Talk:Standard error

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One of the 500 most frequently viewed mathematics articles.
edit·history·watch·refresh Stock post message.svg To-do list for Standard error:
  • Standard error calculations for difference between means, proportions and differences between proportions.
  • Different sampling situations for differences between proportions
  • Standard error calculations for median

See also: William M. Connolley 22:45, 2004 Mar 25 (UTC)

Just think about the needs of the reader of an encyclopaedia. Cutler 00:37, 26 Mar 2004 (UTC)


A standard convention for standard error (y, SE, or otherwise) should be used in the equations throughout this article.

BailesB 19:30, 2 October 2007 (UTC)

(User:Joeydream by 4 July 2006)

Stantard Error was used commonly in report of science/physics experiment.

the result was always written as x + (delta)x,

where (delta)x was called standard error.

The physical meaning of standard error is:

if the measurement was repeated, there is 68.2 % that the result was be measured in the range x + (delta)x

The sentence--

"In other words the standard error is the standard deviation of the sampling distribution of the sample statistic (such as sample mean, sample proportion or sample correlation)."

--is incorrect. The SE is an *estimate* of the SD of the sampling distribution. I'm changing this sentence to make it correct in the article.

See the section "Formerly disputed" below. RVS (talk) 20:52, 3 January 2009 (UTC)

standard error an estimate[edit]

The sentence--

"In other words the standard error is the standard deviation of the sampling distribution of the sample statistic (such as sample mean, sample proportion or sample correlation)."

--is incorrect. The SE is an *estimate* of the SD of the sampling distribution. Someone should change this sentence (and all other instances of the same mistake) in the article.

See the section "Formerly disputed" below. RVS (talk) 20:52, 3 January 2009 (UTC)


In the section: standard error of the mean, shouldn't the definition of sigma be "sample standard deviation" instead of "the mean" —Preceding unsigned comment added by (talk) 13:41, 2 November 2007 (UTC)

Standard Error and Students t-distribution[edit]

The standard error is only an estimate of the standard deviation. If you know a sample to come from a normal distribution, you cannot use the standard error as if it were the standard deviation. An additional uncertainty is added to the stochastic nature of the probalistic variable when using an estimate instead of the true standrard deviation. To overcome this problem when dealing with normally distributed variable student's t-distribution is used. Someone should write something about this, or else the section about using the standard error together with the normal distribution should be deleted. —Preceding unsigned comment added by (talk) 17:30, 12 March 2008 (UTC)

Moved to end to follow convention. Melcombe (talk) 18:05, 12 March 2008 (UTC)

Added something to article intro to start to cover above point. Possibly better elsewhere if article extended. Melcombe (talk) 18:05, 12 March 2008 (UTC)

== Standard Error of Estimate? == ok

Misunderstood between Standard Error and Standard Error of Estimate.

This the same thing, because in the litterature we talk about "Standard Error of Estimate" and no "Standard Error"

That somebody can resolve this misunderstood? —Preceding unsigned comment added by Philogik (talkcontribs) 20:43, 16 March 2008 (UTC)

But I think it is common to see some thing like "the estimate is ... and its standrard error is ..." Melcombe (talk) 10:01, 17 March 2008 (UTC)


The sentence: "The standard error of the mean (SEM), an unbiased estimate of expected error in the sample estimate of a population mean, is the sample estimate of the population standard deviation (sample standard deviation) divided by the square root of the sample size (assuming statistical independence of the values in the sample)"

is a run-on and difficult for the lay reader to understand. It needs to be split into two sentences (one defining SEOM and the other introducing the equation) and "dummed down" & cleaned up grammatically (sorta like this sentence). (talk) 03:56, 3 September 2008 (UTC)

Try to provide a better sentence, so that it can be inserted in the article. --Cyclopia (talk) 15:17, 3 September 2008 (UTC)

Another "huh?"[edit]

In the "Standard error of the mean" section, the article says " is the sample standard deviation (i.e. the sample based estimate of the standard deviation of the population)." Or from the formula, )

In the "Assumptions and usage" section, the article says "s is equal to the standard error for the sample mean."

Isn't this inconsistency a problem? --K keith (talk) 21:31, 24 September 2008 (UTC)

Formerly disputed[edit]

Inasmuch as this page is one of the 100 most frequently viewed math articles, it ought to be made correct. This talk page shows there's a lot of confusion and inconsistency. In my opinion, the problem is that the primary definition of standard error is the standard deviation of the sampling distribution of a statistic. This is the definition at, for example, Sampling distribution, Encyclopedia Britannica, and most other readily found references on the web. A secondary definition would be an estimate of that standard deviation calculated for a particular sample. This definition is given at, e.g., Wolfram MathWorld. (I have no doubt that the term is sometimes used this way as well, equivocally.) This article tries to take the secondary definition as primary, leading to confusion and inconsistency. The article should be rewritten to clearly distinguish between the quantity (which depends only on the population) and its estimate (which depends also on a particular sample). RVS (talk) 01:06, 24 December 2008 (UTC)

I have tried to revise the intro appropriately and I have added a reference. However, feel free to join in and make changes. You might like to look at the activity at WP:WPSTAT . Melcombe (talk) 10:44, 29 December 2008 (UTC)
Changed "Disputed" to "Formerly disputed" in the talk page, and removed Disputed template from main page. RVS (talk) 20:52, 3 January 2009 (UTC)
Made further revisions to intro as well as "Standard error of the mean" to more clearly distinguish between the the two usages. RVS (talk) 02:49, 6 January 2009 (UTC)

Estimate of error versus variation in distribution[edit]

One paragraph of the intro tries to distinguish between the standard error as standard deviation of error in the estimation method, and standard error as expressing the distribution of the estimated values. My feeling is that this is probably a false distinction and that these concepts are essentially identical, or at least numerically identical. This also impacts the section on "Standard error of the mean", where in the course of rewriting I stated this more explicitly than was originally present. I'll try to analyze this eventually, but I hope someone more expert than I can beat me to it. RVS (talk) 02:49, 6 January 2009 (UTC)

Rewrote this paragraph to say that the two concepts are numerically identical if the estimator is unbiased. (It would follow that if the estimator is biased, the standard error -- defined, properly, as on this page -- is not the same as the standard deviation of the error.) RVS (talk) 02:56, 8 January 2009 (UTC)

Correction for correlation[edit]

I find this section confusing and inadequate. Is this a standard, accepted result, or somebody's recent research? No citations or examples, etc.

nMSE? NMSE?[edit]

nMSE redirects here though I have not been able to find anything related to it here. I am not sure if what I was looking for is this NMSE. Or if there is another measure called nMSE for time series forecating error. Arauzo (talk) 11:20, 11 April 2009 (UTC)

interpretation of the term "standard error"[edit]

this article says

The term "standard error" is derived from the fact that, as long as the estimator is unbiased, the standard deviation of the error (the difference between the estimate and the true value) is the same as the standard deviation of the estimates themselves;

i think a more intuitive interpretation is that, as stated in the [mean squared error] article,

for an unbiased estimator, the [root mean square error] is ... known as the standard error.

Moderatemax (talk) 21:12, 10 May 2009 (UTC)

Seems like these two quotes are saying the pretty much the same thing, or at least are two sides of the same coin. RVS (talk) 00:18, 20 May 2009 (UTC)
I can almost guarentee that for 99% of the non electrical engineers on wikipedia, RMS is pretty darn confusing. — Preceding unsigned comment added by (talk) 18:57, 23 November 2011 (UTC)

Image and caption check[edit]

Can someone sanity check whether the caption I wrote for the image makes sense, or if there's a simpler way of depicting it? It feels like a wordy caption for a relatively simple concept. —AySz88\^-^ 23:58, 2 November 2009 (UTC)

"Standard Error of the Difference Between the Means of Two Samples"[edit]

Hi all,

I think this article also needs to address "Standard Error of the Difference Between the Means of Two Samples"

What do you think ?

Talgalili (talk) 16:52, 15 February 2010 (UTC)

Quantiles of the normal distribution[edit]


"If the data are assumed to be normally distributed, quantiles of the normal distribution and the sample mean and standard error can be used to calculate approximate confidence intervals for the mean. The following expressions can be used to calculate the upper and lower 95% confidence limits, where is equal to the sample mean, SE is equal to the standard error for the sample mean, and 1.96 is the .975 quantile of the normal distribution:"

,why does the 95% confidence level correspond with the 0.975 quantile of the normal distribution? Perhaps this could be explained more clearly. Also, it would be very useful to have the multiples of the SE multiple for a range of quantiles, for example, (90, 95, 99, 99.9). I'd appreciate it if a knowledgeable editor could look into making these changes. Doug (talk) 13:14, 12 April 2010 (UTC)

Regarding the first question - It is because it the CI is for two sided test. This is actually a quite deep subject to go into since CI (a.k.a: confidence intervals), can be made in various ways. I also hope someone more knowledgeable then me will expend on it. Talgalili (talk) 14:38, 12 April 2010 (UTC)

Requested move[edit]

The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the move request was: moved to Standard error. Favonian (talk) 18:06, 22 February 2012 (UTC)

Standard error (statistics)Standard error – Most common usage, disambiguation to the Unix Standard Error can be put on top of page with no loss of information. (talk) 14:59, 15 February 2012 (UTC)

  • Support, as Standard error stream is not an article but merely a redirect to Standard streams#Standard error (stderr), so standard error (statistics) is clearly the primary topic. Qwfp (talk) 19:21, 15 February 2012 (UTC)
  • Note. Those concerned with article Standard streams would have no idea this is being proposed. Since "standard error" (on its own) is common usage is computing, I have left a note at Talk:Standard streams about this proposal. Melcombe (talk) 19:42, 15 February 2012 (UTC)
  • Support This is orthodox. Whereas the statistics article is primary per Qwfp, the hatnote solution follows per WP:TWODABS. ENeville (talk) 21:46, 15 February 2012 (UTC)
  • Comment I'd also like to note that 9/10 of the top Google results refer to the statistical term, with the other being a Ruby class unrelated to the Unix stream. The most common term used for standard error in Unix is stderr. - (talk) 22:50, 15 February 2012 (UTC)
  • Support For reasons given above, not one of which is bad or trivial. Rwflammang (talk) 23:00, 15 February 2012 (UTC)
  • Support; the i/o stream is a specialized topic of very specialized and limited interest. When there are only two options, I believe we can lower the "primary topic" bar, and the statistical term is well over that lowered bar. Powers T 02:05, 16 February 2012 (UTC)
  • Support: The statistical term is clearly the primary topic. — Bility (talk) 19:39, 20 February 2012 (UTC)
The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Section comparing and contrasting with Standard Deviation is needed[edit]

What makes the standard error of the mean confusing is that it is commonly used in scientific articles as a replacement for the standard deviation. This leads the naive reader to expect that the SEM is a statistic that measures variability. But it is not a statistic, it is an equation that provides a rough bound to the size of the error when estimating a population mean by sampling from the population. THis is a distinction of kind; the statistic is descriptive, this is analytic and is a weak estimate of how sampling error fades in light of the the central limit theorem. THe article should take some time to clarify this misconception. It is a common one because scientists often use the SEM so as to minimize the size of error bars in their figures. Mrdthree (talk) 13:52, 23 February 2012 (UTC)

==I was about to post somthing like this, please do so. Also, the image should be changed. Though it works, it would mislead the casual read to think SD and SE are the same. Thank you! (talk) 12:40, 5 April 2012 (UTC)

== Here's a source contrasting standard error with standard deviation: Briancady413 (talk) 23:29, 19 February 2015 (UTC)

Recent long (and possibly tedious) additions to this article[edit]

Recently, Michaelg2015 introduced some very long and, I suggest, tedious material to the article: [1]. I propose that this material be removed. Isambard Kingdom (talk) 17:13, 14 January 2017 (UTC)

Isambard Kingdom has proposed deletion of introductory material on the Standard error. I would point out the frequent criticism that Wikipedia statistics articles are not understandable to non-statisticians. Here are examples from some statistics article Talk pages:

  • "Please, somebody, take pity on those of us who need more fundamental understanding, and write an introduction to this subject that would be useful and graspable by anybody with the basic interest to look it up. That's how to make Wikipedia better; make it useful."
  • "Would it be possible to write an introductory section that gives just a conceptual description…?"
  • "This article is quite technical. It would be nice to have a simpler layman's description too."

That said, there are readers with more advanced knowledge, such as Kingdom, who find the introductory material too detailed and tedious. To address this issue, I have moved the introductory material to the end of the article. The material is now in the section with the title "Introduction to the standard error for the novice".

Readers who wish for a brief, mathematical, highly technical explanation can get that first, while readers who wish for a more comprehensible lay-oriented explanation can find it at the end.

Michaelg2015 (talk) 20:59, 14 January 2017 (UTC)

Reason for removing paragraph[edit]

The section Standard error#Correction for finite population says without citation

When sampling biological populations in particular, the population size N must be carefully expressed in "sample units". For example, a biologist counts beach clams in 1 square-metre quadrats along a 1000 m long sandy ocean beach. The biologist samples 10 random locations from a grid with 10 m intervals and calculates the FPC = √{(100 − 10)/(100 - 1)} = 0.95. Alternatively, the sampling interval could have been 20 m and FPC = √{(50 − 10)/(50 - 1)} = 0.90. Both of these corrections are wrong because the sampling frames are arbitrary. The correct N = 1000/1 = 1000 and the correct FPC = √{(1000 − 10)/(1000 - 1)} = 0.995. If the biologist were to perform a complete count of 1000 quadrats then every clam has been counted (in theory, at least), the sum of the quadrat counts equals the true population size, not an estimate, and the FPC = √{(1000 − 1000)/(1000 - 1)} = 0, so that the standard error of the mean count (and true population size) is zero.

Both finite-sample correction calculations are right since they apply to different sampling scenarios. In the first case, the biologist has counted clams along 100 meters of beachfront. In the second case, he has counted clams along 200 meters of beachfront. So of course in the latter case the standard error calculation has to be adjusted down more, since more of the finite population has been sampled. So I'm deleting this passage. Loraof (talk) 19:10, 3 July 2017 (UTC)