Difference Between Standard Error And Margin Of Error
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Are Margin Of Error And Standard Deviation The Same
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Confidence Interval Margin Of Error
top What is the difference between “margin of error” and “standard error”? up vote 9 down vote favorite 4 Is "margin of error" the same as "standard error"? A (simple) example to illustrate the difference would be great! definition share|improve this question edited Sep 23 '11 at 18:04 whuber♦ 145k17281541 asked Sep 23 '11 at 17:06 Adhesh Josh 91293356 add a comment| 3 Answers 3 active oldest votes up vote 13 down vote accepted Short meaning of margin of error answer: they differ by a quantile of the reference (usually, the standard normal) distribution. Long answer: you are estimating a certain population parameter (say, proportion of people with red hair; it may be something far more complicated, from say a logistic regression parameter to the 75th percentile of the gain in achievement scores to whatever). You collect your data, you run your estimation procedure, and the very first thing you look at is the point estimate, the quantity that approximates what you want to learn about your population (the sample proportion of redheads is 7%). Since this is a sample statistic, it is a random variable. As a random variable, it has a (sampling) distribution that can be characterized by mean, variance, distribution function, etc. While the point estimate is your best guess regarding the population parameter, the standard error is your best guess regarding the standard deviation of your estimator (or, in some cases, the square root of the mean squared error, MSE = bias$^2$ + variance). For a sample of size $n=1000$, the standard error of your proportion estimate is $\sqrt{0.07\cdot0.93/1000}$ $=0.0081$. The margin of error is the half-width of the associated confidence interval, so for the 95% confidence level, you would have $z_{0.975}=1.96$ resulting in a margin of error $0.0081\cdot1.96=0.0158$. share|improve this answer edited Sep 23 '11 at 21:2
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test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers Probability Bayes rule Combinations/permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator books AP calculator review http://stattrek.com/estimation/margin-of-error.aspx Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3148365/ practice exam Problems and solutions Formulas Notation Share with Friends Margin of Error In a confidence interval, the range of values above and below the sample statistic is called the margin of error. For example, suppose we wanted to know the percentage of adults that exercise daily. We could devise a sample design to ensure that our margin of sample estimate will not differ from the true population value by more than, say, 5 percent (the margin of error) 90 percent of the time (the confidence level). How to Compute the Margin of Error The margin of error can be defined by either of the following equations. Margin of error = Critical value x Standard deviation of the statistic Margin of error = Critical value x Standard error of the statistic margin of error If you know the standard deviation of the statistic, use the first equation to compute the margin of error. Otherwise, use the second equation. Previously, we described how to compute the standard deviation and standard error. How to Find the Critical Value The critical value is a factor used to compute the margin of error. This section describes how to find the critical value, when the sampling distribution of the statistic is normal or nearly normal. The central limit theorem states that the sampling distribution of a statistic will be nearly normal, if the sample size is large enough. As a rough guide, many statisticians say that a sample size of 30 is large enough when the population distribution is bell-shaped. But if the original population is badly skewed, has multiple peaks, and/or has outliers, researchers like the sample size to be even larger. When the sampling distribution is nearly normal, the critical value can be expressed as a t score or as a z score. When the sample size is smaller, the critical value should only be expressed as a t statistic. To find the critical value, follow these steps. Compute alpha (α): α = 1 - (confidence level / 100) Find the critical probability (p*): p* = 1 - α/2 To express th
Health Search databasePMCAll DatabasesAssemblyBioProjectBioSampleBioSystemsBooksClinVarCloneConserved DomainsdbGaPdbVarESTGeneGenomeGEO DataSetsGEO ProfilesGSSGTRHomoloGeneMedGenMeSHNCBI Web SiteNLM CatalogNucleotideOMIMPMCPopSetProbeProteinProtein ClustersPubChem BioAssayPubChem CompoundPubChem SubstancePubMedPubMed HealthSNPSRAStructureTaxonomyToolKitToolKitAllToolKitBookToolKitBookghUniGeneSearch termSearch Advanced Journal list Help Journal ListClin Orthop Relat Resv.469(9); 2011 SepPMC3148365 Clin Orthop Relat Res. 2011 Sep; 469(9): 2661–2664. Published online 2011 May 10. doi: 10.1007/s11999-011-1908-9PMCID: PMC3148365In Brief: Standard Deviation and Standard ErrorDavid J. Biau, MD, PhDDepartement de Biostatistique et Informatique Medicale, Hôpital Saint-Louis, 1 avenue Claude Vellefaux, 75475 Paris Cedex 10, France David J. Biau, Email: rf.oohay@uaibmjd.Corresponding author.Author information ► Article notes ► Copyright and License information ►Received 2011 Mar 1; Accepted 2011 Apr 20.Copyright © The Association of Bone and Joint Surgeons® 2011This article has been cited by other articles in PMC.I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the ``Law of Frequency of Error’’. … Whenever a large sample of chaotic elements are taken in hands and marshalled in the order of their magnitude, an unsuspected and most beautiful form of regularity proves to have been latent all along. The tops of the marshalled row form a flowing curve of invariable proportion; and each element, as it is sorted in place, finds, as it were, a pre-ordained niche, accurately adapted to fit it.Sir Francis Galton (Natural Inheritance, 1889:66).BackgroundPhysicians often confuse the standard deviation and