----- Original Message ---- From: "ted.hard...@manchester.ac.uk" <ted.hard...@manchester.ac.uk> To: r-help@r-project.org Cc: Stephen Liu <sati...@yahoo.com> Sent: Wed, August 18, 2010 4:41:11 PM Subject: RE: [R] How to read ANOVA output
Hi Ted, Thanks for your advice. - snip - >You need to understand how that works (basic >statistical theory) before even thinking of looking at the >Tukey thing (omitted in this reply). I have been googling a while. There were many documents discovered. I wonder where shall I start? Which direction shall I choose? Could you please shed me some hints. TIA I found follows; Basic Inferential Statistics: Theory and Application http://owl.english.purdue.edu/owl/resource/672/05/ Basic Statistics-I http://works.bepress.com/durgesh_chandra_pathak/10/ file download basic_Statistics-I-fulltext.pdf >The following is an explanation of your 1-way ANOVA written >entirely in R (preceded by a duplicate of your ANOVA output): Performed following steps:- ## 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 > nG [1] 12 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 [1] 0.2047 ( I suppose - ^2 here means a raised to the power of 2) ?? ( SSres is the sum of squares residual (or sum of squares error it is sometimes called), which is the variation in the dependent variable that is not predicted by the model. Adding the SSreg to the SSres gives the SStotal, which represents how much variation there is in the data overall) ?? SSeff <- nA*(mA-mG)^2 + nB*(mB-mG)^2 + nC*(mC-mG)^2 SSeff # = 2.057867 [1] 2.057867 (What does SSeff refer to here)?? ## Number of groups = 3 hence df.groups = (3-1) = 2 (?df Description: Density, distribution function, quantile function and random generation for the F distribution with ‘df1’ and ‘df2’ degrees of freedom (and optional non-centrality parameter ‘ncp’). What does df refer here? ) ?? df.groups <- 2 meanSSeff <- SSeff/df.groups meanSSeff # = 1.028933 [1] 0.02274444 ## 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 [1] 0.02274444 ## Fisher's F-ratio statistic = meanSSeff/meanSSres: F <- meanSSeff/meanSSres F # = 45.23889 [1] 45.23889 (Fisher's F-ratio F-test ??? http://en.wikipedia.org/wiki/F-test ) ## 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 [1] 2.015227e-05 (The P-values for the Popular Distributions http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/pvalues.htm ) ?? If I'm wrong please correct me. TIA B.R. Stephen ______________________________________________ R-help@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.