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

[Fox, John]

Dear Nhat Tran,

One more thing: You could specify the model even more compactly as

  mod <- lm(KIC ~ (tem + ac + av + thick)^2)

Best,
 John

> -----Original Message-----
> From: R-help [mailto:r-help-bounces using r-project.org] On Behalf Of Fox, John
> Sent: Tuesday, November 6, 2018 8:41 PM
> To: Thanh Tran <masternhattt using gmail.com>
> Cc: r-help using r-project.org
> Subject: Re: [R] Sum of Squares Type I, II, III for ANOVA
> 
> 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.
> > ______________________________________________
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> ______________________________________________
> 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.