Dear Nhat Tran, The output that you show is unreadable and as far as I can see, the data aren't attached, but perhaps the following will help: First, if you want Anova() to compute type III tests, then you have to set the contrasts properly *before* you fit the model, not after. Second, you can specify the model much more compactly as
mod <- lm(KIC ~ tem*ac + tem*av + tem*thick + ac*av +ac*thick + av*thick) Finally, as sound general practice, I'd not attach the data, but rather put your recoded variables in the data frame and then specify the data argument to lm(). I hope that this helps, John ----------------------------------------------------------------- John Fox Professor Emeritus McMaster University Hamilton, Ontario, Canada Web: https://socialsciences.mcmaster.ca/jfox/ > -----Original Message----- > From: R-help [mailto:r-help-boun...@r-project.org] On Behalf Of Thanh Tran > Sent: Tuesday, November 6, 2018 6:58 PM > To: r-help@r-project.org > Subject: [R] Sum of Squares Type I, II, III for ANOVA > > Hi everyone, > I'm studying the ANOVA in R and have some questions to share. I investigate > the effects of 4 factors (temperature-3 levels, asphalt content-3 levels, air > voids-2 levels, and sample thickness-3 levels) on the hardness of asphalt > concrete in the tensile test (abbreviated as KIC). These data were taken from > a > acticle paper. The codes were wrriten as the follows: > > > data = read.csv("Saha research.csv", header =T) > > attach(data) > > tem = as.factor(temperature) > > ac= as.factor (AC) > > av = as.factor(AV) > > thick = as.factor(Thickness) > > model = > lm(KIC~tem+ac+av+thick+tem:ac+tem:av+tem:thick+ac:av+ac:thick+av:thick) > > anova(model) #Type I tests > > library(car) Loading required package: carData > > anova(lm(KIC~tem+ac+av+thick+tem:ac+tem:av+tem:thick+ac:av+ac:thick+av > :thick),type=2) > Error: $ operator is invalid for atomic vectors > > options(contrasts = c("contr.sum", "contr.poly")) > > Anova(model,type="3") # Type III tests > > Anova(model,type="2") # Type II tests > > With R, three results from Type I, II, and III almost have the same as > follows. > > Analysis of Variance Table Response: KIC Df Sum Sq Mean Sq F value Pr(>F) > tem 2 15.3917 7.6958 427.9926 < 2.2e-16 *** ac 2 0.1709 0.0854 4.7510 > 0.0096967 ** av 1 1.9097 1.9097 106.2055 < 2.2e-16 *** thick 2 0.2041 > 0.1021 5.6756 0.0040359 ** tem:ac 4 0.5653 0.1413 7.8598 6.973e-06 *** > tem:av 2 1.7192 0.8596 47.8046 < 2.2e-16 *** tem:thick 4 0.0728 0.0182 > 1.0120 0.4024210 ac:av 2 0.3175 0.1588 8.8297 0.0002154 *** ac:thick 4 > 0.0883 0.0221 1.2280 0.3003570 av:thick 2 0.0662 0.0331 1.8421 0.1613058 > Residuals 190 3.4164 0.0180 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ > 0.05 ‘.’ 0.1 ‘ ’ 1 > > However, these results are different from the results in the article, > especially > for the interaction (air voids and sample thickness). The results presented in > the article are as follows: > Analysis of variance for KIC, using Adjusted SS for tests. Source DF Seq SS > Adj > MS F-stat P-value Model findings Temperature 2 15.39355 7.69677 426.68 > <0.01 Significant AC 2 0.95784 0.47892 26.55 <0.01 Significant AV 1 0.57035 > 0.57035 31.62 <0.01 Significant Thickness 2 0.20269 0.10135 5.62 <0.01 > Significant Temperature⁄AC 4 1.37762 0.34441 19.09 <0.01 Significant > Temperature⁄AV 2 0.8329 0.41645 23.09 <0.01 Significant > Temperature⁄thickness 4 0.07135 0.01784 0.99 0.415 Not significant AC⁄AV 2 > 0.86557 0.43279 23.99 <0.01 Significant AC⁄thickness 4 0.04337 0.01084 0.6 > 0.662 Not significant AV⁄thickness 2 0.17394 0.08697 4.82 <0.01 Significant > Error 190 3.42734 0.01804 Total 215 23.91653 > > Therefore, I wonder that whether there is an error in my code or there is > another type of ANOVA in R. If you could answer my problems, I would be > most grateful. > Best regards, > Nhat Tran > Ps: I also added a CSV file and the paper for practicing R. > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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. ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.