Hi folks, Where can I find document re "how to read anova output"? Google found many of them. But seemingly non of them can explain to me following output:-> tabA = c(5.67, 5.67, 5.55, 5.57) > tabB = c(5.75, 5.47, 5.43, 5.45) > tabC = c(4.74, 4.45, 4.65, 4.94) > tabs = data.frame(tabA, tabB, tabC)> tablets = stack(tabs)> anova(lm(values ~ ind, data = tablets))Analysis of Variance Table Response: values Df Sum Sq Mean Sq F value Pr(>F) ind 2 2.05787 1.02893 45.239 2.015e-05 *** Residuals 9 0.20470 0.02274 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1> TukeyHSD(aov(values ~ ind, data = tablets))Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = values ~ ind, data = tablets) $ind diff lwr upr p adj tabB-tabA -0.09 -0.3877412 0.2077412 0.6866791 tabC-tabA -0.92 -1.2177412 -0.6222588 0.0000321 tabC-tabB -0.83 -1.1277412 -0.5322588 0.0000731 Please help. TIA B.R. Stephen L
On Wed, 2010-08-18 at 00:42 -0700, Stephen Liu wrote:> Hi folks, > > > Where can I find document re "how to read anova output"? Google found many of > them. But seemingly non of them can explain to me following output:- > > > > tabA = c(5.67, 5.67, 5.55, 5.57) > > tabB = c(5.75, 5.47, 5.43, 5.45) > > tabC = c(4.74, 4.45, 4.65, 4.94) > > tabs = data.frame(tabA, tabB, tabC) > > > tablets = stack(tabs) > > > > anova(lm(values ~ ind, data = tablets)) > Analysis of Variance Table > Response: values > Df Sum Sq Mean Sq F value Pr(>F) > ind 2 2.05787 1.02893 45.239 2.015e-05 *** > Residuals 9 0.20470 0.02274 > --- > Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1That output is designed to look like ANOVA tables from classical text books, so any introductory textbook designed for your particular background or area of knowledge would probably help you understand it. Many of the R books that do introductory stats aren't really concerned with teaching the stats side of things so might not go into much detail explaining the table, assuming that this is covered elsewhere. There will be exceptions of course. HTH G> > > TukeyHSD(aov(values ~ ind, data = tablets)) > Tukey multiple comparisons of means > 95% family-wise confidence level > Fit: aov(formula = values ~ ind, data = tablets) > $ind > diff lwr upr p adj > tabB-tabA -0.09 -0.3877412 0.2077412 0.6866791 > tabC-tabA -0.92 -1.2177412 -0.6222588 0.0000321 > tabC-tabB -0.83 -1.1277412 -0.5322588 0.0000731 > > > Please help. TIA > > > B.R. > Stephen L > > > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.-- %~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~% Dr. Gavin Simpson [t] +44 (0)20 7679 0522 ECRC, UCL Geography, [f] +44 (0)20 7679 0565 Pearson Building, [e] gavin.simpsonATNOSPAMucl.ac.uk Gower Street, London [w] http://www.ucl.ac.uk/~ucfagls/ UK. WC1E 6BT. [w] http://www.freshwaters.org.uk %~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%
On 18-Aug-10 07:42:23, Stephen Liu wrote:> Hi folks, > Where can I find document re "how to read anova output"? > Google found many of them. But seemingly non of them can > explain to me following output:- > >> tabA = c(5.67, 5.67, 5.55, 5.57) >> tabB = c(5.75, 5.47, 5.43, 5.45) >> tabC = c(4.74, 4.45, 4.65, 4.94) >> tabs = data.frame(tabA, tabB, tabC) > >> tablets = stack(tabs) > >> anova(lm(values ~ ind, data = tablets)) > Analysis of Variance Table > Response: values > Df Sum Sq Mean Sq F value Pr(>F) > ind 2 2.05787 1.02893 45.239 2.015e-05 *** > Residuals 9 0.20470 0.02274 > --- > Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The above is the basic standard format for the results of a 1-way analysis of variance (differences between means of groups compared with within-group differences between observations and group means). You need to understand how that works (basic statistical theory) before even thinking of looking at the Tukey thing (omitted in this reply). The following is an explanation of your 1-way ANOVA written entirely in R (preceded by a duplicate of your ANOVA output): ## anova(lm(values ~ ind, data = tablets)) ## Analysis of Variance Table ## Response: values ## Df Sum Sq Mean Sq F value Pr(>F) ## ind 2 2.05787 1.02893 45.239 2.015e-05 *** ## Residuals 9 0.20470 0.02274 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 tabA = c(5.67, 5.67, 5.55, 5.57) tabB = c(5.75, 5.47, 5.43, 5.45) tabC = c(4.74, 4.45, 4.65, 4.94) nA <- length(tabA) ; nB <- length(tabB) ; nC <- length(tabC) nG <- nA + nB + nC mG <- mean(c(tabA,tabB,tabC)) mA <- mean(tabA) ; mB <- mean(tabB) ; mC <- mean(tabC) SSres <- sum((tabA-mA)^2) + sum((tabB-mB)^2) + sum((tabC-mC)^2) SSres # = 0.2047 SSeff <- nA*(mA-mG)^2 + nB*(mB-mG)^2 + nC*(mC-mG)^2 SSeff # = 2.057867 ## Number of groups = 3 hence df.groups = (3-1) = 2 df.groups <- 2 meanSSeff <- SSeff/df.groups meanSSeff # = 1.028933 ## df for residuals in each group = (n.group - 1): df.res <- (nA-1) + (nB-1) + (nC-1) ## = 3 + 3 + 3 = 9 meanSSres <- SSres/df.res meanSSres # = 0.02274444 ## Fisher's F-ratio statistic = meanSSeff/meanSSres: F <- meanSSeff/meanSSres F # = 45.23889 ## P-value for F as test of difference between group means ## relative to within-group residuals (upper tail): Pval <- pf(F, df.groups, df.res, lower.tail=FALSE) Pval # = 2.015227e-05 Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk> Fax-to-email: +44 (0)870 094 0861 Date: 18-Aug-10 Time: 09:41:08 ------------------------------ XFMail ------------------------------
Hi, Take a look at http://www.khanacademy.org/ Look near the bottom of the page and there is a whole section on statistics and 3 videos on ANOVA. It is a very good introduction and I find it very useful to know how the test works so that I'm not using a "Black Box" Also I wrote up a little section on ANOVA that you can see at: https://sites.google.com/site/davidsstatistics/using-r/anova-nonparameteric Take Care David ----- Take Care David Doyle -- View this message in context: http://r.789695.n4.nabble.com/How-to-read-ANOVA-output-tp2329457p4605879.html Sent from the R help mailing list archive at Nabble.com.