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Paper 2012, Deel 3. ANOVA & Meervoudige Regressie; two-way ANOVA interacti...

Author*The author of this computation has been verified*
R Software Modulerwasp_Two Factor ANOVA.wasp
Title produced by softwareTwo-Way ANOVA
Date of computationSun, 16 Dec 2012 13:07:06 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/16/t13556812739c9o9ddwcwknxh2.htm/, Retrieved Fri, 29 Mar 2024 06:12:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200533, Retrieved Fri, 29 Mar 2024 06:12:09 +0000
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Original text written by user:
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User-defined keywords
Estimated Impact82
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [Paper 2012, Deel ...] [2012-12-16 18:07:06] [e4c351aee2a0bb2c047702ea90f356fa] [Current]
- R P     [Two-Way ANOVA] [Paper 2012, Deel ...] [2012-12-17 15:06:03] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
2	'HI'	'HI'
2	'HI'	'HI'
2	'LO'	'LO'
1	'LO'	'LO'
2	'HI'	'HI'
2	'HI'	'HI'
2	'HI'	'HI'
2	'HI'	'HI'
2	'HI'	'HI'
2	'HI'	'HI'
1	'HI'	'HI'
2	'HI'	'HI'
1	'HI'	'LO'
2	'HI'	'HI'
2	'LO'	'HI'
1	'LO'	'HI'
1	'HI'	'HI'
2	'HI'	'HI'
1	'HI'	'HI'
2	'LO'	'HI'
1	'LO'	'HI'
2	'LO'	'LO'
2	'HI'	'HI'
2	'HI'	'LO'
1	'HI'	'HI'
2	'HI'	'LO'
1	'HI'	'HI'
2	'LO'	'HI'
2	'LO'	'HI'
1	'HI'	'LO'
2	'LO'	'HI'
1	'LO'	'LO'
2	'HI'	'HI'
2	'HI'	'HI'
1	'HI'	'HI'
1	'LO'	'HI'
1	'LO'	'LO'
1	'HI'	'HI'
2	'LO'	'HI'
1	'HI'	'LO'
1	'HI'	'HI'
2	'HI'	'HI'
1	'HI'	'HI'
1	'HI'	'LO'
2	'HI'	'LO'
2	'HI'	'LO'
2	'HI'	'HI'
2	'LO'	'HI'
2	'HI'	'HI'
1	'HI'	'LO'
2	'LO'	'HI'
1	'LO'	'HI'
1	'LO'	'LO'
2	'HI'	'LO'
1	'LO'	'LO'
2	'HI'	'HI'
2	'HI'	'HI'
2	'LO'	'HI'
1	'HI'	'LO'
2	'HI'	'LO'
1	'LO'	'LO'
1	'HI'	'LO'
2	'HI'	'LO'
2	'LO'	'HI'
2	'HI'	'HI'
1	'HI'	'LO'
2	'HI'	'LO'
1	'LO'	'LO'
2	'HI'	'HI'
1	'HI'	'HI'
1	'HI'	'HI'
2	'LO'	'HI'
2	'HI'	'HI'
1	'HI'	'HI'
1	'HI'	'LO'
2	'HI'	'LO'
2	'HI'	'HI'
2	'HI'	'LO'
1	'LO'	'HI'
1	'HI'	'LO'
1	'LO'	'HI'
1	'HI'	'HI'
2	'HI'	'HI'
1	'HI'	'HI'
2	'LO'	'HI'
2	'LO'	'HI'
1	'HI'	'HI'
2	'LO'	'HI'
2	'LO'	'LO'
2	'LO'	'LO'
2	'LO'	'HI'
2	'HI'	'LO'
2	'HI'	'HI'
2	'LO'	'HI'
2	'LO'	'LO'
2	'HI'	'HI'
2	'HI'	'LO'
2	'HI'	'HI'
1	'HI'	'HI'
1	'LO'	'HI'
2	'HI'	'HI'
1	'HI'	'LO'
2	'HI'	'HI'
1	'LO'	'LO'
2	'LO'	'HI'
1	'HI'	'LO'
2	'HI'	'HI'
1	'HI'	'HI'
1	'HI'	'LO'
2	'HI'	'LO'
2	'LO'	'HI'
2	'LO'	'LO'
2	'LO'	'LO'
1	'LO'	'HI'
2	'HI'	'HI'
1	'HI'	'HI'
2	'LO'	'HI'
2	'HI'	'HI'
2	'LO'	'HI'
2	'HI'	'HI'
2	'LO'	'LO'
2	'LO'	'HI'
2	'HI'	'HI'
2	'HI'	'HI'
2	'LO'	'HI'
2	'LO'	'LO'
1	'HI'	'HI'
2	'HI'	'HI'
2	'LO'	'HI'
2	'HI'	'HI'
1	'LO'	'LO'
1	'LO'	'LO'
2	'HI'	'HI'
1	'LO'	'HI'
1	'HI'	'HI'
2	'LO'	'HI'
1	'LO'	'LO'
1	'HI'	'HI'
2	'LO'	'LO'
2	'HI'	'HI'
1	'LO'	'LO'
2	'LO'	'HI'
1	'LO'	'HI'
2	'LO'	'HI'
1	'LO'	'HI'
2	'HI'	'HI'
2	'LO'	'HI'
1	'HI'	'LO'
1	'LO'	'LO'
1	'HI'	'LO'
2	'HI'	'HI'
2	'HI'	'LO'
1	'HI'	'HI'
2	'HI'	'LO'
2	'HI'	'LO'
2	'LO'	'LO'
2	'HI'	'LO'
2	'LO'	'HI'
2	'LO'	'HI'
2	'HI'	'LO'
2	'LO'	'LO'
2	'HI'	'LO'




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
R Framework error message & 
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=200533&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=200533&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200533&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.







ANOVA Model
Response ~ Treatment_A * Treatment_B
means1.651-0.0920.074-0.153

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 1.651 & -0.092 & 0.074 & -0.153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200533&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]1.651[/C][C]-0.092[/C][C]0.074[/C][C]-0.153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200533&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200533&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

ANOVA Model
Response ~ Treatment_A * Treatment_B
means1.651-0.0920.074-0.153







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.8920.8923.8170.052
Treatment_B10.0120.0120.0510.822
Treatment_A:Treatment_B10.2120.2120.9090.342
Residuals15836.9150.234

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.892 & 0.892 & 3.817 & 0.052 \tabularnewline
Treatment_B & 1 & 0.012 & 0.012 & 0.051 & 0.822 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.212 & 0.212 & 0.909 & 0.342 \tabularnewline
Residuals & 158 & 36.915 & 0.234 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200533&T=2

[TABLE]
[ROW][C]ANOVA Statistics[/C][/ROW]
[ROW][C] [/C][C]Df[/C][C]Sum Sq[/C][C]Mean Sq[/C][C]F value[/C][C]Pr(>F)[/C][/ROW]
[ROW][C][/C][C]1[/C][C][/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Treatment_A[/C][C]1[/C][C]0.892[/C][C]0.892[/C][C]3.817[/C][C]0.052[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.012[/C][C]0.012[/C][C]0.051[/C][C]0.822[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.212[/C][C]0.212[/C][C]0.909[/C][C]0.342[/C][/ROW]
[ROW][C]Residuals[/C][C]158[/C][C]36.915[/C][C]0.234[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200533&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200533&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.8920.8923.8170.052
Treatment_B10.0120.0120.0510.822
Treatment_A:Treatment_B10.2120.2120.9090.342
Residuals15836.9150.234







Tukey Honest Significant Difference Comparisons
difflwruprp adj
LO-HI-0.154-0.310.0020.052
LO-HI0.017-0.1360.170.822
LO:HI-HI:HI-0.092-0.3590.1750.808
HI:LO-HI:HI0.074-0.180.3280.873
LO:LO-HI:HI-0.171-0.4670.1260.443
HI:LO-LO:HI0.166-0.1270.4590.456
LO:LO-LO:HI-0.079-0.4090.2520.926
LO:LO-HI:LO-0.245-0.5650.0750.197

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
LO-HI & -0.154 & -0.31 & 0.002 & 0.052 \tabularnewline
LO-HI & 0.017 & -0.136 & 0.17 & 0.822 \tabularnewline
LO:HI-HI:HI & -0.092 & -0.359 & 0.175 & 0.808 \tabularnewline
HI:LO-HI:HI & 0.074 & -0.18 & 0.328 & 0.873 \tabularnewline
LO:LO-HI:HI & -0.171 & -0.467 & 0.126 & 0.443 \tabularnewline
HI:LO-LO:HI & 0.166 & -0.127 & 0.459 & 0.456 \tabularnewline
LO:LO-LO:HI & -0.079 & -0.409 & 0.252 & 0.926 \tabularnewline
LO:LO-HI:LO & -0.245 & -0.565 & 0.075 & 0.197 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200533&T=3

[TABLE]
[ROW][C]Tukey Honest Significant Difference Comparisons[/C][/ROW]
[ROW][C] [/C][C]diff[/C][C]lwr[/C][C]upr[/C][C]p adj[/C][/ROW]
[ROW][C]LO-HI[/C][C]-0.154[/C][C]-0.31[/C][C]0.002[/C][C]0.052[/C][/ROW]
[ROW][C]LO-HI[/C][C]0.017[/C][C]-0.136[/C][C]0.17[/C][C]0.822[/C][/ROW]
[ROW][C]LO:HI-HI:HI[/C][C]-0.092[/C][C]-0.359[/C][C]0.175[/C][C]0.808[/C][/ROW]
[ROW][C]HI:LO-HI:HI[/C][C]0.074[/C][C]-0.18[/C][C]0.328[/C][C]0.873[/C][/ROW]
[ROW][C]LO:LO-HI:HI[/C][C]-0.171[/C][C]-0.467[/C][C]0.126[/C][C]0.443[/C][/ROW]
[ROW][C]HI:LO-LO:HI[/C][C]0.166[/C][C]-0.127[/C][C]0.459[/C][C]0.456[/C][/ROW]
[ROW][C]LO:LO-LO:HI[/C][C]-0.079[/C][C]-0.409[/C][C]0.252[/C][C]0.926[/C][/ROW]
[ROW][C]LO:LO-HI:LO[/C][C]-0.245[/C][C]-0.565[/C][C]0.075[/C][C]0.197[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200533&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200533&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Tukey Honest Significant Difference Comparisons
difflwruprp adj
LO-HI-0.154-0.310.0020.052
LO-HI0.017-0.1360.170.822
LO:HI-HI:HI-0.092-0.3590.1750.808
HI:LO-HI:HI0.074-0.180.3280.873
LO:LO-HI:HI-0.171-0.4670.1260.443
HI:LO-LO:HI0.166-0.1270.4590.456
LO:LO-LO:HI-0.079-0.4090.2520.926
LO:LO-HI:LO-0.245-0.5650.0750.197







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group31.2310.3
158

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.231 & 0.3 \tabularnewline
  & 158 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200533&T=4

[TABLE]
[ROW][C]Levenes Test for Homogeneity of Variance[/C][/ROW]
[ROW][C] [/C][C]Df[/C][C]F value[/C][C]Pr(>F)[/C][/ROW]
[ROW][C]Group[/C][C]3[/C][C]1.231[/C][C]0.3[/C][/ROW]
[ROW][C] [/C][C]158[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200533&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200533&T=4

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group31.2310.3
158



Parameters (Session):
par1 = 1 ; par2 = 3 ; par3 = 2 ; par4 = TRUE ;
Parameters (R input):
par1 = 1 ; par2 = 3 ; par3 = 2 ; par4 = TRUE ;
R code (references can be found in the software module):
par4 <- 'TRUE'
par3 <- '3'
par2 <- '2'
par1 <- '1'
cat1 <- as.numeric(par1) #
cat2<- as.numeric(par2) #
cat3 <- as.numeric(par3)
intercept<-as.logical(par4)
x <- t(x)
x1<-as.numeric(x[,cat1])
f1<-as.character(x[,cat2])
f2 <- as.character(x[,cat3])
xdf<-data.frame(x1,f1, f2)
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
(V3 <-dimnames(y)[[1]][cat3])
names(xdf)<-c('Response', 'Treatment_A', 'Treatment_B')
if(intercept == FALSE) (lmxdf<-lm(Response ~ Treatment_A * Treatment_B- 1, data = xdf) ) else (lmxdf<-lm(Response ~ Treatment_A * Treatment_B, data = xdf) )
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Model', length(lmxdf$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, lmxdf$call['formula'],length(lmxdf$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'means',,TRUE)
for(i in 1:length(lmxdf$coefficients)){
a<-table.element(a, round(lmxdf$coefficients[i], digits=3),,FALSE)
}
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Statistics', 5+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',,TRUE)
a<-table.element(a, 'Df',,FALSE)
a<-table.element(a, 'Sum Sq',,FALSE)
a<-table.element(a, 'Mean Sq',,FALSE)
a<-table.element(a, 'F value',,FALSE)
a<-table.element(a, 'Pr(>F)',,FALSE)
a<-table.row.end(a)
for(i in 1 : length(rownames(anova.xdf))-1){
a<-table.row.start(a)
a<-table.element(a,rownames(anova.xdf)[i] ,,TRUE)
a<-table.element(a, anova.xdf$Df[1],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[i], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[i], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'F value'[i], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Pr(>F)'[i], digits=3),,FALSE)
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'Residuals',,TRUE)
a<-table.element(a, anova.xdf$'Df'[i+1],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[i+1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[i+1], digits=3),,FALSE)
a<-table.element(a, ' ',,FALSE)
a<-table.element(a, ' ',,FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
bitmap(file='anovaplot.png')
boxplot(Response ~ Treatment_A + Treatment_B, data=xdf, xlab=V2, ylab=V1, main='Boxplots of ANOVA Groups')
dev.off()
bitmap(file='designplot.png')
xdf2 <- xdf # to preserve xdf make copy for function
names(xdf2) <- c(V1, V2, V3)
plot.design(xdf2, main='Design Plot of Group Means')
dev.off()
bitmap(file='interactionplot.png')
interaction.plot(xdf$Treatment_A, xdf$Treatment_B, xdf$Response, xlab=V2, ylab=V1, trace.label=V3, main='Possible Interactions Between Anova Groups')
dev.off()
if(intercept==TRUE){
thsd<-TukeyHSD(aov.xdf)
names(thsd) <- c(V2, V3, paste(V2, ':', V3, sep=''))
bitmap(file='TukeyHSDPlot.png')
layout(matrix(c(1,2,3,3), 2,2))
plot(thsd, las=1)
dev.off()
}
if(intercept==TRUE){
ntables<-length(names(thsd))
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Tukey Honest Significant Difference Comparisons', 5,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ', 1, TRUE)
for(i in 1:4){
a<-table.element(a,colnames(thsd[[1]])[i], 1, TRUE)
}
a<-table.row.end(a)
for(nt in 1:ntables){
for(i in 1:length(rownames(thsd[[nt]]))){
a<-table.row.start(a)
a<-table.element(a,rownames(thsd[[nt]])[i], 1, TRUE)
for(j in 1:4){
a<-table.element(a,round(thsd[[nt]][i,j], digits=3), 1, FALSE)
}
a<-table.row.end(a)
}
} # end nt
a<-table.end(a)
table.save(a,file='hsdtable.tab')
}#end if hsd tables
if(intercept==FALSE){
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'TukeyHSD Message', 1,TRUE)
a<-table.row.end(a)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Must Include Intercept to use Tukey Test ', 1, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')
}
library(car)
lt.lmxdf<-levene.test(lmxdf)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Levenes Test for Homogeneity of Variance', 4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ', 1, TRUE)
for (i in 1:3){
a<-table.element(a,names(lt.lmxdf)[i], 1, FALSE)
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Group', 1, TRUE)
for (i in 1:3){
a<-table.element(a,round(lt.lmxdf[[i]][1], digits=3), 1, FALSE)
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ', 1, TRUE)
a<-table.element(a,lt.lmxdf[[1]][2], 1, FALSE)
a<-table.element(a,' ', 1, FALSE)
a<-table.element(a,' ', 1, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')