Margin Ratios in Polling - Question (No Politics)

James_S

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Can someone please explain the +/- margin in elections, I don’t want this to turn into anything political just curious, and I am no math genius nor do I claim to be.
Example A: If a 1000 people are polled and lets say Candidate A gets 50% and Candidate B gets 44% and there is a +/- ratio of 4.5%. How can that be a dead heat?
Example B: If a 1000 people are polled and candidate receives 500 votes or 50% of the vote and Candidate gets 440 votes or 44% and the there is 60 people (6%) undecided how can there be a margin of error, lets say of 3.5%?
Is it human input or ?????.
Thanks for the help!
James
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Steve Tannehill

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Example A:
If the margin of error is 4.5 percent, then they are saying that Candidate A's actual percentage could range from 45.5 to 54.5 percent of the vote.
Candidate B could range from 39.5 to 49.5 percent of the vote.
Candidate A and B's ranges overlap. Therefore, there are points in that range where both candidates could have an equal percentage of the vote.
For example, both candidates could have 48 percent of the vote, leaving 4 percent undecided.
That's a statistical dead heat.
- Steve
 

Denward

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[propellor beany]
In statistical terminology, a public opinion poll is a sampling. You're trying to determine the percentage of the entire population that has opinion Z. If you could get a response from everyone, your results would be perfect. (This ignores the fact that people might change their mind or lie to you.) But since you can't ask everyone, you ask N people what they think. If you ask 10 people and get an 8-2 split, how confident are you that 80% of the country feels this way? If you ask 1,000,000 people and still get an 80/20 split, now you're feeling much more confident about things. When you see this on the news, they will say the poll says 80% with a margin for error of, say, +/- 4%. What they're really saying is, "We can't afford to ask the whole country what they think. Instead, we asked 1000 people and 80% said yes. There is an X% chance that the real answer for the whole country is somewhere between 76-84%." What is X%? They never tell you. According to common statistical practice, it's probably somewhere between 80%-95%. As someone already mentioned and as we intuitively would guess, the margin gets smaller as you ask more people. The margin also gets smaller as X% gets smaller.
[/propellor beany]
You learn this stuff when you start taking stats in college.
To relate this just slightly to actual recent events, even elections are samplings (since only some people vote) which are subject to margin for error. So even though Gore got more of the popular vote than Bush nationwide and Bush got more of the votes in Florida, neither one of them probably has a valid mathematical argument that the country or Florida liked him better.
[Edited last by Denward on November 07, 2001 at 02:42 PM]
 

CharlesD

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As the other replies indicate a poll is an exercise in probability. IF a poll says 45% of people prefer chocolate ice cream to vanilla and has a margin of +/- 5%, it is really saying that there is a 90% chance that somewhere between 40 and 50 % of people prefer chocolate ice cream to vanilla. The 90% "confidence" figure in this example is based, IIRC, on the size of the sample (generally the confidence if 90 or 95%).
The calculation of these figures is based on solid mathematics, people who don't like the outcome of a particular poll (esp. political ones) basically don't understand the mathematics.
If you pay attention the election results next year, you will see that the results of at least 95% of the various House and Senate races will fall within the predicted margin of error.
They key to an accurate poll is having an appropriately sized sample, and that sample must be truly random. Getting a truly random sample is the hardest part, and good polling organizations go to extreme lengths to achieve this.
Another factor in polling is the wording of any questions. Sometimes polls are conducted with the purpose of supporting a particular cause/view and the questions are worded in such a way to yield a desired result. Microsoft once allegedly conducted a poll that showed a large majority of programmers supported their "right to innovate", but to get their desired result they had to concoct a several paragraph "question". Other, more straight-forward wordings, yielded results no-where near what Microsoft wanted.
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James_S

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Got It, I figured somebody would know.
You guys are the Best!!!
Thanks
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Do you spend time with your family.....
Cause a man that doesn't spend time with his family can never be a real man.
- Marlon Brando, The Godfather 1972
 

Denward

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If you pay attention the election results next year, you will see that the results of at least 95% of the various House and Senate races will fall within the predicted margin of error.
Hmmm, I don't have any facts but I would disagree with this statement. I'll have to do a little figuring but I would think that if there were a total of 500,000 votes cast, the margin would be very small, even up to the 99% confidence level. Out of 500 congressional elections every other year, I would guess maybe 50 would fall within the 99% confidence interval. I'll try to be back in a few hours with an answer.
 

CharlesD

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Denward,
I meant that at least 95% of the actual results would fall within the range predicted by the polls. I would imagine that the polls are conducted have a 95% confidence factor, and from observing the results of (House and Senate) elections over the past few cycles, I would say that at least 95% of the predictions from the polls turn out to be correct.
This of course includes situations where the Poll predicts candidate A wins, but has a lead of less than the margin of error, but Candidate B wins and the percentage of actual votes cast for each candidadte falls with in the predicted range.
I have never formally counted the numbers of success vs failures, this is just my observation. Certain groups tend to distrust polling, especially when the results don't agree with their particular world view, so I have paid particular attention to just how accurate these polls turn out to be so that i can be confident that they are wrong.
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Denward

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Ooops. My bad, Charles. I misunderstood your post. FYI, I found a site with 2000 election results and of the 435 House races, 60 were won with
 

Dave Morton

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Actually, these things follow a binomial distribution where the standard deviation is square root of (np(1-p)) where p=probability or percentage of the candidate of interest. Then we take that value and divide by the square root of n, the sample size. This will give the standard error of the distribution. Thus as someone says, the sample size does make a difference. The larger the sample the smaller the standard error. It is really a measure of the dispersion of the data.
OK, I'm a statistician and I can really geek out with this stuff.
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Hugh Jackes

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Also the people that you poll produce variances in the degree of confidence. If you take a nationwide poll and ask only those who live in traditionally liberal or traditionally conservative states/counties/towns, your poll results are not going to be accurate re: the nation as a whole.
Likewise, if you poll only during certain hours of the day. If you phone people's homes during working hours, your "electorate" will be heavily burdened with retirees (likely AARP voters), housewives (perhaps concerned more about children's issues?), and the unemployed (probably concerned more about unemployment insurance and job training than, oh say, gun control or foreign aid). If you are polling about political or social issues, you'll get a different response from these people than from folks who are in a workplace drawing a paycheck every day and contented with their lives.
Another consideration in the accuracy of your poll, assuming it's a political question, is the electoral status of the people that you call. Only about half of registered voters in the USA vote. Registered voters may make different choices than likely-to-voters, in part because they probably do not educate themselves about the issues as thoroughly as people who absolutely intend to vote.
[Edited last by Hugh Jackes on November 08, 2001 at 06:10 PM]
 

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