# Statistics question: polling margin of error **URL:** \ **Category:** Factual Questions\ **Created:** [June 9, 2008, 2:03pm UTC](https://boards.straightdope.com/t/statistics-question-polling-margin-of-error/452318 "2008-06-09T14:03:02Z")\ **Posts on this page:** 7\ **Page:** 2
**Author:** ![AHunter3](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ahunter3/32/368_2.png) [@AHunter3](https://boards.straightdope.com/u/AHunter3)\ **Post date:** [June 9, 2008, 5:56pm UTC](https://boards.straightdope.com/t/statistics-question-polling-margin-of-error/452318/21 "2008-06-09T17:56:07Z")
Exactly. Like driving on the right instead of the left, it doesn’t really matter which choice is the answer to “this is what we went with” (as the UK dopers will quickly testify if asked); it _does_ kind of matter that “yes we have a convention that we have decided to use and you should use it too, please” See prior comment on comparing one study to another. EDIT: it always pagewraps when I didn’t quote! this is about going with 95% confidence and whether doing so is arbitrary. **Ultrafilter** said “this”. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 9, 2008, 6:16pm UTC](https://boards.straightdope.com/t/statistics-question-polling-margin-of-error/452318/22 "2008-06-09T18:16:54Z")
If you know what you’re doing, you can construct statistics for any confidence interval you’d like. I might say, for instance, that Smith has 49 ± 1 at a confidence level of 90%; he has 49 ± 3 at a confidence level of 95%; and he has a 49 ± 5 at a confidence level of 99%. This would mean that his true level of support has a 90% chance of being between 48 and 50, a 95% chance of being between 46 and 52, and a 99% chance of being between 44 and 54. I could pick any of those numbers to publicize, or all of them, and which one I choose is just a matter of convention. I could even, if I wanted, calculate the margin of error for a 73.2% confidence interval, or something silly like that, and have perfectly valid statistics, but nobody else uses 73.2% confidence intervals, so it would probably just confuse folks. On the question of why standard deviation is used instead of some other measure of width of a distribution, there are a good number of folks who do prefer other measures. For one thing, not all distributions have a standard deviation. Heck, there are even some perfectly valid (though contrived) distributions which don’t even have a mean. However, all distributions will always have a median, and all distributions will always have a 50 percentile width, so some folks prefer to use those as their measures of the typical value and width of a distribution. ---
**Author:** ![Rysto](https://avatars.discourse-cdn.com/v4/letter/r/ecccb3/32.png) [@Rysto](https://boards.straightdope.com/u/Rysto)\ **Post date:** [June 9, 2008, 6:29pm UTC](https://boards.straightdope.com/t/statistics-question-polling-margin-of-error/452318/23 "2008-06-09T18:29:12Z")
[QUOTE=Whack-a-Mole] Or is it more that, “We know the 95% number is mathematically sound…why we picked 95% to be good enough instead of a study that provides 90% or 98% we have no idea…just seemed a good number to us.” [/QUOTE] I was under the impression that it’s related to the fact that in a normal distribution, 95% of all data lie within two standard deviations of the mean. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [June 9, 2008, 6:48pm UTC](https://boards.straightdope.com/t/statistics-question-polling-margin-of-error/452318/24 "2008-06-09T18:48:43Z")
[QUOTE=Rysto] I was under the impression that it’s related to the fact that in a normal distribution, 95% of all data lie within two standard deviations of the mean. [/QUOTE] But wouldn’t this still be arbitrary? Why _two_ standard deviations? ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [June 9, 2008, 7:46pm UTC](https://boards.straightdope.com/t/statistics-question-polling-margin-of-error/452318/25 "2008-06-09T19:46:45Z")
The number of standard deviations (or sigma) required is determined by the type of testing being done and level of confidence needed to convince others. Two sigma is realistic for population sampling. It’s inadequate for testing physics. > **[Inflation deflated? The big bang's toughest test](https://www.newscientist.com/article/mg19826591-500-inflation-deflated-the-big-bangs-toughest-test/)** > > SOMETIMES cosmology talks can be exciting – riveting even. Take, for instance, the occasion when a young graduate student called Alan Guth heard all about the serious problems with the big bang theory. It was so provocative and stimulating it led... > [@](#): > > There is a get-out, though. Wandelt’s analysis is not yet statistically significant enough for him to be able to claim that he has detected non-gaussianity. His error bars are too big: in physics parlance he has a 2.8 sigma result, or better than 99 cent chance that the result is trustworthy and replicable. He’d need something like 5 sigma, or 99.99995 per cent, before anyone is sure the non-gaussianity cannot be dismissed. ---
**Author:** ![Punoqllads](https://avatars.discourse-cdn.com/v4/letter/p/d2c977/32.png) [@Punoqllads](https://boards.straightdope.com/u/Punoqllads)\ **Post date:** [June 9, 2008, 8:56pm UTC](https://boards.straightdope.com/t/statistics-question-polling-margin-of-error/452318/26 "2008-06-09T20:56:09Z")
[QUOTE=Thudlow Boink] But wouldn’t this still be arbitrary? Why _two_ standard deviations? [/QUOTE] Basically, the error bounds goes down as the inverse of the square root of the number of sample points. So if 1000 people gets you about 95% accuracy, then to get a 99% accuracy you’d need to sample 25,000 people, and then 100,000 people to get 99.5% accuracy. Historically, folks thought that 95% wasn’t unreasonable for their needs, and that sampling 1000 people wasn’t too onerous a burden. ---
**Author:** ![cerberus](https://avatars.discourse-cdn.com/v4/letter/c/71e660/32.png) [@cerberus](https://boards.straightdope.com/u/cerberus)\ **Post date:** [June 10, 2008, 6:16am UTC](https://boards.straightdope.com/t/statistics-question-polling-margin-of-error/452318/27 "2008-06-10T06:16:30Z")
[I use these to teach basic CI methodology for proportions.](http://www.mindspring.com/%7Ecjalverson/Computing%20Confidence%20Interval%20Proportion.ppt) The margin of error is basically the half-width of the confidence interval estimate, which is on the order of _ZFsqrt(p(1-p)/n)_\* where Z is some sort of multiplier for approximate confidence level, usually the 97.5% point of the Gaussian distribution, or an appropriate t-distribution. F is a factor that accounts for variation in sampling design. Thing is, calculus shows that the sqrt(p_91-p)/n) bit is maximized at p=.50, so one can conservatively plan by using p=.50 for planning purposes. So a gross formula for MoE is something like 2_SQRT(1/4n). The thing to not do is to apply the 95% to the single interval. The 95% confidence applies to the process. [Previous page](https://boards.straightdope.com/t/statistics-question-polling-margin-of-error/452318.md?page=1)