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Margin of error
Message posted by Jim on October 4, 2000 at 12:00 AM (ET)
Here is another of those "margin of error" questions.
I need a formula. I sent out Q questionairres and n were returned. Of the n there were y yeses and (n - y) noes. What is the margin of error for a 95% confidence rating?
READERS RESPOND:
(In chronological order. Most recent at the bottom.)
Re: Margin of error
Message posted by JG on October 4, 2000 at 12:00 AM (ET)
You need a confidence interval for P given p and n. You assume the margin of error such as +/- 2% and confidence level such as 95% and you then calculate the confidence interval for P such as 45% to 58%, etc. See some of the references and links at (129.2.115.68/stats) for more details.
Re: Margin of error
Message posted by SOF on October 5, 2000 at 12:00 AM (ET)
When p=35/200, then the 90% confidence interval for P is .175+/-(1.645)(.0269) where .0269=sq.rt.((.175)(.825)/200))
Re: Margin of error
Message posted by Jim on October 5, 2000 at 12:00 AM (ET)
I'm afraid none of this helps me very much. Where would I find the link referenced above (129.2.115.68/stats).Thanks
Re: Margin of error
Message posted by nancy diehl on October 5, 2000 at 12:00 AM (ET)
The components to calculate the margin of error are comprised of two pieces; one is a table value,
in your case, a Z value that corresponds to 95% confidence. That value is 1.96. The second piece you
need is the estimate of variability from your data. Given your example, you have a binomial situation.
Hence, your estimate for variability will come from calculating your p-hat (let's just call it p for less
typing). p is your #yes/#questionnaires returned. Your margin of error formulat is:
1.96*[SQRT(p(1-p)/n)]So if you receive 300 questionnaires and 120 vote yes, then your margin of error is:
1.96*[SQRT((.4*.6)/300)] = .05544 or 5.5%
Hence your estimate of people answering yes is 40% with a margin or error in your estimate of 5.5%
Re: Margin of error
Message posted by SOF on October 5, 2000 at 12:00 AM (ET)
129.2.115.68/stats is the URL
of a web site dedicated to introductory statistics.
Re: Margin of error
Message posted by Jim on October 9, 2000 at 12:00 AM (ET)
Thanks for all the good information. Sorry to be such a nag but I'm still puzzled. The formula: 1.96*[SQRT(p(1-p)/n)]
doesn't include the sample size. In my case the sample size is small--about 300. I expect to receive 30 to 40 returns. How does the sample size affect the margin of error?Thanks again.
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