Difference Over Sum Error
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article by introducing more precise citations. (September 2016) (Learn how and when to remove this template message) Part of a series on Statistics Regression analysis Models difference over sum normalization Linear regression Simple regression Ordinary least squares Polynomial regression General linear model sum of error squared Generalized linear model Discrete choice Logistic regression Multinomial logit Mixed logit Probit Multinomial probit Ordered logit Ordered probit sum error in excel Poisson Multilevel model Fixed effects Random effects Mixed model Nonlinear regression Nonparametric Semiparametric Robust Quantile Isotonic Principal components Least angle Local Segmented Errors-in-variables Estimation Least squares Ordinary least squares Linear error propagation average (math) Partial Total Generalized Weighted Non-linear Non-negative Iteratively reweighted Ridge regression Least absolute deviations Bayesian Bayesian multivariate Background Regression model validation Mean and predicted response Errors and residuals Goodness of fit Studentized residual Gauss–Markov theorem Statistics portal v t e For a broader coverage related to this topic, see Deviation. In statistics and optimization, errors and residuals are two closely
Error Propagation Mean
related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "theoretical value". The error (or disturbance) of an observed value is the deviation of the observed value from the (unobservable) true value of a quantity of interest (for example, a population mean), and the residual of an observed value is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals. Contents 1 Introduction 2 In univariate distributions 2.1 Remark 3 Regressions 4 Other uses of the word "error" in statistics 5 See also 6 References Introduction[edit] Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model). In this case, the errors are the deviations of the observations from the population mean, while
the difference between means Compute the standard error of the difference between means Compute the probability of a difference between means being above a specified value Statistical analyses are very often concerned with the difference between means. A typical example
Standard Error Of The Difference Between Means
is an experiment designed to compare the mean of a control group with the mean error propagation average standard deviation of an experimental group. Inferential statistics used in the analysis of this type of experiment depend on the sampling distribution of the error propagation mean value difference between means. The sampling distribution of the difference between means can be thought of as the distribution that would result if we repeated the following three steps over and over again: (1) sample n1 scores https://en.wikipedia.org/wiki/Errors_and_residuals from Population 1 and n2 scores from Population 2, (2) compute the means of the two samples (M1 and M2), and (3) compute the difference between means, M1 - M2. The distribution of the differences between means is the sampling distribution of the difference between means. As you might expect, the mean of the sampling distribution of the difference between means is: which says that the mean of the distribution of differences between http://onlinestatbook.com/2/sampling_distributions/samplingdist_diff_means.html sample means is equal to the difference between population means. For example, say that the mean test score of all 12-year-olds in a population is 34 and the mean of 10-year-olds is 25. If numerous samples were taken from each age group and the mean difference computed each time, the mean of these numerous differences between sample means would be 34 - 25 = 9. From the variance sum law, we know that: which says that the variance of the sampling distribution of the difference between means is equal to the variance of the sampling distribution of the mean for Population 1 plus the variance of the sampling distribution of the mean for Population 2. Recall the formula for the variance of the sampling distribution of the mean: Since we have two populations and two samples sizes, we need to distinguish between the two variances and sample sizes. We do this by using the subscripts 1 and 2. Using this convention, we can write the formula for the variance of the sampling distribution of the difference between means as: Since the standard error of a sampling distribution is the standard deviation of the sampling distribution, the standard error of the difference between means is: Just to review the notation, the symbol on the left contains a sigma (σ)
StandardsQuality of Laboratory TestingStatisticsSix SigmaToolsTrendsGuest EssayRisk ManagementQC ApplicationsQC DesignBasic QC PracticesMethod ValidationSix SigmaSigma Metric AnalysisQuality StandardsLessonsBasic QC PracticesBasic Planning for QualityBasic Method ValidationZ-Stats / Basic StatisticsQuality ManagementAdvanced Quality Management / Six Sigma"Westgard Rules"Patient https://www.westgard.com/lesson35.htm Safety ConceptsHigh ReliabilityISOCLIA & QualityQuality RequirementsCLIA Final RuleDownloadsStoreResourcesAbout UsFeedback Form http://stats.stackexchange.com/questions/118/why-square-the-difference-instead-of-taking-the-absolute-value-in-standard-devia Survey Says... Here's what US labs think about their IQCPs Here's what Global Labs think about their IQCPs Here are the unvarnished comments from the labs themselves. Forget the hype. Here's the truth. Sysmex XN 2000 Sigma-metric analysis of the Sysmex error propagation XN 2000 Hematology Analyzer NEW BOOK! Basic QC Practices 4th Edition Just Published! The 4th Edition of Basic QC Practices. THE book on QC has been updated for IQCP, QC Frequency and Westgard Sigma Rules On the Blog Booth 3739: The Philadelphia (Quality) Story Thank you, Hanoi! Thank you, Mexico difference over sum City! Westgard Booth Raffle HomeLessonsZ Stats / Basic StatisticsZ-5: Sum of Squares, Variance, and the Standard Error of the Mean WESTGARD WEB Z-5: Sum of Squares, Variance, and the Standard Error of the Mean Written by Madelon F. Zady. When you compare monthly QC data or perform initial method validation experiments, you do a lot of mean comparison. Dr. Madelon F. Zady, Ph.D., talks about the means of means and other important statistical calculations. EdD Assistant ProfessorClinical Laboratory Science Program University of LouisvilleLouisville, KentuckyJune 1999 A simulated experiment Calculation of the mean of a sample (and related statistical terminology) Scores, Mean, Deviation scores First moment, Sum of squares Variance, Standard deviation Calculation of the mean of the means of samples (or standard error of the mean) Mean of means, Deviations or errors Sum of squares, variance of means Standard deviation of means, standard error of the mean Sample distribution of means Why are the stan
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 Us Learn more about Stack Overflow the company Business Learn more about hiring 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 a question Anybody can answer The best answers are voted up and rise to the top Why square the difference instead of taking the absolute value in standard deviation? up vote 245 down vote favorite 165 In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute value of the difference instead and get the expected value (mean) of those, and wouldn't that also show the variation of the data? The number is going to be different from square method (the absolute-value method will be smaller), but it should still show the spread of data. Anybody know why we take this square approach as a standard? The definition of standard deviation: $\sigma = \sqrt{E\left[\left(X - \mu\right)^2\right]}.$ Can't we just take the absolute value instead and still be a good measurement? $\sigma = E\left[|X - \mu|\right]$ standard-deviation definition share|improve this question edited Jul 28 '11 at 16:42 mbq 17.7k849103 asked Jul 19 '10 at 21:04 c4il 1,4244118 14 In a way, the measurement you proposed is widely used in case of error (model quality) analysis -- then it is called MAE, "mean absolute error". –mbq Jul 19 '10 at 21:30 3 In accepting an answer it seems important to me that we pay attention to whether the answer is circular. The normal distribution is based on these measurements of variance from squared error terms, but that isn't in and of itself a justification for using (X-M)^2 over |X-M|. –rpierce Jul 20 '10 at 7:59 1 Do you think the term standard means this is THE standard toda