Dear Thanh Tran,
When you start a discussion on r-help, it's polite to keep it there so other
people can see what transpires. I'm consequently cc'ing this response to the
r-help list.
The problem with your code is that anova(), as opposed to Anova(), has no type
argument.
Here's what I get with your data. I hope that the code and output don't get too
mangled:
> data <- read.csv("Saha research.csv", header=TRUE)
> data <- within(data, {
+ tem <- as.factor(temperature)
+ ac <- as.factor (AC)
+ av <- as.factor(AV)
+ thick <- as.factor(Thickness)
+ })
> library(car)
Loading required package: carData
> options(contrasts = c("contr.sum", "contr.poly"))
> mod <- lm(KIC ~ tem*ac + tem*av + tem*thick + ac*av +ac*thick + av*thick,
+ data=data)
> anova(mod) # type I (sequential)
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
> Anova(mod) # type II
Anova Table (Type II tests)
Response: KIC
Sum Sq Df F value Pr(>F)
tem 15.3917 2 427.9926 < 2.2e-16 ***
ac 0.1709 2 4.7510 0.0096967 **
av 1.9097 1 106.2055 < 2.2e-16 ***
thick 0.2041 2 5.6756 0.0040359 **
tem:ac 0.5653 4 7.8598 6.973e-06 ***
tem:av 1.7192 2 47.8046 < 2.2e-16 ***
tem:thick 0.0728 4 1.0120 0.4024210
ac:av 0.3175 2 8.8297 0.0002154 ***
ac:thick 0.0883 4 1.2280 0.3003570
av:thick 0.0662 2 1.8421 0.1613058
Residuals 3.4164 190
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> Anova(mod, type=3) # type III
Anova Table (Type III tests)
Response: KIC
Sum Sq Df F value Pr(>F)
(Intercept) 102.430 1 5696.4740 < 2.2e-16 ***
tem 15.392 2 427.9926 < 2.2e-16 ***
ac 0.171 2 4.7510 0.0096967 **
av 1.910 1 106.2055 < 2.2e-16 ***
thick 0.204 2 5.6756 0.0040359 **
tem:ac 0.565 4 7.8598 6.973e-06 ***
tem:av 1.719 2 47.8046 < 2.2e-16 ***
tem:thick 0.073 4 1.0120 0.4024210
ac:av 0.318 2 8.8297 0.0002154 ***
ac:thick 0.088 4 1.2280 0.3003570
av:thick 0.066 2 1.8421 0.1613058
Residuals 3.416 190
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
If you have questions about Minitab there's probably another place to ask. It's
not my opinion that type-III tests are generally preferable to type-II tests.
Focus, in my opinion, should be on what hypotheses are being tested. If you
want to see more detail, you could consult the book with which the car package
is associated: see citation(package="car").
Best,
John
> -----Original Message-----
> From: Thanh Tran [mailto:masternha...@gmail.com]
> Sent: Tuesday, November 6, 2018 9:15 PM
> To: Fox, John <j...@mcmaster.ca>
> Subject: Re: [R] Sum of Squares Type I, II, III for ANOVA
>
> Dear Prof. John Fox,
> Thank you for your answer. The CSV data was added as the attached file again.
> I try to set the contrasts properly *before* I fit the model but I received a
> problem as follows.
>
> > setwd("C:/NHAT/HOC TAP/R/Test/Anova") 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)
> > library(car)
> Loading required package: carData
> > options(contrasts = c("contr.sum", "contr.poly")) mod <- lm(KIC ~
> > tem*ac + tem*av + tem*thick + ac*av +ac*thick + av*thick)
> > anova(mod,type= 3)
> Error: $ operator is invalid for atomic vectors
>
>
> Another problem is that in the paper that I read, the authors used MINITAB to
> analyze Anova. The authors use "adjusted sums of squares" calculate the p-
> value. So which should I use? Type I adjusted SS or Type III sequential SS?
> Minitab help tells me that I would "usually" want to use type III adjusted
> SS, as
> type I sequential "sums of squares can differ when your design is unbalanced"
> - which mine is. The R functions I am using are clearly using the type I
> sequential SS.
>
> Thanks
> Nhat Tran
>
>
> Vào Th 4, 7 thg 11, 2018 vào lúc 10:41 Fox, John <j...@mcmaster.ca
> <mailto:j...@mcmaster.ca> > đã viết:
>
>
> 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 <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 <mailto: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 <mailto:R-help@r-project.org> mailing list --
> To UNSUBSCRIBE and more, see
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> > PLEASE do read the posting guide http://www.R-project.org/posting-
> > guide.html
> > and provide commented, minimal, self-contained, reproducible
> code.
>
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