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Converting standard error to standard deviation? up vote 17 down vote favorite 6 Is it sensible to convert standard error to standard deviation? And if so, is this formula appropriate? $$SE = \frac{SD}{\sqrt{N}}$$ standard-deviation standard-error share|improve this question edited Jul 16 '12 at 11:34 Macro 24.1k496130 asked Sep 13 '11 at 13:54 Bern 86113 add a comment| 1 Answer 1 active oldest votes up vote 21 down vote Standard error refers to the standard deviation how to convert standard deviation to probability of the sampling distribution of a statistic. Whether or not that formula is appropriate depends on what statistic we are talking about. The standard deviation of the sample mean is $\sigma/\sqrt{n}$ where $\sigma$ is the (population) standard deviation of the data and $n$ is the sample size - this may be what you're referring to. So, if it is the standard error of the sample mean you're referring to then, yes, that formula is appropriate. In general, the standard deviation of a statistic is not given by the formula you gave. The relationship between the standard deviation of a statistic and the standard deviation of the data depends on what statistic we're talking about. For example, the standard error of the sample standard deviation (more info here) from a normally distributed sample of size $n$ is $$ \sigma \cdot \frac{\Gamma( \frac{n-1}{2} )}{ \Gamma(n/2) } \cdot \sqrt{\frac{n-1}{2} - \left( \frac{ \Gamma(n/2) }{ \Gamma( \frac{n-1}{2} ) } \right)^2 } $$ In other situations there may be no relationship at all between the standard error and the population standard deviation. For example, if $X_1, ..., X_n \sim N(0,\sigma^2)$, then number of observations which exceed $0$ is ${\rm Binomial}(n,1/2)$ so its standard error is $\sqrt{n/4}$, regardless of $\sigma$. share|improve this answer edited Oct 3 '12 at 12:53 answered Sep 13 '11 at 14:12 Macro 24.1k496130 add a c

Electrical Calculators Digital Computations Mechanical Calculators Environmental Calculators Finance Calculators All Finance Categories Mortgage Calculators Loan Calculators Interest Calculators Investment Calculators Credit & Debt how to convert standard deviation to z score Calculators Profit & Loss Calculators Tax Calculators Insurance Calculators Financial Ratios how to convert standard deviation to variance Finance Chart Currency Converter Math Tables Multiplication Division Addition Worksheets @: Home»Math Worksheets»Statistics Worksheet Calculate Standard standard deviation from standard error calculator Deviation from Standard Error This worksheet help users to understand the relationship between the standard deviation and standard error. The step by step calculation for for http://stats.stackexchange.com/questions/15505/converting-standard-error-to-standard-deviation calculating standard deviation from standard error illustrates how the values are being exchanged and used in the formula to find the standard deviation. Standard Deviation In the theory of statistics and probability for data analysis, standard deviation is a widely used method to measure the variability or dispersion value or to estimate http://ncalculators.com/math-worksheets/calculate-standard-deviation-standard-error.htm the degree of dispersion of the individual data of sample population. Standard Error In the theory of statistics and probability for data analysis, Standard Error is the term used in statistics to estimate the sample mean dispersion from the population mean. The relationship between standard deviation and standard error can be understood by the below formula From the above formula Standard deviation (s) = Standard Error * √n Variance = s2 The below solved example problem illustrates how to calculate standard deviation from standard error. Solved Example ProblemFor the set of 9 inputs, the standard error is 20.31 then what is the value standard deviation? Standard deviation (s) = Standard Error * √n = 20.31 x √9 = 20.31 x 3 s = 60.93 variance = σ2 = 60.932 = 3712.46 For more information for dispersion value estimation, go to how to estimate sample & population standard deviation.

Similar Worksheets How to Calculate Standard DeviatioHealth Search databasePMCAll DatabasesAssemblyBioProjectBioSampleBioSystemsBooksClinVarCloneConserved DomainsdbGaPdbVarESTGeneGenomeGEO DataSetsGEO ProfilesGSSGTRHomoloGeneMedGenMeSHNCBI Web SiteNLM CatalogNucleotideOMIMPMCPopSetProbeProteinProtein ClustersPubChem https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1255808/ BioAssayPubChem CompoundPubChem SubstancePubMedPubMed HealthSNPSRAStructureTaxonomyToolKitToolKitAllToolKitBookToolKitBookghUniGeneSearch termSearch Advanced Journal list http://mtweb.mtsu.edu/ajetton/Graphing_Guides/Excel_Guide_Std_Error.htm Help Journal ListBMJv.331(7521); 2005 Oct 15PMC1255808 BMJ. 2005 Oct 15; 331(7521): 903. doi:Â 10.1136/bmj.331.7521.903PMCID: PMC1255808Statistics NotesStandard deviations and standard errorsDouglas G Altman, professor of statistics in medicine1 and J Martin Bland, professor of health standard deviation 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 â–º Copyright and License information â–ºCopyright © 2005, BMJ Publishing Group Ltd.This article convert standard deviation 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 measure of variability regardless of the distribution. About 95% of o

the toolbar at the top. 2. A menu will appear that says “Paste Function”. Select “Stastical” from the left hand side of the menu, if necessary. Scroll down on the right hand side of the menu and select “STDEV”; then click “OK”. 3. Click on the picture of the spreadsheet, and highlight the numbers you averaged earlier, just as you did when taking the average. Hit enter, and “OK” to calculate the standard deviation. 4. With the cursor still on the same cell, now click in the formula bar at the top of the spreadsheet (the white box next to the “=” sign) to put the cursor in that bar so you can edit the formula. 5. Put a “(“ in front of STDEV and a “)” at the end of the formula. Add a “/” sign to indicated you are dividing this standard deviation. Put 2 sets of parentheses “(())” after the division symbol. Put the cursor in the middle of the inner set of parentheses. 6. Now click on the fx symbol again. Choose “Statistical” on the left hand menu, and then “COUNT” on the right hand menu. 7. Click on the spreadsheet picture in the pop-up box, and then highlight the list of numbers you averaged. Hit enter and “OK” as before. 8. Move the cursor to be between the 2 sets of parentheses, and type “SQRT”. Hit enter. The standard error of the mean should now show in the cell. Your formula in the formula bar should look something like this, “=(STDEV(A1:A2))/(SQRT(COUNT(A1:A2)))”. (This formula would calculate the standard error of the mean for numbers in cells A1 to A2.) NOTE: We have calculated standard error of the mean by dividing the standard deviation of the mean by the square root of n. Given the formula that Excel uses for calculation of standard deviation of the mean, this gives the standard error of the mean after adjusting for a small sample size. This is usually the case in physiology experiments. The formula would be different with a very large sample size. I do not know why Excel still does not include a formula for calculating the standard error of the mean.

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