Talk:Margin of error

message: There are some concerns about this article's depiction of the margin of error as a statistic used specifically for polling.  There is a discussion below about whether the margin of error is synonymous with the confidence interval and whether, as such, it should be more broadly defined.  Fadethree 8:36, 19 Oct 2004 (UTC)
thread_title: Concerns

message: Near the end of the section on comparing percentages we see this:
::=normdist((A_1-B_1),0,A_2,1)
This seems to be a dangling phrase, not part of any sentence; it needs to be clarified.  I'm guessing it mean the cumulative distribution function of a specified normal distribution; it so, there are clearer ways of saying that. Michael Hardy 00:22, 4 Oct 2004 (UTC)
thread_title: TeX (moved to Wikibooks)

message: If I'm not going completely mad, isn't use of the word poll a little inaccurate? Shouldn't it be a sample or sample survey? Or at least it is according to my textbook! Please advise... I'd hate to incorrectly edit a front page article
Also, I would have said, for example, 5% significance level rather than 95% confidence level. Does this equate to the same thing, or is a difference in terminology across the Big Pond. If so, should both definitions be included?
:How is poll inaccurate?  We've been having a discussion below about assumptions that the margin of error is synonymous with the confidence interval.  Is this your assumption?  If so, note that this article defines the margin of error as a quite specific confidence interval; they are not equivalent.  As to your second point, I am fairly certain that 95% confidence level is synonymous with 5% significance level.  I would think that confidence is not as apt to be misconstrued as "significance."  This talk section has been largely concerned with semantics, and while semantics are nontrivial, I would argue that the dominant audience of this article is people who are trying to understand the margin of error without a statistics background.  I would like to err on the side of parsimony.  Your thoughts?  Fadethree 21:27, 19 Oct 2004 (UTC)
replies: text: Wow! I will admit that I'm being a little pedantic here, and certainly didn't mean to rub someone up the wrong way, but found during my lessons in stats terminology was very important. Point taken on both counts - the pedant in me is perhaps more needed on the statistics page! Cheers --Mark Lewis 14:34, 20 Oct 2004 (UTC)
thread_title: "poll"

message: 1) The last section of the article provides a formula for the standard error of the difference between two perfectly negatively correlated survey options, one chosen by p percent of the respondents, and one chosen by q percent of the respondents. The article notes that the assumption of perfect negative correlation "may not be a tenable assumption when there are more than two possible poll responses." The article then describes how the formula would be applied to the results of a 2004 Newsweek poll that reported voter support for John Kerry and George W. Bush. 
The choice between Kerry and Bush probably wasn't perfectly negatively correlated, but the formula is applied to the Kerry-Bush example anyway. Is the formula, then, a reasonable approximation of the probability that one option is truly preferred if the two options are almost perfectly negatively correlated? (My question is sincere. I have a math background, but limited experience with statistics.)
2) Referring again to the formula for the standard error of the difference: The response to the questions immediately below on this "Talk" page states that "perfect negative correlation does not necessitate q=1-p," and that "q+p=1 ... is rarely true in most polls." Further below, however, under the discussion headed "Comparing percentages: the probability of leading," there appears to be agreement that the formula itself is based on the assumption that p+q=1. 
    a) If the assumption p+q=1 was used in deriving the formula, should that assumption be added to the text of the article? 
    b) Does there need to be an edit or correction to the statement "perfect negative correlation does not necessitate q=1-p"? (I realize that the statement could easily be true even if p+q=1 was assumed. I just want to ensure a correction wasn't overlooked, given that there seems to have been at least momentary confusion about the use of the assumption p+q=1 in deriving the formula.) 
    c) If the assumption p+q=1 was used to derive the formula, can't the formula for the standard error of the difference then be simplified, as the questioner below suggests, to twice the (approximate) standard error for a survey percentage p? And if the answer is yes, might it make sense to go ahead and show the simplified formula in the article? 
3) The article states that "the difference between two percentage estimates may not be statistically significant even when they differ by more than the reported margin of error." This may well be true, but I suspect many people are assuming that the difference is statistically meaningful when the two percentages differ not by more than the reported margin of error, but by more than twice the reported margin of error. The thinking would run this way: Candidate A is favored by 51%; Candidate B is favored by 46%; and I can be 95% confident that Candidate A is truly ahead since the margin of error is ±2 percentage points, meaning that Candidate A has at least 49%, while Candidate B has at most 48%.
    a) Would the statement still hold for twice the margin of error — that is, would the statement still be true if it said that "the difference between two percentage estimates may not be statistically significant even when they differ by more than twice the reported margin of error"? If so, an edit might be worthwhile, since it would probably address the more common assumption about the margin of error.
    b) Does "statistically significant" in the sentence above refer to the significance measured using a t-test for a single population? If so, might there value in mentioning this parenthetically or in a footnote in the article for people trying to connect the various statistical measures of confidence? I do recognize the article is meant primarily for the average reader trying to make sense of a phrase commonly used in public opinion surveys, but I imagine there are some who, like me, are trying to gain greater clarity on just how statisticians themselves view the survey findings and the context they would judge those findings against. That curiosity is not entirely unnatural, given that the sentence itself includes a hyperlink to the Wikipedia entry on statistical significance. 
    c) Can the statement above also be taken to mean that if the two percentages differ by less than the margin of error — or alternatively, by less than twice the margin of error — the difference is definitely not statistically significant?
    d) If the answer to my question 2c above is yes, could the statement I'm referring to in question 3 be made more specific, given the mathematical relationship between the (approximate) standard error of the point estimate p and the margin of error for the survey?
This has proved to be a useful article, by the way. Thanks to all the contributors. 
Nahodha (talk) 17:57, 21 March 2016 (UTC)
thread_title:  questions 

message: I have done a survey of polls, and I have concluded that 95% is certainly common enough to be designated "common."  I have reorganized the opening to be more concise and take note of the different standards that are out there, and I have added formulas for the 95% (and 90%) confidence levels as well.  I think this makes for a much more well-rounded article, and I'd like to thank Wolfman and Jgm for highlighting this issue for me.  Best, Fadethree 21:48, 13 Oct 2004 (UTC)
thread_title: Revisions

message: It says:
:The margin of error can be calculated directly from the sample size (the number of poll respondents) and may be reported at three different levels of confidence.
Surely it can be reported at far more than just three levels.  Nothing stops a statistician from reporting a 98% or 97% margin of error.  Maybe what is meant is that those three levels are frequently mentioned?  If so, maybe this should be rephrased. Michael Hardy 01:14, 19 Oct 2004 (UTC)
replies: text: Absolutely right, Michael.  I have clarified this as follows, "...and is commonly reported at one of three different levels of confidence. The 99 percent level is the most conservative, the 95 percent level is the most widespread, and the 90 percent level is rarely used."  I wonder if I should be more explicit... feel free to try another wording.  Thanks also for your helpful edits to the opening.  Best, Fadethree 01:47, 19 Oct 2004 (UTC)
thread_title: Levels of confidence

message: Should this article have a section about the need for the poll to have a truely random sample for the result the valid. ie. the idea that doing the Bush/Kerry poll by sampling everybody who works at the White House would not give an acurate result. I know this isn't strictly "margin of error", but some people won't realise this and (maybe) it whould be pointed out Steven jones 01:41, 19 Oct 2004 (UTC)
replies: text: Thanks, Steven.  There is a note about this under the caveats section, "...due to its unfortunate name (it neither establishes a "margin" nor is the whole of "error")..." and under the arguments against... section, "Perhaps most importantly, there are many different sources of error in polling..."  In my first drafts for the article, I placed the misconceptions and overinterpretations at the center of the article, but many people noted, correctly, I think, that the article should center first on what the margin of error is and second on the overinterpretations.  Your thoughts?  Fadethree 02:00, 19 Oct 2004 (UTC)
thread_title:  Margin of Error not the only posible poll error 

message: It's a common intuitive assumption that the ratio of (same size) / (population size) impacts the margin of error at a given confidence level: that is, a sample size of 1000 out of a population of 10,000,000 is more accurate than 1000 out of 100,000,000.  This isn't the case for "large enough" populations, but isn't discussed in this article.  I don't know the details well enough to discuss it precisely, but it's a frequent misconception, so should probably be mentioned. --Delirium 02:31, Oct 19, 2004 (UTC)
:Yes, that is a very common misconception.  I think it may be more appropriate for the sampling (statistics) page, however.  The margin of error is, of course, a statistic that is derived from sampling theory, however the misconception applies to all sampling theory, not just the margin of error.  I'd be happy to see it added at that page, of course.  Does this make sense?  Fadethree  03:00, Oct 19, 2004 (UTC)
::I took the liberty of adding a section discussing this (in somewhat informal terms), at the margin-of-error page, but perhaps it should eventually be moved to the sampling page; I'm agnostic about this.  Terry 18:15, 21 Oct 2004 (UTC)
replies: text: I appreciate the contribution, Terry.  I do think that the topic is an imperfect fit here and that it makes more sense at the sampling page.  Still, if this is the one-stop place for people who want to understand the topic, your addition will certainly be appreciated here.  Wherever it ends up, I think it will be very helpful.  Fadethree 10:26, 23 Oct 2004 (UTC)
thread_title:  population size 

message: "Given the actual percentage difference p − q (2 percent or .02) and the standard error of the difference, above (=.03), use a program like Microsoft Excel to calculate the probability that .02 is greater than zero given a normal distribution with mean 0 and standard deviation .03."
:I am trying to wrap my mind around how .02 can be less than zero...
::Should this read: "Given the actual percentage difference p − q (2 percent or .02) and the standard error of the difference calculated above (.03), use a program like Microsoft Excel to calculate the probability that a sample from a normal distribution with mean .02 and standard deviation .03 is greater than 0."?
:I just changed it to the above because I think it's clearer.
::Can someone fix this bit, as I think it's confusing and incomplete. I am not a statistician, although I have a good grounding in maths, but this is where I get lost in the article.
::(a) please show an example of the Excel formula used to calculate the probability. Is it NORMDIST? How can the probability (by implication) be independent of the confidence level?
::(b) the standard error (deviation?) of the lead is unconnected to the standard error or margin of error in the table. I don't see how using the standard error of the lead can confirm any probability in the table...RodCrosby 19:45, 7 December 2006 (UTC)
replies: text: The wording is a bit odd. What they're saying, for example, is that if I take a poll with a margin of error of 5% and a confidence level of 99%, and 50% of people polled choose A, then we can conclude that in reality there is a 99% chance that between 45% and 55% of all people would choose A. If more or less than 50% of people polled chose A, it's a little bit more complicated - for example, if 99% choose A, then in reality there is a better than 99% chance that it's the actual percentage is between 94% and 100%. It's a little technical - maybe we can gloss over it all somehow without being totally wrong. Deco 01:08, 25 Jun 2005 (UTC)
replies: text: Aha, I've got it. Fixing. I made it just talk about "at least 99%" probability that it's within one margin of error, which is accurate and hopefully gets the idea across. Deco 01:10, 25 Jun 2005 (UTC)
thread_title:  unclear sentences 

message: Shouldn't the title use the word "sampling"? Maurreen 6 July 2005 12:55 (UTC)
:I agree that "Margin of sampling error" would be more correct. But the more common usage is "Margin of error", and we should probably follow that in our title. -- Avenue 01:16, 2 May 2006 (UTC)
thread_title: Title

message: I'm mathematically inclined, but not a statistician, and currently I'm a little uncertain of the meaning of MOE. Is the following correct:
 Given this information:
 
 Level of confidence: 95 %
 Margin of error: 4%
 Results:
  A:50%
  B:30%
  C:20%
 
 There is a 95 % chance that A is within 4% of correct.
 There is a larger than 95% chance that b is within 4% of correct.
 There is an even larger percent chance that C is within 4% of correct.
Is that all correct? Overall this seems to be relatively useless. It seems polls would be better to leave off the MOE, but give the sample size, allowig people who care to calulate the MOE themselves for whatever confidence level they desire. 71.0.197.230 03:07, 24 May 2006 (UTC)
replies: text: Roughly speaking, that's all correct. And if it was a simple random sample from a large population, you could just give the sample size and let people calculate their own MOEs. But usually most of the the audience for survey results wouldn't know how, or be able to calculate it even if you showed them how. More importantly, many surveys use more complex survey designs, meaning that it becomes much more difficult to calculate MOEs. People would need access to the survey data, details of the sample design, specialised software and statistical expertise to calculate their own margins of error. -- Avenue 04:37, 24 May 2006 (UTC)

text: The anonymous editor who posted that query almost three years ago is probably long gone, but FWIW, you seem to be misinterpreting their question. The problem is that "margin of error" is a vague term; it is sometimes used to mean "the half-width of a confidence interval for a specific statistic" (which is how you've interpreted it here), but often means "the maximum confidence interval half-width for any statistic" (across percentages based on the whole sample for a particular survey, say). The second meaning seems to be what the original query was about, since they quoted one margin of error that applied to three different results (A, B and C). -- Avenue (talk) 23:13, 17 March 2009 (UTC)
replies: text: Actually I did interpret it as the conservative maximum confidence interval assuming p = 0.5.  Otherwise I would not have stated “If using the same sample size, one may have A = 49%, 52%, 53% with the same MOE (4%).” Because MOE would change according to p even with the same sample size unless the maximum interval is assumed.  No matter what confidence interval is used for MOE, the original statements such as  “There is a 95 % chance that A is within 4% of correct.” bear the typical misinterpretation of confidence interval.  I can see a Bayesian can argue it is the same as saying “There is 95% probability the interval of 50% +/-  4% contains A”. Probably I am getting into the type of debate between a Bayesians and frequentists that can never be resolved and will last forever. I personally believe it is better for the public to think the pollsters capture the true value within the margins of error 95% of the time and miss it 5% time than any other interpretation.Zipswich (talk) 15:37, 19 March 2009 (UTC)
replies: text: Sorry, I now see I was mistaken about which of those two MOE definitions you were using. However, I still think you missed the point of the original question. I believe they were surprised to learn that the coverage probabilities for the intervals derived from a single maximum MOE for a given sample size will vary depending on the value of the estimate, and couldn't see the point of reporting a maximum MOE if it had that property. While I agree with your point that they did not exhibit a correct frequentist understanding of probability in their question, I think that would have been far from the most germane response, especially as the question did make sense under a Bayesian interpretation. -- Avenue (talk) 08:59, 20 March 2009 (UTC)

text: As far as I can see, I'd say that when you take samples of a population, the samples can give a range of answers for a what is a single figure when calculated for the whole population. Let's consider the mean. The population has one unambiguous population mean. Different samples can produce different sample means. In other words, sampling introduces uncertainty in estimates of the population mean. The larger the size of the samples, the less uncertainty there is. The margin of error as a percentage of a sample mean (at 95% confidence, for example) says something like: 95% of the time, the true population mean will lie within the margin of error either side of sample mean. If the sample mean is 40 and the MOE (at 95% confidence) is 3% (of the mean), then 95% of the time the true population mean will be in the range 40 +/- 1.2, i.e. 38.8 - 41.2. MOEs can be calculated with any other level of confidence. Have I got it right? Acorrector (talk) 18:35, 8 November 2021 (UTC)
thread_title:  Meaning of MOE 

message: I've been working on and off over the last month to correct various problems with this article. Some of the most glaring problems are now fixed; in particular the complete omission of any reference to the maximum margin of error (when that was what all the figures referred to) or to the assumption of a simple random sample made by all the formulae. Also the limited focus on polls, when margins of error apply to most sample surveys, and the misuse of N instead of n to denote the sample size. There are still some major problems remaining, which I've started to work through:
1) the technically inaccurate descriptions of what a margin of error or confidence interval means;
2) some unstated assumptions about the sample designs assumed by the various formulae and calculations shown; and 
3) the fact that most statements in the article apply to only the very few surveys that use simple random sampling with replacement.
Each of these remaining problems on its own would mean the article fails to meet some of the featured article criteria (factual accuracy for problems 1 and 2, and comprehensiveness for problem 3). The third point will be the hardest to address properly, but is probably also the most important. Even if 1 and 2 are fixed, so that our article would not be actively misleading, I believe it would still be of limited use in most practical situations until 3 is dealt with. -- Avenue 15:28, 27 May 2006 (UTC)
replies: text: It also only has a single reference which appears to be of very limited scope. --MarSch 10:44, 29 May 2006 (UTC)
thread_title: Serious problems with the article

message: The challenge of accurately describing what a margin of error or confidence interval means is that not many people can appreciate.  I see people who use confidence intervals all the time without having true understanding of its accurate meaning. Let me use an example to give it a shot.   If one uses a method called M to generate an margin of error 4% for confidence level 95% on certain test sample, it means if this method M is used many times on different samples to generate MOE’s which vary from sample to sample (e.g. 3.11% for one sample, 5.02% for another sample, 3.66% for another,  etc.), 95% of the time the true statistic (e.g. percentage voting for one candidate) is captured within the margins of error.  You can see the confidence level is a probability about the method, not directly associated with the statistic.  One common misunderstanding of  MOE or confidence interval is that regarding the confidence level (e.g. 95%) as the probability that the statistic falls in the interval formed by MOE’s (e.g. 47%-4% to 47%+4%).  The statistic is one unknown constant that does not have probability distribution.   The confidence level is all about the method we use to chase this unknown constant.  I think the sentence in this article “This level is the probability that a margin of error around the reported percentage would include the "true" percentage” is a good one. Zipswich (talk) 21:39, 17 March 2009 (UTC)
replies: text: Your post seems completely unrelated to the three-year-old discussion just above, so I have taken the liberty of giving it a fresh section heading. What you say seems correct, at least for the more restricted meaning of margin of error that refers to just a single statistic (see my response to your other post above), and under the traditional frequentist interpretation. Do you see something in the article that you think should therefore be changed? -- Avenue (talk) 23:26, 17 March 2009 (UTC)

text: I was trying to address one of the problems you mentioned:1) the technically inaccurate descriptions of what a margin of error or confidence interval means; Zipswich (talk) 12:59, 18 March 2009 (UTC)
replies: text: Well, I made that comment about the article back in May 2006, when it looked like this. I think the descriptions here have been made more technically accurate since then, although there is always room for improvement. In particular, the article currently flips back and forth between frequentist confidence intervals and (at least implicitly) Bayesian credible intervals, without being very clear about the distinction. While this might not bother a naive reader, I think it could confuse readers who have some understanding of one method, but not the other. The sentence you picked out about the confidence level is carefully worded to make sense under each paradigm; I'm glad you like it. -- Avenue (talk) 01:41, 19 March 2009 (UTC)
thread_title: Description

message: I recommend changing the main running example to a 2-person contest. The Bush/Gore/Nader race confuses because it isn't a straightforward enough example. The rest of the discussion never refers again to the Nader statistic--that's a problem and I imagine many readers will wonder about it, making the discussion of the example seeming incomplete. In reality, no presidential race is truly 2-person, but something where the 3rd, 4th etc. candidates are minimal-enough values to be discarded is better. Perhaps with the disclaimer that there is a slight variation from reality. 
Nader is a particular problem because of how well-known he is, contra many 3rd party candidates. However, since many situations do involve more than 2 options, a US presidential race of more than 2 that would work well is 1992 when Ross Perot got something like 19%. That works better given how small Nader’s figure was for 2004 and that his figure isn’t high enough to include the whole range of MOE values—his “bottoms out.” Don’t know how US-centric this article is mean to be, but obviously races in other Western nations offer mostly >2 candidate races.  Perhaps the 3-person example could be segregated to separate section to keep the 2-person example clearer rather than being intermingled with a 3-person example.
Another issue is that the sections introducing the example do not state the MOE right upfront. That should be immediately stated--anyways--but given that it's an MOE article, all the more. I kept waiting for the shoe to drop, so to speak, on that but it didn't come until (too much) later.
I recommend that the example(s) be spelled out in greater detail to demonstrate that the meaning of MOE as applies to each subject individually, not to the difference between the candidates. I see journalists frequently misstate the MOE calculation as applying to the difference rather than to each candidate. As an example: Candidate A is polled at 53% with B at 47%, MOE of 4. The ranges should be spelled out as for A 57 to 49%; for B 51 to 43%. That gives a concrete example, and can be used to better illustrate the (correct) distinction/importance of considering the application of MOE to candidates A and B individually rather than to the difference of the figure of 4, which would indicate--in that misread of the difference of 6% being (inaccurately reported) outside that MOE of 4.
A brief commentary is made in the dead-heat discussion about the difference and concomitant likelihood, but returning to the running example to spell out the relative (colloquially speaking) the significance (colloquially) of a result for A in the MOE of 57 vs. 49 vs. 53%--how likely is it that 53% is correct vs. 57/49/other percents.
As with many of the math/statistics entries, the issue of very technical explanation vs. man-on-the-street arises. This entry seems to shift from a heuristically useful real-world running example to hardcore calculations. Not sure how to deal with this, but extending the running example to be used in the more technical section about how to calculate the equations could be illustrated better by using the figures from the running examples rather than leaving it more hypothetical and generally abstract--as consistent with the use of a real-world example in the rest of the section. JackWikiSTP (talk) 17:40, 6 May 2008 (UTC)
thread_title:  Running Example issues 

message: Margin of error is a very different topic from Engineering tolerance. One is the actual amount of random variation in estimates from a sample survey; the other is the allowable variation in physical measurements or properties of engineering components. I can't see any benefit in trying to merge the two articles. Does anyone object to the merge tag being removed? -- Avenue (talk) 14:04, 10 May 2008 (UTC)
replies: text: Tag now removed. --Salix alba (talk) 17:04, 10 May 2008 (UTC)
thread_title:  Proposed merge with Engineering tolerance 

message: Hi, 
I'm researching using standard deviation to calculate maximuns and minimum and while this site is getting me close to an answer it doesn't quite clearly explain what I need to know. I'm adding my example so that maybe you can make a clear explanation for other users.
I am a geologist and have some rock powder (a standard sample) that the I have bought from a laboratory which has tested it thousands of times to the point where the laboratory claims the amount of gold in the rock is 6ppm with a standard deviation of 0.2. Now I'm going to put this rock powder in with some other rock samples that I'm sending to another laboratory, which they're going to test for gold, so that I can check the accuracy of this other laboratory. I need to create a minimum and maximum value from the standard deviation for the amount of gold to say whether I accept this result as a pass or fail for the value that returns from the laboratory. Usually a 95% confidence level is used. Now I believe that 95% confidence is 2 standard deviations, therefore the max-min range for 95% confidence will be from 5.6ppm to 6.4ppm.  
Is this correct?  —Preceding unsigned comment added by 125.160.164.105 (talk) 08:17, 3 November 2008 (UTC)
replies: text: Your question seems somewhat off-topic here; you might find more useful information at confidence interval, or our Reference Desk might be able to help. There seem to be a few unstated assumptions in your description of the problem; e.g. that the second lab will give you only a point estimate, not a range, and that getting a lab to carry out one measurement will give you enough information to "pass or fail" them. -- Avenue (talk) 23:39, 17 March 2009 (UTC)
thread_title:  Calculating Max / Min from Standard Deviation 

message: This is an article about margin of error, yet no formulas are given to help readers calculate the margin of error.  Some of the basic formulas would be nice; MOE for proportions, for means, for standard deviations, etc...  — Preceding unsigned comment added by 71.89.54.202 (talk) 22:00, 22 December 2012 (UTC)
thread_title: Formulae

message: The figure in this article shows and describes Bayesian credible intervals, assuming a uniform prior over true values of the parameter. Not confidence intervals/margin of error. The caption gets the MOE interpretation wrong: as discussed elsewhere in Talk, an X% margin of error does not tell you that the true value of the parameter probably falls within X% of the sample estimate. It tells you that if you repeated the survey/experiment infinitely many times, only X% of the margins of error you calculated would not contain the true value. 
I'm loathe to remove the figure altogether, since it is a nice diagram, but it is misleading as an illustration of the topic of the article generally. If a new section on "comparison with credible intervals" was added, that would be a good place to put it.  — Preceding unsigned comment added by 192.133.61.10 (talk) 19:11, 21 March 2013 (UTC)
thread_title:  Figure not directly relevant 

message: In "Calculations assuming random sampling" the formulas given do not output the results provided. There seems to be a term, possibly ^.5 based on my reading, missing from them.  — Preceding unsigned comment added by 167.206.48.221 (talk) 06:01, 31 March 2013 (UTC)
thread_title:  Are the Formulas Wrong? 

message: Couple of points:
- I don't see direct references to multiplying the std error by a confidence level as in this article http://www.dummies.com/how-to/content/how-sample-size-affects-the-margin-of-error.html. Seems like a formula including a zValue (or tValue) should be included.
- Overall that article does a better job of explaining the concept whereas this page is overly complex 
- How are 0% and 100% values handled?  — Preceding unsigned comment added by Bpatton (talk • contribs) 14:54, 24 April 2015 (UTC)
thread_title:  Questions/Comments 

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thread_title:  External links modified 

message: Two things. Firstly I feel as if this section is written slightly too informally, including the beginning 'Polls **basically** ...', and the crude calculation of the probability that the entirety of the sample votes for one candidate; this does not feel at home on this article but elsewhere in Random Sample, if at all.
Secondly, the blasé 'pollsters take smaller samples that are intended to be representative, that is, a random sample of the population' ignores the fact that random sampling is far from the most common polling method. See the Report of the Inquiry into the 2015 British general election opinion polls's recommendations section for a fairly recent example of this.
--Hu5k3rDu (talk) 14:01, 17 July 2018 (UTC)
thread_title:  Small gripe on the quality of (the start of) the 'Basic Concept' subsection 

message: I came to this article to better understand the relationship between the terms Confidence Level and Margin of Error. I got as far as the bowler example in the second paragraph and found myself becoming confused over layman usage and terminology before getting into mathematical and technical definitions in the subsequent paragraphs.
First, it appears from the very first sentence of the first paragraph that the presumption is that the term Margin of Error is pretty much a technical term that applies to sampling and statistics. However, in the second paragraph there is also an acknowledgement that there is a usage that relates to observational error and also a colloquial usage that relates to accuracy (although the writer included the term "precision" as opposed to accuracy - likely a topic for another discussion). So, with regard to this colloquial usage, it appears, at least to me, that there can be two significant interpretations: one expressed as double sided tolerance and another expressed as a combined tolerance. For example, if one is referring to an exact target or referencing by an exact number, then the margin of error or the accepted tolerance would typically be described as a margin to either side of that target or number. In contrast, if one is carrying a 35-inch wide refrigerator though a 36-inch wide doorway, one might describe the margin as being one inch rather than as being plus or minus one-half inch. This appears to make sense in the two examples because in the first example the objective might be to hit the target dead center, where as in the second example the objective is likely to simply get the refrigerator safely through the doorway. In the case of the bowler example in the second paragraph, the objective is more appropriately like the first example, that is, to strike the pin with the ball, not to get the ball through a window or between two pins. Relating this concept to the remaining article, I would suspect that in most cases, at least in my experience, the Margin of Error is normally provided as a double sided value, though possibly not always symmetrically equal.
Second, given my understanding as described above, I simply do not understand the calculation where a 4.75-inch wide bowling pin and an 8.5-inch wide bowling ball can be represented as having a margin of error as 21.75 inches in relationship to the ball striking the pin. If we assume that the ideal strike or the ideal aiming point is a direct center-to-center strike, then the tolerance (or margin of error) on that center-to-center strike on each side would be 6.625 inches ((8.5 + 4.75) / 2). Accordingly, if the center of the ball is beyond 6.625 inches from the center of the pin, the ball will not strike the pin. Furthermore, even if the bowler had the objective to simply nick the pin on one side (possibly to project the pin sideways), the maximum margin of error might be less than an inch to accomplish that objective and a maximum high of 13.25 inches to the opposite side for simply striking the pin though not accomplishing the objective. Accordingly, I fail to understand the meaning of saying that "a bowler has a 21.75 inch margin of error when trying to hit a specific pin to earn a spare."
BillinSanDiego (talk) 23:48, 4 December 2020 (UTC)
thread_title:  The Definition of Margin of Error and the Bowler Example in the Second Paragraph 

message: With due regard for the technical knowledge of whomever may have contributed to this article, an "editor" to be interpreted as a person familiar with the English language, grammar, popular lexicon, and intelligibility, is what is required here.
The last editor of the talk page raises a very important point, which is commonly ignored in Wikipedia.  Alas, Wikipedia has a popularity that is undeserved.  The bowling pin example should be removed,  It is indiscernible to everyone but the American Bowling Association and whoever wrote it!
Secondly, the definition of Confidence Interval suggests that it is tied to a 95% probability.  It is not.
Third, the article starts right away in formulas without introducing any basic concepts.
Was Wikipedia not the "people's encyclopedia"?
It is nearly impossible to come to a Wikipedia page without finding glaring errors, disparate statements, and irreconcilable contradictions.  Maybe y'all can correct this page!
70.231.83.189 (talk) 16:56, 18 September 2021 (UTC)
thread_title:  Poorly Written 

message: There doesn't seem to be a home on Wikipedia for the more colloquial, less statistical/scientific, use of the term margin for error. The present article relates to sampling error, and the engineering concept of Margin of safety#Factor of safety does not even involve the word "error" per se. Is there an overarching concept I'm not thinking of? Please enter your thoughts below. —RCraig09 (talk) 22:19, 11 February 2022 (UTC)
thread_title:  Broader concept