# Sum of Squares Type I, II, III for ANOVA

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## 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. ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Sum of Squares Type I, II, III for ANOVA

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