of all, I really appreciate everyone sharing their analyses regardless of their position. It is up to the reader to form their own opinion. At least we can all agree to disagree. ;)

My conclusions are based on the facts for this project. The fact is; the project is incomplete and we have yet to see the whole puzzle. I was sharing my *current* position on the issue and it is not set in stone. To form a final opinion on this subject and disregard everything would be foolish.

There is a stack of precinct reports on my desk for other Florida counties. What are the odds of finding the “twins” in almost every county? (So far, these numbers only show up when combining the Voter statistics and precinct reports for the 2004 election.) Most can agree that the odds are higher against finding more. Well, let’s take a look. If it is anything like Dade it may get more interesting.

DADE COUNTY

143 FIRST CHURCH OF NORTH MIAMI 1200 NE 135 ST 627 (69.8%) 124 74.7%)
144 FIRST CHURCH OF NORTH MIAMI 1200 NE 135 ST 236 (69.8%) 83 (98.8%)

777 MIAMI ELK'S LODGE #948 10301 SW 72 ST 126 (75.0%) 190 (65.5%)
778 MIAMI ELK'S LODGE #948 10301 SW 72 ST 6 (75.0%) 21 (60.0%)

429 IGLESIA ADVENTISTA EBENEZER 6566 SW 33 ST 219 (61.9%) 392 58.0%)

430 IGLESIA ADVENTISTA EBENEZER 6566 SW 33 ST 267 (71.8%) 598 (58.0%)

2. Call me naïve, perhaps someone forgot to follow the forum rules. I don’t care about personal politics. However, I do have strong reservations against someone producing unnecessary noise in the thread. It can make some wonder if it was an intentional act to distract from the real issue.

3. A link to the original post is available for anyone to review. How does it stifle discussion?

We are all free to form our own opinions. Dissent all you want isn’t that what democraticunderground.com is for?

[Name removed]

9. Deleted message

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

[adolfo]

10. More serious than you think

1.) Can you provide the post #’s your conclusion is based on so we can discuss its merits? If it is any of the deleted posts then by all means repost it (exclude content against DU rules).

2.) All the bickering is not productive. The unnecessary noise described was the name calling and finger pointing between qwghlmian and other members.

3.) You can rectify the problem by reposting qwghlmian’s argument. There are no special DU privileges just basic rules to follow. The “abuse of power” you described does not exist since I have no involvement with the deletions.

There is no need for your personal attacks. It is a waste of everyone’s time and does a disservice to us all. I will let the facts stand for itself.


DADE COUNTY

143 FIRST CHURCH OF NORTH MIAMI 1200 NE 135 ST 627 (69.8%) 124(74.7%)
144 FIRST CHURCH OF NORTH MIAMI 1200 NE 135 ST 236 (69.8%) 83 (98.8%)

777 MIAMI ELK'S LODGE #948 10301 SW 72 ST 126 (75.0%) 190 (65.5%)
778 MIAMI ELK'S LODGE #948 10301 SW 72 ST 6 (75.0%) 21 (60.0%)

429 IGLESIA ADVENTISTA EBENEZER 6566 SW 33 ST 219 (61.9%) 392 (58.0%)
430 IGLESIA ADVENTISTA EBENEZER 6566 SW 33 ST 267 (71.8%) 598 (58.0%)



"... The present is theirs. The future, for which I really worked, is mine."

Nikola Tesla

[TruthIsAll]

11. Simulation w/6 matched pair;reasonable vote/reg ratio. Prob (14+)= 0.36%

	Vote	Register	PCT	Diff		
High	300	600	50.0			
Low	50	300	16.7			
						
AVG	176	450	40.7	22.1		
MAX	300	600	97.4	84.5		
MIN	50	300	8.5	0.0		
Diff	250	300	88.9	84.5		
StdDev	73.25	88.10	19.37	16.57		
Sim Match	6	
Prob= 0.16%	 or 1 in 633		

Probability (>=14)= 0.36%  or 1 in	278		
						
						
Prct	Vote	Reg	Pct	Diff	 
423	251	439	57.2	23.8	1	Match
424	291	509	57.2	0.0	1	Match
1298	168	423	39.7	13.8	1	Match
1299	238	599	39.7	0.0	1	Match
1538	164	347	47.3	1.7	1	Match
1539	274	579	47.3	0.0	1	Match
2353	254	350	72.6	57.5	1	Match
2354	270	372	72.6	0.0	1	Match
3303	239	560	42.7	2.1	1	Match
3304	131	307	42.7	0.0	1	Match
3536	157	508	30.9	43.5	1	Match
3537	151	488	30.9	0.0	1	Match

[TruthIsAll]

13. A very simple probability calculation

To calculate the probability P of getting at least n=14 matches out of 3800 adjacent pairs, given that the expected number of matches from the simulation =6:

The probability of an adjacent pair match = PM =6/3800:

The probability of at least n matches is given by:
P(min. n matches) = 1-BINOMDIST(n-1,3800,PM,TRUE)

Therefore, the probability of at least n=14 matches is given by:

P(of a minimum 14 matches) = 1-BINOMDIST(13,3800,6/3800,TRUE)
= 0.003599813 or 1 in 278

[TruthIsAll]

17. Nine simulations over various vote and registration ranges...

I assume a uniform distribution, no clustering around the
mean.
I tried various combinations to see the effects on the
probability of exceeding 14 matches.

Recall that in at least a few precincts, Repub votes far
exceeded registrations. That's one good reason NOT to assume a
normal distribution, but we will have to see more precinct
data before we can jump to conclusions 

Simulation 
1	2	3	4	5	6	7	8	9

Vote Range	
1-400 1-400	1-400	1-300	1-300	1-300	1-200	1-200	1-200
Regist. Range
2-400	3-600	4-800	2-400	3-600	4-800	2-400	3-600	4-800
									
Exp.Vote/Range Ratio
83.3%	55.6%	41.7%	66.7%	44.4%	33.3%	50.0%	33.3%	25.0%
									
Matched pairs
2	3	4	5	6	9	10	12	22

Prob (14+ matches)
0.00%	0.00%	0.01%	0.07%	0.36%	7.36%	13.52%	31.83%	97.25%

Odds:
1 in 
34,729,290 298,340 13263	1447	278	14	7	3	1
									

[TruthIsAll]

14. adolfo, please explain this statement...

"The odds are greater against finding more “twins”. Private research in this area will continue and I encourage anyone interested to get involved".

Why do you say that the "odds are greater against...?

[adolfo]

27. Odds

I think most will agree; as more twins are found, the chances of it being a random occurrence is diminished. It doesn't take a genius to see something is out of whack if these results show up everywhere.

[eomer]

15. Here are my latest simulation results.

First simulation:

Simulation based on a range of turnout percentages from 33.62 to 74.63 where the turnout is assumed to follow a uniform distribution. Average number of adjacent matches = 8.9 out of 3800.

Probability of at least 14 matches if the rate is 8.9 out of 3800 = 1-BINOMDIST(13,3800,8.9/3800,TRUE) = 6.9%.

Second simulation:

Simulation based on turnout assumed to follow a normal distribution with mean of 54.12 and standard deviation of 10. Average number of adjacent matches = 10.94 out of 3800.

Probability of at least 14 matches if the rate is 10.94 out of 3800 = 1-BINOMDIST(13,3800,10.94/3800,TRUE) = 21.3%.

These results show that the question of whether the data follows a uniform distribution, a normal distribution or some other distribution has a significant effect on the answer.

My results seem to fall into the DMZ where they could probably be taken to support either side of the argument. I'll just let everyone draw their own conclusions.

[eomer]

16. One point that I made in the original thread...

but probably got lost in the shouting and name calling, is the question of how the 9 counties that we are looking at were selected.

Out of 67 Florida counties, we are looking at 9 counties. Were these 9 selected out of the 67 based on finding adjacent matches in them or were they selected randomly?

If the answer is the former then all the calculations everyone is doing here, including mine, are basically wrong.

[Iceburg]

18. Has anyone here actually looked at the data and tested it for normalcy?

I have looked at two counties Polk and Dade. The data is
neither uniform nor normal by standard statisical measures.
Look at the quartiles folks. Take Dade for instance...

Looking at the Dem side of the equation only (for now)we have:

DVR(DemVotes/Registration) by Quartile Group : Dade County
(749 precincts)
Group    n       Mean    SD      SE         Median       DVR
Range
1Q      191     48.64%  15.188% 1.099%      53.10%   0.0% to 
62.1%
IQR     374     71.04%  5.080%  0.263%      70.50%  62.2% to 
80.6%
4Q      184     97.13%  33.929% 2.501%      88.60%  80.7% to
400.0%
       -----
        749 precincts


              Possible Number of 
Group 	n     Values in the DVR Range
----    ---   ---------------------
1Q 	191   620   in 0.0% to 62.1%
1QR 	374   184   in 62.2% to  80.6%
4Q 	184   3019  in 80.7% to 400.0%

For the moment, forget the pct id, and focus only on n, and
DVR - the number of values in each quartile. Now, what are the
odds of simply finding a matching pair in the set of NV for
the inner quartile range (IQR). We have a total of 374 numbers
in that set of which 184 are unique. What are the odds of
finding a matching pair? (Chances for: Chances against)

Now we can move on to part 2 of the problem. 

Just for the sake of discussion, let us assume that the
precinct number designations are random (i.e. that there is no
interdependence -- BTW this is a false assumption).

Given the distribution above, is the probability of a match
(adj pct AND DVR the same for each group?

Lets start with the narrowest band, the IQR (Inner Quartile
Range).
There are 374 distinct precincts, each precinct (except the
first and last) has 2 adjacent precincts in the sequence, --
one above and one below. In total there are (n-1) x 2 = 746 
possible adjacent pairs. 
 
Now, there are only 184 distinct numbers in the IQR  (80.6 -
62.2)x10

What is the probability that we will find a set that has both
a matching DVR, AND pct adjacency?

What is the probability that at least 2 pairs will match in
the IQR?
Now Dade has 2 matches on DVR. (It also has one on the
republican side.)
Are these findings not well within the expected range?

Final question, pct ids aside, how many DVRs match to within 1
decimal point in the entire Dade dataset? I've already sorted
them, you just have to count them....

PCT #   K       B       DVR     RVR
294     0       0       0.0%    0.0%
373     0       0       0.0%    0.0%
383     2       6       0.0%    0.0%
386     8       23      0.0%    0.0%
540     0       0       0.0%    0.0%
780     0       1       0.0%    0.0%
789     0       2       0.0%    0.0%
844     0       0       0.0%    0.0%
935     0       1       0.0%    0.0%
948     0       0       0.0%    0.0%
950     7       0       0.0%    0.0%
542     69      87      15.6%   16.8%
983     7       5       19.4%   15.2%
568     2       8       22.2%   100.0%
722     1       6       25.0%   42.9%
103     352     206     26.7%   57.1%
277     5       1       27.8%   50.0%
184     338     188     28.4%   50.9%
52      2       4       28.6%   0.0%
460     2       11      28.6%   61.1%
645     61      119     29.8%   70.4%
582     280     285     31.2%   47.8%
188     1       0       33.3%   0.0%
648     1       0       33.3%   0.0%
20      10      15      35.7%   50.0%
109     452     348     38.4%   66.0%
149     332     229     38.6%   62.4%
723     130     252     38.9%   44.5%
626     71      150     39.9%   72.1%
611     95      236     41.1%   51.1%
977     72      21      41.1%   72.4%
927     7       20      41.2%   62.5%
619     109     183     41.3%   69.8%
628     166     256     41.6%   63.4%
804     289     313     41.6%   51.5%
288     5       1       41.7%   100.0%
946     10      9       41.7%   37.5%
26      115     150     42.1%   131.6%
30      538     317     42.2%   56.0%
102     486     317     42.7%   61.1%
649     169     174     42.7%   58.8%
944     37      22      43.5%   91.7%
29      248     334     43.6%   108.8%
617     340     731     44.0%   62.9%
761     80      135     44.0%   61.9%
943     4       6       44.4%   85.7%
973     24      44      44.4%   46.8%
173     62      6       44.9%   54.5%
186     18      9       45.0%   75.0%
605     153     193     45.5%   42.4%
750     253     550     45.9%   65.4%
998     113     185     46.1%   53.6%
842     57      37      46.7%   92.5%
635     34      42      47.2%   56.0%
751     215     376     47.7%   71.5%
647     92      105     47.9%   66.9%
624     61      103     48.0%   78.6%
932     12      9       48.0%   69.2%
23      315     349     48.1%   56.7%
266     26      3       48.1%   150.0%
517     286     48      48.1%   60.8%
653     102     171     48.3%   84.7%
991     56      155     48.3%   38.1%
754     380     392     48.4%   64.6%
13      274     136     48.7%   29.4%
794     33      48      49.3%   49.0%
830     57      100     49.6%   84.7%
14      286     165     49.8%   42.9%
913     302     518     49.9%   83.7%
22      68      83      50.0%   39.7%
180     3       2       50.0%   33.3%
183     5       4       50.0%   200.0%
924     1       3       50.0%   0.0%
929     30      52      50.0%   81.3%
984     8       5       50.0%   250.0%
24      317     223     50.2%   62.6%
534     62      33      50.4%   126.9%
805     117     191     50.4%   68.0%
110     154     75      50.5%   108.7%
616     222     321     50.5%   73.8%
587     361     239     51.0%   56.1%
809     46      72      51.1%   64.3%
546     235     148     51.2%   58.7%
111     801     432     51.4%   78.0%
623     75      112     51.4%   81.2%
644     133     134     51.4%   64.7%
787     67      118     51.5%   86.1%
914     122     283     51.5%   87.6%
138     266     52      51.7%   82.5%
615     227     453     51.8%   66.9%
105     340     202     52.4%   90.6%
170     102     13      52.6%   54.2%
807     278     305     52.7%   72.3%
631     143     195     52.8%   73.6%
825     622     374     52.8%   52.7%
120     152     128     53.1%   125.5%
614     159     277     53.2%   62.0%
222     1195    69      53.4%   67.0%
636     172     244     53.4%   56.1%
749     300     417     53.6%   62.1%
6       226     191     53.7%   83.0%
436     173     558     54.1%   52.1%
650     72      78      54.1%   64.5%
142     688     163     54.3%   74.1%
175     19      9       54.3%   112.5%
753     485     527     54.3%   72.1%
808     155     267     54.4%   75.2%
106     238     125     54.5%   87.4%
586     352     211     54.8%   53.3%
837     376     501     54.9%   70.6%
901     218     473     54.9%   91.8%
189     199     42      55.3%   75.0%
418     154     365     55.4%   49.1%
446     5       7       55.6%   63.6%
28      165     170     55.7%   132.8%
31      118     60      55.7%   62.5%
718     102     346     55.7%   61.8%
937     78      50      55.7%   60.2%
748     193     263     55.8%   60.3%
101     585     328     55.9%   95.6%
978     262     44      56.0%   74.6%
115     207     134     56.1%   114.5%
716     155     481     56.2%   68.8%
581     35      29      56.5%   74.4%
638     140     211     56.7%   52.2%
187     75      14      56.8%   63.6%
906     29      14      56.9%   66.7%
137     97      23      57.1%   95.8%
376     16      56      57.1%   57.1%
714     216     578     57.4%   65.0%
140     451     101     57.5%   114.8%
840     281     172     57.5%   67.5%
715     259     623     57.7%   63.8%
34      93      75      57.8%   45.5%
630     256     326     57.8%   61.0%
419     103     270     57.9%   40.8%
622     145     166     58.0%   66.1%
221     799     81      58.2%   119.1%
45      127     73      58.5%   100.0%
810     589     701     58.5%   67.5%
504     363     97      58.6%   46.9%
554     129     348     58.6%   43.1%
35      199     89      58.7%   45.6%
118     445     263     58.7%   150.3%
580     44      0       58.7%   0.0%
728     436     402     58.7%   53.9%
3       626     393     59.0%   117.0%
182     154     48      59.0%   70.6%
505     438     29      59.0%   61.7%
992     39      69      59.1%   23.5%
725     237     463     59.3%   61.7%
999     19      9       59.4%   128.6%
305     363     509     59.6%   55.4%
152     459     152     59.8%   87.9%
851     176     90      59.9%   51.1%
289     6       33      60.0%   100.0%
632     439     457     60.0%   71.7%
987     6       11      60.0%   39.3%
371     96      76      60.4%   88.4%
919     301     358     60.4%   68.6%
427     163     354     60.6%   48.8%
637     209     283     60.6%   64.8%
902     317     468     60.7%   84.0%
951     280     167     60.7%   69.3%
174     48      14      60.8%   155.6%
153     804     139     61.0%   91.4%
915     338     443     61.0%   96.5%
139     259     46      61.1%   66.7%
557     173     488     61.1%   48.1%
806     308     260     61.2%   59.1%
172     49      4       61.3%   200.0%
720     223     632     61.3%   70.2%
760     149     209     61.3%   70.4%
610     186     201     61.4%   52.1%
756     586     577     61.4%   74.7%
148     411     199     61.5%   73.2%
350     241     167     61.5%   77.0%
157     313     319     61.6%   78.0%
310     210     564     61.8%   63.9%
515     265     49      61.8%   73.1%
602     191     306     61.8%   49.8%
845     165     111     61.8%   80.4%
429     219     392     61.9%   58.0%
926     153     208     61.9%   100.5%
11      370     318     62.0%   75.9%
590     206     87      62.0%   75.7%
293     82      24      62.1%   92.3%
530     126     62      62.1%   45.9%
606     732     441     62.1%   67.1%
820     486     554     62.1%   69.1%
907     477     545     62.1%   68.8%
625     283     242     62.2%   60.8%
917     69      47      62.2%   97.9%
136     726     146     62.3%   83.4%
729     327     424     62.4%   61.9%
819     247     226     62.4%   71.5%
133     388     128     62.5%   106.7%
212     631     84      62.5%   63.2%
25      291     370     62.6%   90.9%
438     197     624     62.7%   46.6%
995     69      52      62.7%   47.3%
522     827     36      62.8%   44.4%
253     534     45      62.9%   86.5%
441     254     593     63.0%   60.5%
812     630     239     63.0%   74.9%
227     808     115     63.1%   125.0%
21      214     143     63.3%   42.3%
141     507     61      63.3%   77.2%
331     162     563     63.3%   55.2%
596     31      11      63.3%   45.8%
126     943     123     63.4%   82.6%
164     230     63      63.4%   128.6%
506     350     27      63.4%   43.5%
724     215     363     63.4%   66.5%
745     298     339     63.5%   68.5%
426     161     378     63.6%   49.3%
453     7       13      63.6%   72.2%
822     415     396     63.6%   78.3%
130     946     198     63.8%   68.3%
813     1022    254     63.8%   81.4%
207     583     158     63.9%   94.0%
423     191     545     63.9%   62.3%
651     156     185     63.9%   60.7%
131     644     173     64.0%   82.4%
739     488     591     64.2%   63.0%
27      146     147     64.3%   86.5%
824     745     560     64.3%   73.1%
18      397     218     64.4%   63.4%
502     365     98      64.5%   78.4%
721     682     740     64.5%   65.4%
802     772     32      64.5%   80.0%
117     307     119     64.6%   143.4%
377     95      422     64.6%   60.0%
9       654     585     64.8%   79.8%
239     1223    175     64.8%   81.0%
575     249     647     64.8%   47.3%
608     296     492     64.8%   60.1%
618     125     244     64.8%   83.0%
641     147     137     64.8%   65.2%
713     237     602     64.8%   62.2%
113     314     147     64.9%   90.7%
516     351     206     65.0%   67.8%
613     267     371     65.0%   70.7%
177     28      12      65.1%   57.1%
501     757     89      65.1%   83.2%
803     794     44      65.2%   95.7%
912     90      132     65.2%   92.3%
303     441     463     65.3%   78.7%
942     32      14      65.3%   50.0%
553     157     439     65.4%   48.6%
566     344     563     65.5%   53.5%
817     483     113     65.5%   72.4%
158     233     75      65.6%   67.6%
607     168     178     65.6%   58.0%
755     342     440     65.6%   70.6%
821     653     553     65.6%   67.5%
240     1044    78      65.7%   79.6%
37      183     101     65.8%   85.6%
155     459     136     65.8%   74.7%
555     210     583     65.8%   49.9%
719     436     485     65.8%   70.7%
922     765     72      65.9%   85.7%
552     62      172     66.0%   63.7%
206     928     100     66.1%   81.3%
217     830     53      66.1%   98.1%
801     784     57      66.1%   123.9%
941     82      134     66.1%   82.2%
218     668     14      66.2%   53.8%
292     480     30      66.2%   90.9%
846     350     295     66.2%   78.0%
15      216     134     66.3%   73.2%
220     697     46      66.3%   83.6%
324     138     418     66.3%   60.1%
562     258     669     66.3%   52.3%
135     1393    220     66.4%   92.4%
595     314     130     66.4%   72.2%
104     439     195     66.5%   94.7%
256     623     128     66.5%   80.0%
717     375     458     66.5%   64.1%
839     135     69      66.5%   71.9%
949     266     137     66.5%   92.6%
849     219     91      66.6%   52.9%
223     686     62      66.7%   84.9%
259     530     40      66.7%   87.0%
599     2       6       66.7%   100.0%
790     6       27      66.7%   52.9%
795     4       4       66.7%   44.4%
848     48      120     66.7%   76.4%
314     139     511     66.8%   71.5%
601     264     375     66.8%   52.7%
814     689     546     66.8%   73.8%
828     673     262     66.8%   68.2%
248     817     221     67.0%   77.0%
731     233     488     67.0%   74.8%
769     294     311     67.0%   70.8%
274     489     124     67.1%   107.8%
329     108     372     67.1%   66.4%
850     49      79      67.1%   79.8%
238     43      4       67.2%   30.8%
380     62      207     67.4%   59.5%
12      102     142     67.5%   92.8%
268     626     77      67.5%   82.8%
338     170     673     67.5%   61.6%
372     140     186     67.6%   50.8%
375     63      230     67.7%   73.5%
612     153     258     67.7%   71.9%
150     305     42      67.8%   67.7%
317     141     452     67.8%   65.5%
249     848     62      67.9%   58.5%
44      117     81      68.0%   71.1%
147     109     95      68.1%   77.9%
161     482     87      68.1%   113.0%
445     49      106     68.1%   48.2%
707     81      267     68.1%   78.1%
244     723     80      68.2%   79.2%
270     840     41      68.2%   73.2%
431     187     299     68.2%   53.5%
202     399     143     68.3%   87.7%
576     280     534     68.3%   48.6%
32      294     274     68.4%   45.4%
262     648     21      68.4%   46.7%
836     132     290     68.4%   81.5%
709     135     290     68.5%   59.3%
734     185     288     68.5%   78.0%
107     291     116     68.6%   146.8%
518     668     93      68.6%   91.2%
523     232     90      68.6%   84.9%
831     621     306     68.6%   69.2%
422     143     384     68.8%   58.5%
524     318     451     68.8%   66.4%
434     257     565     68.9%   66.9%
564     171     338     69.0%   47.5%
741     542     453     69.0%   65.0%
770     58      212     69.0%   61.8%
154     412     122     69.1%   79.2%
275     186     141     69.1%   83.4%
8       346     158     69.2%   82.3%
512     720     29      69.2%   67.4%
594     27      34      69.2%   69.4%
762     868     721     69.2%   66.0%
985     54      9       69.2%   128.6%
308     203     306     69.3%   58.2%
5       453     382     69.4%   91.4%
401     396     533     69.4%   54.4%
19      187     129     69.5%   65.2%
273     565     49      69.5%   61.3%
409     116     397     69.5%   57.3%
425     203     510     69.5%   59.1%
519     730     52      69.5%   81.3%
520     731     25      69.6%   53.2%
832     397     252     69.6%   71.4%
156     515     298     69.7%   87.6%
132     44      7       69.8%   70.0%
143     627     124     69.8%   74.7%
144     236     83      69.8%   98.8%
224     792     71      69.8%   75.5%
307     338     586     69.8%   68.5%
759     1244    1538    69.8%   70.3%
592     51      16      69.9%   114.3%
752     378     355     69.9%   70.0%
904     377     326     69.9%   74.6%
146     608     453     70.0%   91.5%
185     7       2       70.0%   100.0%
216     925     68      70.0%   90.7%
123     735     541     70.1%   89.4%
215     639     66      70.1%   81.5%
514     535     27      70.1%   60.0%
219     586     23      70.2%   92.0%
783     238     347     70.2%   77.3%
47      52      72      70.3%   70.6%
214     971     81      70.3%   73.6%
706     289     639     70.3%   61.3%
928     52      54      70.3%   84.4%
420     190     556     70.4%   49.8%
627     314     355     70.4%   76.5%
652     157     220     70.4%   71.9%
145     158     17      70.5%   130.8%
229     732     191     70.5%   91.4%
947     55      36      70.5%   109.1%
639     36      47      70.6%   57.3%
833     886     51      70.6%   63.8%
213     855     81      70.7%   88.0%
230     492     328     70.7%   70.5%
432     220     419     70.7%   60.3%
548     157     475     70.7%   61.8%
565     251     418     70.7%   52.1%
567     208     373     70.7%   60.8%
921     65      24      70.7%   120.0%
263     595     27      70.8%   84.4%
424     231     558     70.9%   50.3%
918     236     202     70.9%   89.4%
976     205     16      70.9%   55.2%
127     652     112     71.0%   83.6%
269     712     29      71.0%   72.5%
981     120     97      71.0%   45.8%
225     1057    71      71.1%   68.9%
252     1099    30      71.1%   78.9%
811     396     301     71.1%   76.6%
228     408     22      71.2%   100.0%
291     218     174     71.2%   55.1%
128     743     101     71.4%   82.1%
203     1070    36      71.6%   73.5%
208     906     231     71.6%   90.9%
352     613     1797    71.8%   65.9%
430     267     598     71.8%   58.0%
765     372     331     71.8%   67.1%
421     291     667     71.9%   47.1%
48      378     313     72.0%   61.1%
204     370     26      72.0%   136.8%
521     1026    36      72.0%   57.1%
574     233     514     72.1%   54.6%
940     98      81      72.1%   96.4%
242     842     173     72.2%   100.0%
597     26      11      72.2%   61.1%
301     269     474     72.3%   77.6%
727     274     279     72.3%   75.8%
306     317     359     72.4%   65.2%
333     118     356     72.4%   56.4%
838     157     98      72.4%   66.7%
116     713     141     72.5%   91.0%
264     562     22      72.5%   53.7%
162     475     55      72.6%   87.3%
835     347     324     72.6%   76.8%
428     194     355     72.7%   50.5%
990     16      12      72.7%   63.2%
40      405     180     72.8%   63.4%
815     327     313     72.8%   80.3%
290     153     106     72.9%   69.3%
925     46      49      73.0%   81.7%
827     636     208     73.1%   63.0%
560     202     477     73.2%   56.6%
816     834     270     73.2%   90.0%
36      432     165     73.3%   61.3%
121     283     104     73.3%   120.9%
302     242     521     73.3%   86.0%
318     143     467     73.3%   67.3%
583     316     180     73.3%   69.5%
211     278     36      73.4%   81.8%
726     298     823     73.4%   64.3%
771     312     266     73.4%   78.5%
847     550     437     73.4%   70.6%
123     759     214     73.5%   100.0%
251     616     50      73.5%   119.0%
339     222     661     73.5%   59.7%
362     161     393     73.5%   52.8%
442     120     245     73.6%   44.0%
356     14      52      73.7%   73.2%
931     363     310     73.8%   98.4%
33      250     93      74.0%   45.1%
226     863     56      74.0%   86.2%
181     80      68      74.1%   93.2%
243     746     59      74.1%   77.6%
261     788     17      74.2%   50.0%
437     164     537     74.2%   55.6%
543     339     550     74.3%   54.8%
823     321     266     74.5%   70.9%
108     580     271     74.6%   94.1%
241     653     99      74.6%   69.7%
584     629     75      74.6%   45.2%
529     596     335     74.8%   82.5%
369     6       33      75.0%   110.0%
763     306     450     75.0%   63.3%
777     126     190     75.0%   65.5%
778     6       21      75.0%   60.0%
933     18      7       75.0%   63.6%
972     51      119     75.0%   59.2%
282     308     8       75.1%   61.5%
710     263     516     75.1%   69.1%
328     252     700     75.2%   62.5%
254     806     46      75.3%   71.9%
332     119     328     75.3%   62.1%
711     494     670     75.3%   65.0%
736     504     516     75.3%   77.4%
250     551     27      75.4%   90.0%
513     321     2       75.4%   10.0%
767     490     437     75.4%   75.5%
361     37      104     75.5%   70.7%
604     361     270     75.5%   58.1%
232     393     108     75.6%   79.4%
433     198     581     75.6%   64.3%
370     157     155     75.8%   92.8%
405     204     395     75.8%   44.9%
354     104     337     75.9%   64.6%
634     146     5       76.0%   62.5%
7       472     296     76.1%   97.0%
260     538     15      76.2%   65.2%
126     575     117     76.4%   115.8%
633     356     320     76.4%   71.3%
738     508     453     76.4%   75.4%
788     359     291     76.4%   75.2%
841     315     257     76.5%   71.4%
407     131     384     76.6%   56.3%
507     577     19      76.6%   65.5%
705     351     652     76.6%   70.3%
280     227     11      76.7%   220.0%
541     244     255     76.7%   71.2%
559     138     364     76.7%   56.0%
551     199     336     76.8%   56.1%
561     208     389     76.8%   59.0%
743     288     317     76.8%   78.3%
325     140     425     76.9%   61.8%
404     287     776     76.9%   55.7%
569     805     877     77.0%   64.7%
603     258     316     77.0%   57.7%
209     928     187     77.1%   87.4%
17      430     227     77.2%   81.1%
205     491     32      77.2%   97.0%
320     302     737     77.2%   68.2%
746     311     199     77.2%   71.8%
235     886     273     77.4%   81.5%
246     395     439     77.5%   88.9%
358     245     230     77.5%   73.7%
768     79      103     77.5%   77.4%
747     468     489     77.6%   66.9%
234     364     21      77.8%   60.0%
267     424     151     77.8%   93.2%
531     396     39      77.8%   72.2%
547     242     620     77.8%   63.9%
703     671     825     77.8%   69.7%
455     159     231     77.9%   45.0%
316     170     555     78.0%   78.6%
910     477     486     78.1%   85.6%
1       561     396     78.2%   86.8%
556     302     546     78.2%   52.0%
996     97      82      78.2%   74.5%
573     292     570     78.3%   59.4%
779     18      42      78.3%   93.3%
980     101     93      78.3%   103.3%
545     273     508     78.4%   62.9%
712     294     608     78.6%   70.9%
785     198     168     78.6%   74.7%
905     1325    482     78.7%   78.4%
544     398     259     78.8%   71.0%
829     208     181     78.8%   72.1%
179     176     113     78.9%   91.9%
742     371     375     78.9%   66.7%
231     485     428     79.0%   82.0%
558     102     285     79.1%   52.4%
159     654     111     79.2%   83.5%
233     513     92      79.2%   110.8%
503     122     256     79.2%   61.8%
247     423     143     79.4%   80.3%
257     506     11      79.4%   45.8%
272     423     370     79.4%   84.3%
378     77      236     79.4%   54.6%
509     181     470     79.4%   65.8%
532     216     26      79.4%   51.0%
550     200     578     79.4%   73.2%
237     619     40      79.5%   81.6%
456     35      100     79.5%   56.8%
853     303     402     79.5%   88.7%
735     421     493     79.6%   71.1%
39      433     178     79.7%   70.6%
319     149     387     79.7%   76.0%
579     428     659     79.7%   57.8%
916     278     165     79.7%   109.3%
343     472     598     80.0%   80.3%
930     4       6       80.0%   85.7%
786     129     108     80.1%   57.4%
920     411     43      80.1%   82.7%
953     292     333     80.4%   90.5%
46      370     202     80.6%   47.9%
435     216     546     80.6%   52.8%
570     203     362     80.6%   55.4%
793     625     809     80.6%   73.1%
258     457     28      80.7%   96.6%
330     96      330     80.7%   62.3%
585     417     18      80.7%   72.0%
2       256     189     80.8%   81.5%
340     333     814     80.8%   65.0%
834     759     84      80.8%   68.9%
511     792     19      80.9%   38.0%
642     140     127     80.9%   81.4%
945     17      15      81.0%   250.0%
744     458     476     81.3%   74.5%
176     188     43      81.4%   74.1%
993     31      52      81.6%   38.8%
321     407     809     81.7%   71.5%
443     210     252     81.7%   56.0%
994     76      183     81.7%   62.7%
406     279     357     81.8%   52.7%
416     323     572     82.0%   50.9%
535     457     101     82.0%   78.3%
115     776     357     82.1%   95.5%
245     749     51      82.2%   75.0%
440     191     533     82.3%   66.1%
757     1223    1238    82.4%   77.9%
151     597     271     82.5%   91.9%
733     766     1098    82.5%   70.9%
412     303     1070    82.6%   64.6%
255     348     10      82.7%   62.5%
549     221     488     82.8%   77.7%
621     937     186     82.9%   66.4%
766     721     635     82.9%   78.2%
344     439     574     83.0%   88.6%
508     909     19      83.0%   61.3%
355     594     283     83.1%   85.5%
411     309     436     83.1%   63.8%
417     292     561     83.2%   43.8%
591     362     356     83.2%   77.7%
826     347     7       83.2%   29.2%
536     305     30      83.3%   93.8%
997     35      105     83.3%   75.0%
911     311     256     83.4%   109.4%
342     184     509     83.6%   72.5%
336     185     487     83.7%   55.4%
345     479     491     84.0%   87.7%
346     377     541     84.0%   88.8%
740     652     633     84.1%   81.4%
315     213     638     84.5%   70.6%
774     201     150     84.5%   70.1%
43      181     67      84.6%   68.4%
53      22      2       84.6%   33.3%
781     284     267     84.8%   70.6%
525     90      104     84.9%   83.2%
125     133     62      85.3%   98.4%
539     122     23      85.3%   88.5%
952     29      20      85.3%   76.9%
364     476     519     85.5%   83.2%
538     342     136     85.5%   82.9%
403     542     634     85.6%   61.9%
402     713     1865    85.7%   54.5%
304     1059    738     86.0%   75.7%
42      488     145     86.1%   68.1%
134     31      13      86.1%   76.5%
986     124     116     86.1%   64.1%
764     872     1577    86.2%   66.9%
169     176     45      86.3%   91.8%
510     82      242     86.3%   65.4%
165     242     65      86.4%   74.7%
382     102     272     86.4%   84.7%
236     500     38      86.5%   62.3%
284     90      169     86.5%   80.5%
449     129     372     86.6%   58.2%
526     202     352     86.7%   63.0%
385     277     705     86.8%   63.2%
527     237     299     86.8%   72.0%
348     53      144     86.9%   110.8%
166     94      30      87.0%   136.4%
326     398     951     87.1%   66.0%
776     1037    1020    87.3%   79.9%
533     1101    34      87.4%   61.8%
10      7       11      87.5%   64.7%
818     685     22      87.6%   73.3%
337     288     817     87.8%   69.0%
381     72      185     87.8%   62.1%
201     356     395     87.9%   103.7%
975     73      21      88.0%   77.8%
41      673     222     88.1%   65.9%
379     104     416     88.1%   73.9%
775     702     849     88.1%   68.0%
708     186     352     88.2%   68.0%
988     38      88      88.4%   87.1%
265     138     7       88.5%   116.7%
572     185     363     88.5%   60.5%
732     239     441     88.5%   67.7%
16      242     126     88.6%   86.3%
271     101     3       88.6%   33.3%
444     248     547     88.6%   56.8%
451     203     771     88.6%   65.2%
593     101     219     88.6%   62.9%
323     174     533     88.8%   69.8%
571     242     385     89.0%   64.9%
578     308     580     89.0%   59.8%
353     432     1059    89.1%   61.2%
903     480     75      89.2%   113.6%
439     360     1083    89.3%   57.6%
312     287     447     89.4%   75.6%
311     365     619     89.7%   58.8%
351     1011    551     89.7%   90.3%
843     26      7       89.7%   100.0%
450     337     392     89.9%   66.2%
210     578     150     90.0%   92.6%
704     278     592     90.0%   67.1%
276     82      58      90.1%   85.3%
563     212     438     90.2%   54.5%
413     217     843     90.4%   57.9%
457     122     326     90.4%   67.2%
448     200     240     90.5%   58.1%
974     29      98      90.6%   63.2%
577     346     470     90.8%   63.9%
702     653     1270    90.8%   85.6%
737     338     265     90.9%   89.5%
335     303     452     91.0%   64.9%
357     205     481     91.1%   79.2%
758     675     839     91.1%   80.8%
528     148     106     91.4%   77.4%
365     843     997     91.6%   77.4%
322     521     809     91.7%   82.5%
408     553     512     92.2%   56.3%
730     566     423     92.6%   75.9%
909     552     202     92.6%   89.0%
415     437     789     92.8%   71.8%
701     361     651     92.8%   62.9%
620     208     246     92.9%   69.9%
537     227     118     93.0%   86.1%
447     284     352     93.1%   58.5%
979     55      2       93.2%   0.0%
334     226     420     94.6%   66.2%
368     323     816     94.7%   85.6%
374     125     227     94.7%   73.9%
459     91      217     94.8%   54.5%
112     293     89      95.4%   129.0%
936     70      17      95.9%   77.3%
38      162     137     96.4%   94.5%
363     154     285     96.9%   76.6%
454     133     155     97.1%   68.3%
285     75      142     97.4%   68.9%
772     349     489     97.5%   69.3%
309     437     946     98.9%   79.1%
4       393     238     99.2%   87.2%
281     11      21      100.0%  65.6%
283     3       0       100.0%  0.0%
588     20      26      100.0%  78.8%
589     11      10      100.0%  90.9%
908     2       3       100.0%  42.9%
359     495     929     100.6%  77.5%
349     718     1315    100.7%  72.9%
773     350     753     101.7%  68.0%
414     283     786     101.8%  73.8%
278     32      27      103.2%  50.9%
50      476     607     103.3%  77.9%
458     28      3       103.7%  60.0%
313     23      7       104.5%  46.7%
327     327     443     104.5%  80.3%
982     68      22      104.6%  43.1%
347     335     334     105.0%  86.8%
452     710     741     105.8%  82.1%
598     30      22      107.1%  91.7%
49      375     438     110.6%  77.0%
410     485     842     111.0%  58.8%
51      476     675     113.9%  87.4%
360     368     724     115.4%  78.8%
366     257     342     118.4%  87.9%
384     121     174     118.6%  83.7%
341     4       0       133.3%  0.0%
938     4       5       133.3%  0.0%
989     8       10      133.3%  71.4%
923     15      6       136.4%  85.7%
640     710     355     138.7%  92.9%
852     7       9       140.0%  112.5%
279     10      1       142.9%  100.0%
367     218     312     144.4%  97.5%
286     6       1       150.0%  33.3%
791     7       7       175.0%  175.0%
287     21      2       210.0%  200.0%
178     5       1       250.0%  0.0%
939     3       2       300.0%  200.0%
796     8       14      400.0%  77.8%

[Iceburg]

19. There are 4 not 2 matching adjacent pairs/DVRs and

there are 4 not 1 matching adjacent pairs/RVRs. Can you find them?

More questions ...
What reasons might a practicing statistician use for excluding some of these observations in the raw data? Think in terms of outliers with respect to the total number of ballots cast.

Would you give the same weight to an adjacent precinct pair with a combined total of 25 ballots cast as you would to a pair that had a combined 1800 ballots cast?

What practical considerations would you give to a adjacent precinct pair that had say 21 and 837 ballots cast respectively?

If after all of this, you are still remain convinced there is a smoking gun here, I AM truly worried about our ability to prosecute the evil doers. Lord, Buddha ...whomever, let common sense resume.

[TruthIsAll]

20. Here are the four matched pairs and a probability table.

PCT #	K	B	DVR	RVR	Match pairs
143	627	124	69.80%	74.70%	1
144	236	83	69.80%	98.80%	1

345	479	491	84.00%	87.70%	1
346	377	541	84.00%	88.80%	1

588	20	26	100.00%	78.80%	1
589	11	10	100.00%	90.90%	1

777	126	190	75.00%	65.50%	1
778	6	21	75.00%	60.00%	1


Probability of N or more matches for each range:		
	Range	Range	Range
N	184	620	3019

1	63.31%	25.70%	5.91%
2	26.42%	3.61%	0.18%
3	7.98%	0.34%	0.00%
4	1.87%	0.02%	0.00%
5	0.35%	0.00%	0.00%
6	0.06%	0.00%	0.00%
7	0.01%	0.00%	0.00%
8	0.00%	0.00%	0.00%

For Range = 184, the probability of at least 2 matches is:
Prob = 1 - BINOMDIST(1, 184,1/184,TRUE) = 26.42%


For Range = 620, the probability of at least 2 matches is:
Prob = 1 - BINOMDIST(1, 620,1/620,TRUE) = 3.61%


For Range = 3019, the probability of at least 2 matches is:
Prob = 1 - BINOMDIST(1, 3019,1/3019,TRUE) = 0.18%

[Iceburg]

22. Well done TIA, now we have at least established that the probabilities

vary tremendously within a single county. Now what about the oultiers in terms of ballots cast ... should they be given any special treatment?

We know also that the entire range (all three groups combined) is neither uniform nor normal. Now consider each quartile group separarately -- do they have a uniform distribution or is there still some clustering that may effect the outcome of our tests?

Moving on to the big picture, given that the distribution varies from county to county (in terms of strongholds) and hence their respective quartiles, should we estimate each county separately or do you think it is reasonable to throw them all into one big melting pot?

PS: I appreciate your work very much TIA ... even if we disagree at times.

[TruthIsAll]

23. Thanks. I appreciate your work as well as eomer's. You are not afraid to

step in and crunch numbers. We need more of that and less of the petty, personal attacks which serve no useful purpose.
I have never claimed to know all the answers. Cooperation, not blind naysaying is the key.

You:
..vary tremendously within a single county. Now what about the outliers in terms of ballots cast ... should they be given any special treatment?

Me:
The outliers are very significant.
How do you get more ballots than registrations.

You:
We know also that the entire range (all three groups combined) is neither uniform nor normal. Now consider each quartile group separarately -- do they have a uniform distribution or is there still some clustering that may effect the outcome of our tests?

Me:
I doubt they are normal.
Do a histogram.

You:
Moving on to the big picture, given that the distribution varies from county to county (in terms of strongholds) and hence their respective quartiles, should we estimate each county separately or do you think it is reasonable to throw them all into one big melting pot?

Me:
I say do both.
1) Do the differences in the counties offer clues? They might.
2) Does an exhaustive data set of all th counties show us the big picture and effectively eliminate individual the outlier concern? I believe it does.



PS: I appreciate your work very much TIA ... even if we disagree at times

[Iceburg]

25. I jump in when I can ... but I have my own little nest of eggs

that I must tend to. I'll pm you in the next few days regarding some anomalies and correlations wrt Cuyahoga that I need a 2nd opinion on.
Back to the problem...

You: "How do you get more ballots than registrations.?"

Me:
One way is switching parties. The registrations in this problem set are part registrations not regristrations to vote. I believe in another post on another topic (How many Bush/Republicans from 2000 voted for Kerry?), I indirectly cited a huge shift from voters who voted for independents (or voted for Bush in 2000) that went with Kerry in 2004 (re: Bush loses ground in his Top 10 Cities (of 2000) in Cuyahoga County)

In most of the work/analysis that I do on Cuyahoga, I exclude the precincts that have less than 50 ballots cast (unless the underying reason for the low numbers is turnout). That said, I don't ignore them completely but I wouldn't use them in lets say a regression model. The fact that precincts exist with only 4 registered voters is of more importance to me, not whether Bush got 00% of 100% in that precinct. The answer to -- Why would you establish a precinct for 4 regsitered voters, and assign it two voting machines (the minimum machine assigment in Cuyahoga) -- I call'em faux polls for now. Thus, I would tend to want to exclude them and all the precincts that have 0 ballots cast (about 20 or so) in this current exercise.

Re: Normalcy, uniformity etc of subgroups within a county. TIA, you should know me better than that ... I did the histograms before I posed the question.

RE:should we estimate each county separately ?...
You:
I say do both.
1) Do the differences in the counties offer clues? They might.
2) Does an exhaustive data set of all th counties show us the big picture and effectively eliminate individual the outlier concern? I believe it does.

Good questions, but I'm afraid I will beg out ... I must get back to my work in quantifying the number of votes mistabulated in Cuyahoga.
Good luck.

[eomer]

21. Friendly amendment

"There are 374 distinct precincts, each precinct (except the
first and last) has 2 adjacent precincts in the sequence, --
one above and one below. In total there are (n-1) x 2 = 746
possible adjacent pairs."

I submit that the number of adjacent pairs is (n-1).

In the following list how many adjacent pairs are there?
6.5
7.8
7.8
3.7
9.0

I count 4. If you count (n-1) x 2 = 8 then you are counting some of them twice.

The way I think of the probability is that once you have the first number in the sequence then you have (n-1) tries and the question each try is whether you match the previous number in the list.

If you try to think of the probability in terms of each number in the list possibly matching either the one before it or the one after it then I think you will get it wrong.

The rest of your approach makes total sense to me.

[Iceburg]

24. I stand corrected -- you are right on. n/t

[adolfo]

26. Randomly

They were selected randomly. Still working on the rest.