Anova Standard Error
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women with low daily calcium intakes (400 mg) assigned at random to one of three treatments--placebo, calcium carbonate, calcium citrate maleate). Class Levels Values GROUP 3 CC CCM P Dependent Variable: DBMD05 Sum regression standard error of Source DF Squares Mean Square F Value Pr > F Model 2 44.0070120 regression analysis standard error 22.0035060 5.00 0.0090 Error 78 343.1110102 4.3988591 Corrected Total 80 387.1180222 R-Square Coeff Var Root MSE DBMD05 Mean 0.113679 -217.3832 2.097346 -0.964815 p value standard error Source DF Type I SS Mean Square F Value Pr > F GROUP 2 44.00701202 22.00350601 5.00 0.0090 Source DF Type III SS Mean Square F Value Pr > F GROUP 2 44.00701202 22.00350601 5.00 0.0090 Standard linear regression standard error Parameter Estimate Error t Value Pr > |t| Intercept -1.520689655 B 0.38946732 -3.90 0.0002 GROUP CC 0.075889655 B 0.57239773 0.13 0.8949 GROUP CCM 1.597356322 B 0.56089705 2.85 0.0056 GROUP P 0.000000000 B . . . NOTE: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable. The GLM Procedure Least Squares
Anova Standard Deviation
Means DBMD05 LSMEAN GROUP LSMEAN Number CC -1.44480000 1 CCM 0.07666667 2 P -1.52068966 3 Least Squares Means for effect GROUP Pr > |t| for H0: LSMean(i)=LSMean(j) i/j 1 2 3 1 0.0107 0.8949 2 0.0107 0.0056 3 0.8949 0.0056 NOTE: To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used. Adjustment for Multiple Comparisons: Tukey-Kramer Least Squares Means for effect GROUP Pr > |t| for H0: LSMean(i)=LSMean(j) i/j 1 2 3 1 0.0286 0.9904 2 0.0286 0.0154 3 0.9904 0.0154 The Analysis of Variance Table The Analysis of Variance table is just like any other ANOVA table. The Total Sum of Squares is the uncertainty that would be present if one had to predict individual responses without any other information. The best one could do is predict each observation to be equal to the overall sample mean. The ANOVA table partitions this variability into two parts. One portion is accounted for (some say "explained by") the model. It's the reduction in uncertainty that occurs when the ANOVA model, Yij = + i + ij is fitted to the data. The remaining portion is the uncertainty that remains even after the model is used. The model is considered to be statistically significant if it can account for a large amount of variability in the respons
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Anova Confidence Interval
with us Cross Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated is a question anova t test 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 anova r square 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 How do I deduce the SD from regression and ANOVA tables? up vote -2 down vote favorite This http://www.jerrydallal.com/lhsp/aov1out.htm is a Minitab printout. I want to find the value of A5, or S. I think S is supposed to be the sample standard deviation, but I don't know how to calculate it. Any tips on how I should go about calculating it? estimation self-study share|improve this question edited Mar 31 '11 at 22:35 whuber♦ 144k17280540 asked Mar 31 '11 at 21:48 Beatrice 240248 1 Is this for a homework or a test? "A5", "A6", and "A7" look like they are placeholders for http://stats.stackexchange.com/questions/9023/how-do-i-deduce-the-sd-from-regression-and-anova-tables values that were produced but are being hidden from you on purpose. –whuber♦ Mar 31 '11 at 22:02 It's a homework problem. I can do A6 and A7 by myself, I just need some tips on A5. –Beatrice Mar 31 '11 at 22:28 1 Consider the relationships between SD, variance, and total sum of squares about the mean. –whuber♦ Mar 31 '11 at 22:36 add a comment| 1 Answer 1 active oldest votes up vote 1 down vote accepted I got it! It's the sqrt of residual SS / (n-2). Cheers! share|improve this answer answered Mar 31 '11 at 22:38 Beatrice 240248 1 In that case it's not the "sample standard deviation," but the residual standard deviation. :-) –whuber♦ Mar 31 '11 at 22:51 I see, thanks for your help :) –Beatrice Mar 31 '11 at 23:42 add a comment| Your Answer draft saved draft discarded Sign up or log in Sign up using Google Sign up using Facebook Sign up using Email and Password Post as a guest Name Email Post as a guest Name Email discard By posting your answer, you agree to the privacy policy and terms of service. Not the answer you're looking for? Browse other questions tagged estimation self-study or ask your own question. asked 5 years ago viewed 7070 times active 5 years ago Related 1How to get a weighted-estimate for mean difference?2How do I use student's-t distribution without the sample size?6How to find MLE when samples de
test of goodness-of-fit Power analysis Chi-square test of goodness-of-fit G–test of goodness-of-fit Chi-square test of independence G–test of independence Fisher's exact test Small numbers in chi-square and G–tests Repeated G–tests http://www.biostathandbook.com/standarderror.html of goodness-of-fit Cochran–Mantel– Haenszel test Descriptive statistics Central tendency Dispersion http://www.weibull.com/hotwire/issue95/relbasics95.htm Standard error Confidence limits Tests for one measurement variable One-sample t–test Two-sample t–test Independence Normality Homoscedasticity Data transformations One-way anova Kruskal–Wallis test Nested anova Two-way anova Paired t–test Wilcoxon signed-rank test Tests for multiple measurement variables Linear regression and correlation Spearman rank correlation Polynomial regression Analysis standard error of covariance Multiple regression Simple logistic regression Multiple logistic regression Multiple tests Multiple comparisons Meta-analysis Miscellany Using spreadsheets for statistics Displaying results in graphs Displaying results in tables Introduction to SAS Choosing the right test ⇐ Previous topic|Next topic ⇒ Table of Contents Standard error of the mean Summary Standard error of the mean tells you how accurate regression standard error your estimate of the mean is likely to be. Introduction When you take a sample of observations from a population and calculate the sample mean, you are estimating of the parametric mean, or mean of all of the individuals in the population. Your sample mean won't be exactly equal to the parametric mean that you're trying to estimate, and you'd like to have an idea of how close your sample mean is likely to be. If your sample size is small, your estimate of the mean won't be as good as an estimate based on a larger sample size. Here are 10 random samples from a simulated data set with a true (parametric) mean of 5. The X's represent the individual observations, the red circles are the sample means, and the blue line is the parametric mean. Individual observations (X's) and means (red dots) for random samples from a population with a parametric mean of 5 (horizontal line). Individual observations (X's) and means (circles) for random samples from a population with a parametric mean of 5 (
of variance, or ANOVA, is a powerful statistical technique that involves partitioning the observed variance into different components to conduct various significance tests. This article discusses the application of ANOVA to a data set that contains one independent variable and explains how ANOVA can be used to examine whether a linear relationship exists between a dependent variable and an independent variable. Sum of Squares and Mean Squares The total variance of an observed data set can be estimated using the following relationship: where: s is the standard deviation. yi is the ith observation. n is the number of observations. is the mean of the n observations. The quantity in the numerator of the previous equation is called the sum of squares. It is the sum of the squares of the deviations of all the observations, yi, from their mean, . In the context of ANOVA, this quantity is called the total sum of squares (abbreviated SST) because it relates to the total variance of the observations. Thus: The denominator in the relationship of the sample variance is the number of degrees of freedom associated with the sample variance. Therefore, the number of degrees of freedom associated with SST, dof(SST), is (n-1). The sample variance is also referred to as a mean square because it is obtained by dividing the sum of squares by the respective degrees of freedom. Therefore, the total mean square (abbreviated MST) is: When you attempt to fit a model to the observations, you are trying to explain some of the variation of the observations using this model. For the case of simple linear regression, this model is a line. In other words, you would be trying to see if the relationship between the independent variable and the dependent variable is a straight line. If the model is such that the resulting line passes through all of the observations, then you would have a "perfect" model, as shown in Figure 1. Figure 1: Perfect Model Passing Through All Observed Data Points The model explains all of the variability of the observations. T