[R] Sum of Squares Type I, II, III for ANOVA

[Fox, John]

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-bounces using r-project.org] On Behalf Of Thanh Tran
> Sent: Tuesday, November 6, 2018 6:58 PM
> To: r-help using 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 using 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.