Describe The Relationship Between Sample Size And Standard Error
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Which Of The Following Statements Is True Concerning The Relationship Between Standard Error And Sample Size
Statistics Essentials For Dummies Statistics For Dummies, 2nd Edition SPSS Statistics for Dummies, 3rd Edition relationship between standard deviation and sample size Statistics II for Dummies Load more EducationMathStatisticsHow Sample Size Affects Standard Error How Sample Size Affects Standard Error Related Book Statistics For Dummies,
If The Size Of The Sample Is Increased The Standard Error Will
2nd Edition By Deborah J. Rumsey The size (n) of a statistical sample affects the standard error for that sample. Because n is in the denominator of the standard error formula, the standard error decreases as n sample size standard error calculator increases. It makes sense that having more data gives less variation (and more precision) in your results.
Distributions of times for 1 worker, 10 workers, and 50 workers. Suppose X is the time it takes for a clerical worker to type and send one letter of recommendation, and say X has a normal distribution with mean 10.5 minutes and standard deviation 3 minutes. The bottom curve in the preceding figure shows the distribution of X, sample size margin of error the individual times for all clerical workers in the population. According to the Empirical Rule, almost all of the values are within 3 standard deviations of the mean (10.5) -- between 1.5 and 19.5. Now take a random sample of 10 clerical workers, measure their times, and find the average, each time. Repeat this process over and over, and graph all the possible results for all possible samples. The middle curve in the figure shows the picture of the sampling distribution of Notice that it's still centered at 10.5 (which you expected) but its variability is smaller; the standard error in this case is (quite a bit less than 3 minutes, the standard deviation of the individual times). Looking at the figure, the average times for samples of 10 clerical workers are closer to the mean (10.5) than the individual times are. That's because average times don't vary as much from sample to sample as individual times vary from person to person. Now take all possible random samples of 50 clerical workers and find their means; the sampling distribution is shown in the tallest curve in the figure. The standard error of You can see the average times for 50 clerical workers are even closer to 10.5 than the ones for 10 clerical workers. By the Empirical Rule, almost all of the values faHealth Search databasePMCAll DatabasesAssemblyBioProjectBioSampleBioSystemsBooksClinVarCloneConserved DomainsdbGaPdbVarESTGeneGenomeGEO DataSetsGEO ProfilesGSSGTRHomoloGeneMedGenMeSHNCBI Web SiteNLM
The Relationship Between Sample Size And Sampling Error Is Quizlet
CatalogNucleotideOMIMPMCPopSetProbeProteinProtein ClustersPubChem BioAssayPubChem CompoundPubChem SubstancePubMedPubMed HealthSNPSRAStructureTaxonomyToolKitToolKitAllToolKitBookToolKitBookghUniGeneSearch termSearch Advanced purpose of sampling in research Journal list Help Journal ListBMJv.331(7521); 2005 Oct 15PMC1255808 BMJ. 2005 Oct 15; 331(7521):
Reasons For Sampling In Research
903. doi: 10.1136/bmj.331.7521.903PMCID: PMC1255808Statistics NotesStandard deviations and standard errorsDouglas G Altman, professor of statistics in medicine1 and J Martin Bland, http://www.dummies.com/education/math/statistics/how-sample-size-affects-standard-error/ professor of health statistics21 Cancer Research UK/NHS Centre for Statistics in Medicine, Wolfson College, Oxford OX2 6UD2 Department of Health Sciences, University of York, York YO10 5DD Correspondence to: Prof Altman ku.gro.recnac@namtla.guodAuthor information ► Copyright and License information ►Copyright © 2005, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1255808/ BMJ Publishing Group Ltd.This article has been cited by other articles in PMC.The terms “standard error” and “standard deviation” are often confused.1 The contrast between these two terms reflects the important distinction between data description and inference, one that all researchers should appreciate.The standard deviation (often SD) is a measure of variability. When we calculate the standard deviation of a sample, we are using it as an estimate of the variability of the population from which the sample was drawn. For data with a normal distribution,2 about 95% of individuals will have values within 2 standard deviations of the mean, the other 5% being equally scattered above and below these limits. Contrary to popular misconception, the standard deviation is a valid measu
Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings http://stats.stackexchange.com/questions/200392/general-relationship-between-standard-error-and-sample-size and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Cross Validated Questions Tags Users http://onlinestatbook.com/2/sampling_distributions/samp_dist_mean.html 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 sample size takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top General Relationship Between Standard Error and Sample Size up vote 3 down vote favorite Suppose I empirically estimate the standard error of some statistic to be 10% (perhaps I do this by bootstrapping). the relationship between Now, I want to know how much I need to increase the sample size to reduce the error to 5%. The estimate and sample are arrived at through complex procedures, and theoretically determining the relationship between sample size and standard error is not feasible. However, I believe that the standard error decreases as sample sizes increases. Is it plausible to assume that standard error is proportional to the inverse of the square root of n (based on the standard error of a sample mean using simple random sampling)? se = s / sqrt( n ) Do standard errors behave (very) roughly in this way in general in relation to sample size, regardless of the estimate and the sampling procedure? How bad of an assumption is this? standard-error share|improve this question asked Mar 7 at 16:30 Iggy25 748 add a comment| 2 Answers 2 active oldest votes up vote 4 down vote accepted regardless of the estimate and the sampling procedure? No, you will not have a "root-n" effect regardless of those things, since at least some standard errors do not sc
error of the mean State the central limit theorem The sampling distribution of the mean was defined in the section introducing sampling distributions. This section reviews some important properties of the sampling distribution of the mean introduced in the demonstrations in this chapter. Mean The mean of the sampling distribution of the mean is the mean of the population from which the scores were sampled. Therefore, if a population has a mean μ, then the mean of the sampling distribution of the mean is also μ. The symbol μM is used to refer to the mean of the sampling distribution of the mean. Therefore, the formula for the mean of the sampling distribution of the mean can be written as: μM = μ Variance The variance of the sampling distribution of the mean is computed as follows: That is, the variance of the sampling distribution of the mean is the population variance divided by N, the sample size (the number of scores used to compute a mean). Thus, the larger the sample size, the smaller the variance of the sampling distribution of the mean. (optional) This expression can be derived very easily from the variance sum law. Let's begin by computing the variance of the sampling distribution of the sum of three numbers sampled from a population with variance σ2. The variance of the sum would be σ2 + σ2 + σ2. For N numbers, the variance would be Nσ2. Since the mean is 1/N times the sum, the variance of the sampling distribution of the mean would be 1/N2 times the variance of the sum, which equals σ2/N. The standard error of the mean is the standard deviation of the sampling distribution of the mean. It is therefore the square root of the variance of the sampling distribution of the mean and can be written as: The standard error is represented by a σ because it is a standard deviation. The subscript (M) indicates that the standard error in question is the standard error of the mean. Central Limit Theorem The central limit theorem states that: Given a population with a finite mean μ and a finite non-zero variance σ2, th