You haven't explained these plots at all. But it looks like it's the results on the y-axis and the percent of votes tallied on the x-axis? In which case... I don't see anything to do with a confidence interval.
NOTE: UPDATED,
PLEASE SEE MY COMMENT #26
ON PAGE TWO.
Ok... Please be easy on me...
One, I'm new here. Two, it has been a long time since I took a stats class and I don't use stats in my day to day...
I was an 'A' student back in the day, and that said, one thing I recall for certain:
CONFIDENCE INTERVAL BECOMES NARROWER AS SAMPLE SIZE INCREASES
Right?
Ok... explain this then:
Sioux county is how I would expect results for an election to look, ANY ELECTION; variable at first, then leveling out for each candidate; confidence interval becomes narrower as sample size increases. Story County and Iowa as a whole??? I am lost. How in the *$&@ do Romney's results slope upward as time progresses? Further, how in the double *$&@ does that slope INCREASE slightly over time????
Call me a crazy conspiracy theorist... but I see an algorithm after 30% of the vote is in. Do you??? I cannot, in any other way, conceptually account for the exponential slope (or any slope) in Romney's vote %.
What equations can we use to prove just how impossible this is? I don't have the raw data, just these graphs at the moment... working on getting the raw data. Any help much appreciated.
thanks,
presence
Last edited by presence; 02-22-2012 at 05:14 PM.
You haven't explained these plots at all. But it looks like it's the results on the y-axis and the percent of votes tallied on the x-axis? In which case... I don't see anything to do with a confidence interval.
I don't have emotions and sometimes that makes me very sad.
presence (02-22-2012)
Not the "raw vote totals", but each candidate's "% of votes" are on the Y axis.
The "% of votes recorded over time" are on the X axis. Where "x = 100%" means all votes are now counted.
In a "perfect world" (population approaches infinity) shouldn't each candidates percentages each eventually nearly "level out" (slope m=0) as x approaches 100%?
Shouldn't we become more confident in the final outcome of the results, as more results are counted???
All variation in a (large) population of votes should (in my expectation) become relatively balanced by the time 10-30% of the votes are in; it shouldn't become more variable with time.
Gingrich's results in Iowa are what I would expect all results in an election to do... A candidates percentage would be variable at first, becoming clearer with time... then basically leveling out by the time half the results are in... then continuing basically level (unchanged) from 50% counted all the way to 100% counted. Sioux County follows this normal paradigm: Candidates only jockey a half point to a point as the second half of the votes come in.
This is not at all what happens to Romney's results. Romney jumped from 17%, when 30% of results were in, to 25% by the end. Thats 8 points; nearly a 50% increase in his projected share. Romney's % of the vote has a definate positively linear slope, if not slightly exponential algorithmic progression over time in Story County and in Iowa as a whole. Ie. it is as if, in Iowa as a whole, after 30% of the votes are in, there is something in the election logic that says for every 100 votes that come in for Bachmann, Perry, Paul, and Santorum, subtract 1 from each of their totals and add 4 to Romney's total. Perry, Paul, Santorum, and Bachmann all trend downwards after 30% have been counted. Statistically speaking... *if population size was infinity* everyone should trend towards level as time progresses. There should be no slope and there certainly shouldn't be increasing absolute slope.
In Story County it looks as if there is an algorithm that is taking votes from Paul and giving them to Romney. Why else would both candidates be trending AWAY FROM their respective means as time progresses?
(**note: this was graphed from the raw data before the recount when santorum was declared the winner)
Last edited by presence; 02-22-2012 at 12:01 AM.
As Dason says, the graphs don't include confidence intervals, so it's hard to directly connect what you're claiming with the graphs you're showing. But I think a big thing to keep in mind here is that votes aren't usually counted in random order. There are often systematic differences between people who vote at different times, resulting in different trajectories for different candidates as the votes are gradually counted. E.g. here in New Zealand, "special votes" such as those by NZers living overseas are counted last, and are said to usually favour the Greens. On the other hand, advance votes (often made by the elderly) tend to favour National (right-wing). Similarly, polling booths in different locations tend to return their votes at different times. If areas that tend to favour a particular candidate also tend to be slower in tallying votes, this could result in that candidate's percentage showing an upward trajectory.
(on the other hand, maybe I'm a part of the conspiracy: from what I've been able to gather over this side of the world, Romney seems like arguably the least-crazy of that set of candidates, so maybe I'm just trying to cover for him...)
i think you do have a point CB... as well as Dason... with, frist, there's nothing about confidence intervals that can be seen, found or even implied from the graphs. second, all that those graphs are telling me is that that probably more votes for Romney were counted at the end... because the graphs do level off. you stop having those sharp spikes that happen around the 0-15% vote margin on the X-axis once more votes were counted. i dont think it should come as a surprise to anyone that if you analyse sub-groups of data (counties) and compare that with the analysis of the whole big group (the state of Iowa), you can end up finding markedly different trends. i mean, just by looking at Sioux County i can see that Romney performed pretty average when compared to the other potential candidates... which you dont see in Story county.
for all your psychometric needs! https://psychometroscar.wordpress.com/about/
presence (02-22-2012)
I just want to point out that Story County is by far the best county in Iowa.
I don't have emotions and sometimes that makes me very sad.
You know I had considered this, and had Romney increased his share by 10%... 20%... I could buy in. But he increased his market share by nearly 50% from the time 30% of the votes were in until the end. That seems to me beyond the scope of "systematic" differences.
I'm going to let this go for the night... *tired* thanks for your input all... interested in any other opinions out there.
Above all, I'm really interested in some means to calculate the odds that romney increased his share in the way he did.
If it helps there were 122255 total votes. At 30% counted: 36676.
much thanks,
presence
I don't have emotions and sometimes that makes me very sad.
Funny I ran into an Ames resident!
Couple of other suggestions: Try adding confidence intervals to your graphs, and see if you can find some examples of similar graphs in other elections. Does this kind of pattern happen often?
I was looking for help in the adding confidence intervals category. I'm not sure how to calculate them from a graphical situation; especially when the data is presented as percentages. I am particualarly interested in what a 99% confidence extrapolation from the data we have, at the point when 30% of votes are counted.
As far as finding similar results... I don't have any to point you to at the moment... but I have seen such in print, and as one would expect they always look like the ones from Sioux County... the results level out where the slope of the curve for each candidate m -> 0, as x -> 100%.
As for the second half of your question... just think about it... If you have a 30% sample of a large population... you're pretty sure of the ratio of things. The situation in question would be the equivilent of intending to roll a dice 10,000 times and of knowing that after you roll a standard dice 3,000 times you have:
16.5% 1's
16.2% 2's
16.8% 3's
16.5% 4's
16.1% 5's
16.9% 6's
After 3000 rolls you can be pretty sure that everything is headed towards 16.667%. The laws of the universe are playing out. Even if the first 5 rolls in your set were 2's and the next three were 4's... as the sample size gets larger... the ratios become more refined: Confidence in predicted results grows.... your dice is a normal dice; its balanced and everything is headed towards 16.667%.
But in our example, as you make rolls # 3001 - 10,000 the odds suddenly begin to shift, so that by the time the 10,000th roll occurs the new odds on your dice are:
24.5% 1's
15.1% 2's
15.0% 3's
15.2% 4's
15.1% 5's
15.1% 6's
Changing the ratio of ones from 16.5 to 24.5 is a 47% increase... just like Romney attained as he went from 17% of the vote to 25%.
That kind of math only occurs
when weighted dice are introduced.
Or algorithm adjusted; tampered black box voting equipment is used
presence
Last edited by presence; 02-22-2012 at 09:08 AM.
http://en.wikipedia.org/wiki/Margin_of_error
"When comparing percentages, it can accordingly be useful to consider the probability that one percentage is higher than another.[10] In simple situations, this probability can be derived with 1) the standard error calculation introduced earlier, 2) the formula for the variance of the difference of two random variables, and 3) an assumption that if anyone does not choose Kerry they will choose Bush, and vice versa; they are perfectly negatively correlated. This may not be a tenable assumption when there are more than two possible poll responses. For more complex survey designs, different formulas for calculating the standard error of difference must be used."
"In the Newsweek poll, Kerry's level of support p = 0.47 and n = 1,013. The standard error (.016 or 1.6%) helps to give a sense of the accuracy of Kerry's estimated percentage (47%). A Bayesian interpretation of the standard error is that although we do not know the "true" percentage, it is highly likely to be located within two standard errors of the estimated percentage (47%). "
My expectation is that at the "30% of votes are in" point... given that at that point our sample size is large (any sampling fraction over 5% is by definition large): 36676, we would have a relatively low standard error... say less than 1%. For Romney to then go from having 17% of the vote to 25% of the vote... that would be more than 8x the standard error; ie IMPOSSIBLE.
Last edited by presence; 02-22-2012 at 09:39 AM.
When I go here:
http://www.nss.gov.au/nss/home.nsf/p...r?OpenDocument
And I input confidence level 99%, population 122225, sample 36676, I get the following results:
Confidence interval: 0.00563
Upper 0.50563
Lower 0.49437
Standard Error 0.00218
Relative Standard Error 0.44
But somehow I don't think these results apply. For one... there was no input for mean and I'm not sure this math works for Y values expressed as percentages.
Help?
I was kinda hoping this board would be able to provide me with more concrete statistical assumptions than armchair phrases like "we might expect something like this to happen". That statement is the armchair skeptic stuff you get in a 911 truther forum. I think; I know we can do better.
Given that we expect there are standard/normal tallying procedures and that a (statistically "large") 30% sample is fairly representative of the whole (ie. "the proportion of the population to have the attribute we are expecting" is 50% or better"): What are the odds that a weird tallying procedure (or any other plausible interference) would produce results like these?
How often might we expect this? <--- THATS MY POINT... that's what I'm looking for you to help me with. There are known maths to establish confidence in a statement such as yours.
What equations do I use?? are there graphical techniques using polygons, etc. to make projections in situations such as these.
I don't mean to be rude, and I appreciate your input/opinion... but I didn't join this forum for opinions on what might have been. You seem to be avoiding the meat and potatoes I would expect from a number crunching statistician. I have a graphical data set and I want to crunch some numbers regarding statistical confidence in the projection of that set at the 30% sample size. Can you guide me or can you point me towards someone on this board who can?
presence
Last edited by presence; 02-22-2012 at 10:11 AM.
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