Posted on 09/25/2012 12:58:11 PM PDT by nhwingut
I think they're counting on bandwagon effects helping 0 so they don't have to run with their tails between their legs when solid methodology carries the day. And they may be able to use the debates for cover if that doesn't happen.
I removed um from my phones phone book too.. I avoid um around the holidays too.
If they could keep their mouth shut I’d do the holidays with them. Since they can’t well. I’m not gonna show up.
There is statistically NO DIFFERENCE between 0bama's percentages and Romney's percentages in this poll.
The sampling error at 95% confidence says that we can say with 95% confidence that the true vote for Romney lies between 40 and 48.6, and between 40.9 and 49.5 for 0bama. That is not the same as your analysis, because these are NOT the true mean values of this statistic, they are sample means.
For example: If the true mean really is Romney 48.6, 0bama 40.9, not only would we rarely see a sampling that gave us 0bama 49.5 - Romney 40, we can make a much stronger statement: with 95% confidence, we can say that we would NEVER see 0bama with 49.5 if his real statistic is 40.9. In that case, you could sample (random) populations a million times and find that with 95% confidence, 0bama doesn't get 49.5.
Sampling over and over again will NOT yield the same distribution centered at 44.3-45.2 -- which is what your example implies -- UNLESS AND ONLY UNLESS -- the TRUE poll result really is 44.3-45.2.
The rest of your statement is correct, and it is the heart of the much more serious problem. The sampling error assumes the errors from the sample mean are RANDOM and we know they are not, because this is not a sample of absolutely truthful people telling us how they have already voted, picked completely at random. This is an imperfect sample which is a) not random, because it includes no refusals b) not composed of 100% truthful respondents, and c) does not consist of people whose votes are already cast.
The real guesswork comes in with trying to get a pure random sample of people who absolutely WILL vote.
Actually not Fred. The poll is statistically significant in that statistically speaking the race is a draw. There is no interpretation involved.
There is statistically NO DIFFERENCE between 0bama's percentages and Romney's percentages in this poll.
Right, which makes the poll statistically significant if one is happy with the methodology.
The sampling error at 95% confidence says that we can say with 95% confidence that the true vote for Romney lies between 40 and 48.6, and between 40.9 and 49.5 for 0bama.
Right, which is exactly what I said. CI means that 95 out of 100 random samples will fall between the error bars. That's it, it's statistics not rocket science.
That is not the same as your analysis, because these are NOT the true mean values of this statistic, they are sample means.
There are no mean values, sample means or otherwise. There is a sample with data. Sample means require values to find the mean. A poll is a single solitary sample with the associated data. There are no means, there are error bars at confidence intervals, in this case 95% because of the sample size.
For example: If the true mean really is Romney 48.6, 0bama 40.9, not only would we rarely see a sampling that gave us 0bama 49.5 - Romney 40, we can make a much stronger statement: with 95% confidence, we can say that we would NEVER see 0bama with 49.5 if his real statistic is 40.9. In that case, you could sample (random) populations a million times and find that with 95% confidence, 0bama doesn't get 49.5.
Outliers have a normal distribution above and below the error bars.
Sampling over and over again will NOT yield the same distribution centered at 44.3-45.2 -- which is what your example implies -- UNLESS AND ONLY UNLESS -- the TRUE poll result really is 44.3-45.2.
My "example" implies no such thing nor did I state it. Your inference is out of left field.
A mean is defined as the average of a numerical set. It is found by dividing the sum of a set of numbers by the number of members in the group A sample mean is defined as a mean of a numerical set that includes an average of only a portion of the numbers within a group.
A sample for a poll contains no sets, nothing is averaged and there are no sample means.
But thanks for the condescension.
What is Gravis’ reputation?
He seems to be one of the more GOP-leaning pollsters.
Also, per 538, they don’t do cellphones, just like Ras, which he argues biases results against Dems.
What are the thoughts of Freepers on that? So many use cells only now that I would hope would not be clinging to hope based upon polls that don’t take into account cell phones.
That said, the latest polling is encouraging, as is the absentee info.
Really? D+10 and Obama ahead by less than 1%?
THIS poll I believe, oversampling Democrats by 10 points and seeing a virtual tie in Ohio I would believe.
Any poll showing Obama with a 5 or 8 point lead in the Buckey state is nonsense.
Obama is probably running 3-5 points up in PA, and that’s with Philly hugely skewing the state D... Ohio does not remotely have a city the size of Philly skewing its vote, Romney I assume is up at least 3-5, probably well beyond that.
I guess I shouldn't expect much from victims of the American public school system.
And speaking of condescension... and this coming from a person who apparently doesn't realize that some of the most advanced tools in mathematical Analysis are used in statistics, and who apparently is confused about where statistics even enters this discussion at all.
But for the benefit of FReepers who can be educated:
In polling, we are not aware of the value of a desired number, say the number of people voting for Mitt Romney. It isn't practical to ask every person doing so, so consequently we call a random sample of people. The tools of statistics that can be brought to bear on this question is 1) How many people do we need to ask for our sample to be representative and 2) is there a practical bound on the error?
This question is answered by the Central Limit Theorem. Roughly this says: the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will, in the limit of large numbers be normally distributed.
So, each time a poll is conducted, we come up with a percentage of Romney voters. Each measurement will be slightly different. However, if we take the average -- or mean -- of these measurements, that average percentage is subject to our theorem, provided we meet its conditions, one of which, is that the variable (number of Romney voters, etc.) is truly random.
And, what the Central Limit Theorem tells us is that ALL of those measurements, with unknown mean, will converge to the true result if we take enough of them. And that result WHICH IS THE MEAN OF ALL OF THE SAMPLES is the mean of a normal or Gaussian distribution. And furthermore, those measurements will also have the SAME STANDARD DEVIATION AS NORMAL DISTRIBUTION.[aside: "variance" is referred to in the theorem. This is mathematically interchangeable with the standard deviation, because the standard deviation is just the positive square root of the variance.]
The variance of a normal distribution is well known, and from it we can calculate a practical bound on a range in which the TRUE MEAN of all these measurements must lie. About 2/3 of all the measurements we take will lie within one standard deviation from the true mean. About 95% will lie within 2 standard deviations, and about 99.7% will lie within three standard deviations. Since we can say that 95% of a random sample lies within two standard deviations of the mean of our samples, this is called a 95% confidence interval, and it can be easily calculated because the variance of a Gaussian Distribution is well known.
So you see folks, there IS a mean involved in this discussion, and there is a standard deviation in this discussion, and now you know it, although FReeper jwalsh07 is unaware of it. And simply understanding this fact, allows you to understand how "margins of error" are calculated.
The WIKIPEDIA entry on "Margin of Error" is actually not too bad (WIKI is generally pretty good on matters mathematical and statistical.) Have a look. In just a few minutes, you will know a great deal more about statistics than the poseur posting so condescendingly here.
Ok Fred, you’re right and I’m wrong on the mean thing.
AN EXAMPLE FROM POLITICS
•Exit poll results can be compared with a normal distribution to make predictions about the results of an election based on a relatively small sample of voters.
In an exit polling situation, voters are asked if they voted for a particular candidate or not. If you ask 100 voters and you find that 75 voted for Candidate A and 25 voted for Candidate B, how representative of the overall tally is this? The mean of this sample is 75% for Candidate A. This is calculated by assigning a score of 1 to a vote for Candidate A and a score of 0 to a vote for Candidate B, multiplying the votes by the scores, adding these results, and dividing by the total number of votes.
Mean =
Intuition tells us that it would be unwise to assume that the final tally of all the votes will exhibit exactly the same ratio as this one sampling. That would be akin to flipping a coin 100 times, getting 75 heads, and assuming that this is what would happen more or less every time. In other words, we can’t assume that the mean value of this one sample of 100 voters is the same as the true mean value of the election at large. Even so, we can say something about how the mean we found in the exit poll relates to the true mean.
We can use the Central Limit Theorem to realize that the distribution of all possible 100-voter samples will be approximately normal, and, therefore, the 68-95-97.5 rule applies. Recall that this rule says that 68% of sample means will fall within one standard deviation of the true mean (the actual vote breakdown of the whole election). However, this rule is useful only if we know the standard deviation and the true mean, and if we knew the true mean, why would we need to conduct an exit poll in the first place?
To find an approximation of the standard deviation, we must first find the variance. Recall from the previous section that the variance is related to the difference between how each person voted and the mean. Because the possible votes are only A or B, and A is assigned a score of 1 whereas B gets a score of 0, then the possible differences are “1 minus the mean,” which corresponds to the people who voted for A, and just the mean, which corresponds to the people who voted for B. The total number of voters multiplied by the mean is the total number of voters who voted for A. The total number of voters multiplied by “one minus the mean” is the total number of voters who voted for B. To find the variance, we square the differences, multiply by the vote proportions, add, and divide by the total number of votes. If the total number of votes is V, then the variance is:
Var =
The Vs cancel out and with a bit of algebra, we find:
Var = mean (1 – mean)
The standard deviation is thus .
The mean in which we are interested here is the true mean, but as yet we have only a sample mean. Luckily, sample means and true means usually give standard deviations that are pretty close to one another, so we can use the standard deviation given by the sample mean to help us find approximately where the true mean lies.
We have now seen how probability theory can be used to make powerful predictions about certain situations. Up until this point, however, we have been chiefly concerned with simple, idealistic examples such as coin tosses, the rolling of dice, and quincunx machines. Let’s now turn our attention to probabilities that are more in line with what happens in the real world.
My posts come across as unnecessarily argumentative, strident, and even nasty.
I allowed my frustration with the manipulation of these polls -- and all kinds of nonsense being propounded by dumbass journalists, who don't have the slightest idea how to do basic arithmetic, let alone mathematics or statistics, to spill over into our discussion.
Can't wait until November.
No need to apologize. You were right, I was wrong. You gave as good as you got. I don’t have a confidence problem Fred :-}, I’m 61 years old and I know my scores on Army IQ testing and GRE’s after my BS in Electronic Engineering. I’m getting old but I can still tutor Calculus.
Now statistics, that’s another question. LOL
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.