Basis for Margin of Error in Opinion Polls?

In summary, the margin of error given in polls is based on the assumption of a binomial distribution and is proportional to the square root of the sample size. This can be extended to multinomial distributions with multiple choices. The margin of error is actually a confidence interval and is calculated using the standard error, which is the standard deviation divided by the square root of the sample size. This assumes that the data follows a normal distribution, which should be checked using chi-square.
  • #1
Bacle
662
1
Hi,

Just curious as to what is the basis of the margin of error given in polls, e.g.,
in statements of the form:" 30% of people are in favor of candidate x. The poll
has a margin of error of +/- 5 %"

Thanks.
 
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  • #2
The error margin is obtained from an assumption of a binomial distribution. The net result is the estimated error is proportional to the square root of the sample size. For example if 10000 people are asked, the error estimate is around 100, which if the answers are split 5000 yes and 5000 no, the error estimate would be about 2%.
 
  • #3
Thanks, M:

Would the result extend to a multinomial if those polled were asked to choose between
more than two alternatives?

Thanks.
 
  • #4
Bacle said:
Thanks, M:

Would the result extend to a multinomial if those polled were asked to choose between
more than two alternatives?

Thanks.
Essentially yes. The proportion to the square root of the sample size remains,
 
  • #5
To get back to basics. Binomial distribution with sample size n and probability of success p, the mean number of successes is np and the variance (square of the standard deviation) is np(1-p). When doing a statistical analysis, p is unknown, so it is usually estimated as the number of successes divided by the sample size.

When used to analyze poling data, the simplest way is to use the binomial for each choice. For example if there are 3 choices with probabilities x, y, z, then the variances can be estimated as nx(1-x), ny(1-y), and nz(1-z).
 
  • #6
Thanks Again.

When you talk about error, is it related to the variance/standard deviation?
Please ignore my ignorance--and the question-- if this is too basic/obvious.
 
  • #7
Never mind the last question and thanks; sorry for being so slow.
 
  • #8
The margin of error given is actually a confidence interval, I think. The assumption for a confidence interval is that the data follows a normal (not binomial) distribution, which is an assumption that should be checked using chi-square first.

The standard error (we'll call it SE) equals the standard deviation (the square root of the variance, which (in this case) = sample size * frequency of x) divided by the square root of the sample size.

The confidence interval is z * the standard error, where z is the Z-score that corresponds to the confidence level of your choice. For example, if your confidence level is 95%, then z = 1.96.
 
  • #9
moonman239 said:
The margin of error given is actually a confidence interval, I think.
Is it really? I think it is the spread corresponding to a specific confidence level. So, if the distribution is roughly Gaussian, then for a 95% confidence, the MoE is about 2 standard deviations.
 
  • #10
moonman239 said:
The margin of error given is actually a confidence interval, I think. The assumption for a confidence interval is that the data follows a normal (not binomial) distribution, which is an assumption that should be checked using chi-square first.

The standard error (we'll call it SE) equals the standard deviation (the square root of the variance, which (in this case) = sample size * frequency of x) divided by the square root of the sample size.

The confidence interval is z * the standard error, where z is the Z-score that corresponds to the confidence level of your choice. For example, if your confidence level is 95%, then z = 1.96.

Gaussian is assumed because for large sample size, binomial is much harder to handle. In practice the average and the estimated deviation are used. The binomial gives the value for the parameters while the Gaussian is used to estimate distribution values.
 

What is the basis for margin of error in opinion polls?

The basis for margin of error in opinion polls is statistical sampling. This means that only a portion of the population is surveyed, and the results are used to estimate the opinions of the entire population.

How is margin of error calculated?

Margin of error is calculated using a formula that takes into account the sample size, the confidence level, and the standard deviation of the results. A larger sample size and a higher confidence level will result in a smaller margin of error.

Why is margin of error important in opinion polls?

Margin of error is important because it helps determine the accuracy and reliability of the poll results. A larger margin of error means that the results are less precise and may not accurately reflect the opinions of the entire population.

How does margin of error affect the interpretation of opinion poll results?

The margin of error should be taken into consideration when interpreting opinion poll results. Results within the margin of error should be seen as similar and not significantly different. Results outside the margin of error may indicate a true difference in opinions.

What are some factors that can influence the margin of error in opinion polls?

The margin of error can be influenced by factors such as the sample size, the sampling method, the wording of the questions, and the response rate. It is important for pollsters to take these factors into account to minimize the margin of error in their polls.

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