Error Bars Normal Distribution
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proportion of samples that would fall between 0, 1, 2, and 3 standard deviations above and below the actual value. The standard error (SE) is the standard deviation of the sampling distribution of a statistic,[1] most commonly of the
Error Bars For Median
mean. The term may also be used to refer to an estimate of that standard distribution of a data set definition deviation, derived from a particular sample used to compute the estimate. For example, the sample mean is the usual estimator of a population what do we call a picture or diagram of data? mean. However, different samples drawn from that same population would in general have different values of the sample mean, so there is a distribution of sampled means (with its own mean and variance). The standard error of http://scienceblogs.com/cognitivedaily/2008/07/31/most-researchers-dont-understa-1/ the mean (SEM) (i.e., of using the sample mean as a method of estimating the population mean) is the standard deviation of those sample means over all possible samples (of a given size) drawn from the population. Secondly, the standard error of the mean can refer to an estimate of that standard deviation, computed from the sample of data being analyzed at the time. In regression analysis, the term "standard error" is also used https://en.wikipedia.org/wiki/Standard_error in the phrase standard error of the regression to mean the ordinary least squares estimate of the standard deviation of the underlying errors.[2][3] Contents 1 Introduction to the standard error 1.1 Standard error of the mean 1.1.1 Sampling from a distribution with a large standard deviation 1.1.2 Sampling from a distribution with a small standard deviation 1.1.3 Larger sample sizes give smaller standard errors 1.1.4 Using a sample to estimate the standard error 2 Standard error of the mean 3 Student approximation when σ value is unknown 4 Assumptions and usage 4.1 Standard error of mean versus standard deviation 5 Correction for finite population 6 Correction for correlation in the sample 7 Relative standard error 8 See also 9 References Introduction to the standard error[edit] The standard error is a quantitative measure of uncertainty. Consider the following scenarios. Scenario 1. For an upcoming national election, 2000 voters are chosen at random and asked if they will vote for candidate A or candidate B. Of the 2000 voters, 1040 (52%) state that they will vote for candidate A. The researchers report that candidate A is expected to receive 52% of the final vote, with a margin of error of 2%. In this scenario, the 2000 voters are a sample from all the actual voters. The sample proportion of 52% is an estimate
Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About http://stats.stackexchange.com/questions/204597/the-principle-of-getting-the-error-bar-of-the-mle-of-the-mean-of-some-univariate Us Learn more about Stack Overflow the company Business Learn more about hiring https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3136454/ developers or posting ads with us Cross Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask error bars a question Anybody can answer The best answers are voted up and rise to the top The principle of getting the error bar of the MLE of the mean of some univariate Gaussian up vote 0 down vote favorite I'm reading the book Information Theory, Inference and Learning Algorithms. In Section 22.1, the author gives an example of finding the MLE of the mean of an univariate error bars normal Gaussian, and then obtaining the error bar of it, given the data and the standard variation. The related text is: If we Taylor-expand the log likelihood about the maximum, we can define approximate error bars on the maximum likelihood parameter: we use a quadratic approximation to estimate how far from the maximum-likelihood parameter setting we can go before the likelihood falls by some standard factor, for example $e^{1/2}$ , or $e^{4/2}$. In the special case of a likelihood that is a Gaussian function of the parameters, the quadratic approximation is exact. Then comes Example 22.2: Find the second derivative of the log likelihood with respect to $\mu$, and find the error bars on $\mu$, given the data and $\sigma$. The solution to this example in the text is: Comparing this curvature with the curvature of the log of a Gaussian distribution over $\mu$ of standard deviation $\sigma_{\mu}$, $\exp(-\mu^2/(2\sigma_{\mu}^2))$, which is $-1/\sigma_{\mu}^2$, we can deduce that the error bars on $\mu$ (derived from the likelihood function) are $$\sigma_{\mu} = \frac{\sigma}{\sqrt{N}}$$ I don't understand the above procedure of finding the error bars by "comparing the curvature", what's the principle behind it? normal-distribution estimation maximum-likelihood share|improve this question asked Mar 30 at 18:
Health Search databasePMCAll DatabasesAssemblyBioProjectBioSampleBioSystemsBooksClinVarCloneConserved DomainsdbGaPdbVarESTGeneGenomeGEO DataSetsGEO ProfilesGSSGTRHomoloGeneMedGenMeSHNCBI Web SiteNLM CatalogNucleotideOMIMPMCPopSetProbeProteinProtein ClustersPubChem BioAssayPubChem CompoundPubChem SubstancePubMedPubMed HealthSNPSRAStructureTaxonomyToolKitToolKitAllToolKitBookToolKitBookghUniGeneSearch termSearch Advanced Journal list Help Journal ListPLoS Onev.6(7); 2011PMC3136454 PLoS One. 2011; 6(7): e21403. Published online 2011 Jul 14. doi: 10.1371/journal.pone.0021403PMCID: PMC3136454Problems with Using the Normal Distribution – and Ways to Improve Quality and Efficiency of Data AnalysisEckhard Limpert1 and Werner A. Stahel2,*Simon Rogers, Editor1ELI-o-Research, Life Sciences, Zurich, Switzerland2Seminar for Statistics, Swiss Federal Institute of Technology (ETH) Zurich, Zurich, SwitzerlandUniversity of Glasgow, United Kingdom* E-mail: hc.zhte.htam.tats@lehatsConceived and designed the investigation: EL. Collected the data: EL. Analyzed the data: WAS. Contributed analysis tools: WAS. Wrote the manuscript: EL WAS.Author information ► Article notes ► Copyright and License information ►Received 2010 Oct 29; Accepted 2011 Jun 1.Copyright Limpert, Stahel. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.This article has been cited by other articles in PMC.AbstractBackgroundThe Gaussian or normal distribution is the most established model to characterize quantitative variation of original data. Accordingly, data are summarized using the arithmetic mean and the standard deviation, by ± SD, or with the standard error of the mean, ± SEM. This, together with corresponding bars in graphical displays has become the standard to characterize variation.Methodology/Principal FindingsHere we question the adequacy of this characterization, and of the model. The published literature provides numerous examples for which such descriptions appear inappropriate because, based on the “95% range check”, their distributions are obviously skewed. In these cases, the symmetric characterization is a poor description and may trigger wrong co