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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Mon, 30 Nov 2015 12:11:39 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/30/t14488855173njktwal1i1laat.htm/, Retrieved Tue, 14 May 2024 13:43:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284576, Retrieved Tue, 14 May 2024 13:43:54 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

131

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Two-Way ANOVA] [] [2015-11-30 12:11:39] [33f7124a987e21c75039d3065d74d143] [Current]

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Dataseries X:

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Histogram

Boxplots

7.5 1.5 2.1
6 2.1 2
6.5 2.1 2
1 1.9 2.1
1 1.6 2
5.5 2.1 2.3
8.5 2.1 2.1
6.5 2.2 2.1
4.5 1.5 2.2
2 1.9 2.1
5 2.2 2.1
0.5 1.6 2.1
5 1.5 2
5 1.9 2.3
2.5 0.1 1.8
5 2.2 2
5.5 1.8 2.2
3.5 1.6 2
3 2.2 2.1
4 2.1 2
0.5 1.9 1.8
6.5 1.6 2.2
4.5 1.9 2.2
7.5 2.2 1.7
5.5 1.8 2.1
4 2.4 2.3
7.5 2.4 2.7
7 2.5 1.9
4 1.9 2
5.5 2.1 2
2.5 1.9 1.9
5.5 2.1 2
3.5 1.5 2
2.5 1.9 2.1
4.5 2.1 2
4.5 1.5 1.8
4.5 2.1 2
6 2.1 2.2
2.5 1.8 2.2
5 2.4 2.1
0 2.1 1.8
5 1.9 1.9
6.5 2.1 2.1
5 1.9 2
6 2.4 1.9
4.5 2.1 2.2
5.5 2.2 2
1 2.2 2
7.5 1.8 1.7
6 2.1 2
5 2.4 2.2
1 2.2 1.7
5 2.1 2
6.5 1.5 2.2
7 1.9 2
4.5 1.8 1.9
0 1.8 2
8.5 1.6 2
3.5 1.2 1.6
7.5 1.8 2.1
3.5 1.5 2.1
6 2.1 2
1.5 2.4 1.9
9 2.4 2.2
3.5 1.5 2.1
3.5 1.8 1.8
4 2.1 2.3
6.5 2.2 2.3
7.5 2.1 2.2
6 1.9 2.1
5 2.1 2.2
5.5 1.9 1.9
3.5 1.6 1.8
7.5 2.4 2.1
6.5 1.9 2
6.5 2.1 2.1
6.5 1.8 2.1
7 2.1 2.1
3.5 2.4 1.8
1.5 2.1 2
4 2.2 2.1
7.5 2.1 1.9
4.5 2.2 2.1
0 1.6 1
3.5 2.4 2.2
5.5 2.1 2.1
5 1.9 1.9
4.5 2.4 2
2.5 2.1 1.9
7.5 1.8 2
7 2.1 1.8
0 1.8 2
4.5 1.9 2
3 1.9 2
1.5 2.4 1.8
3.5 1.8 2
2.5 1.8 1.1
5.5 2.1 1.8
8 2.1 1.8
1 2.4 2
5 1.9 1.9
4.5 1.8 2.1
3 1.8 1.6
3 2.2 2.2
8 2.4 1.9
2.5 1.8 2
7 2.4 2.1
0 1.8 1.3
1 1.9 1.8
3.5 2.4 1.9
5.5 2.1 2.1
5.5 1.9 1.8
0.5 2.1 0.75
7.5 2.7 1.5
9 2.1 3
9.5 2.1 2.25
8.5 2.1 3
7 2.1 1.5
8 2.1 3
10 2.1 3
7 2.1 3
8.5 2.1 0.75
9 2.4 3
9.5 1.95 2.25
4 2.1 1.5
6 2.1 1.5
8 1.95 2.25
5.5 2.1 3
9.5 2.4 3
7.5 2.1 1.5
7 2.25 2.25
7.5 2.4 2.25
8 2.25 1.5
7 2.55 2.25
7 1.95 1.5
6 2.4 2.25
10 2.1 2.25
2.5 2.1 3
9 2.4 3
8 2.1 3
6 2.1 1.5
8.5 2.25 3
6 2.25 3
9 2.4 2.25
8 2.1 2.25
9 2.4 2.25
5.5 2.1 3
7 2.1 2.25
5.5 2.25 3
9 2.25 3
2 2.4 1.5
8.5 2.25 2.25
9 2.25 3
8.5 2.1 2.25
9 2.1 1.5
7.5 2.1 2.25
10 2.7 2.25
9 2.1 1.5
7.5 2.1 2.25
6 2.25 1.5
10.5 2.7 2.25
8.5 2.4 3
8 2.1 3
10 2.1 3
10.5 2.4 3
6.5 1.95 1.5
9.5 2.7 2.25
8.5 2.1 1.5
7.5 2.25 2.25
5 2.1 2.25
8 2.7 2.25
10 2.1 3
7 2.1 1.5
7.5 1.65 2.25
7.5 1.65 2.25
9.5 2.1 3
6 2.1 2.25
10 2.1 3
7 2.1 2.25
3 2.1 1.5
6 2.4 3
7 2.4 1.5
10 2.1 3
7 2.25 3
3.5 2.4 3
8 2.1 3
10 2.1 2.25
5.5 2.4 2.25
6 2.4 0.75
6.5 2.1 3
6.5 2.1 0.75
8.5 2.4 1.5
4 2.1 1.5
9.5 2.7 3
8 2.1 1.5
8.5 2.1 2.25
5.5 2.25 3
7 2.1 3
9 2.4 1.5
8 2.25 3
10 2.25 3
8 2.1 1.5
6 2.1 1.5
8 2.4 2.25
5 2.25 1.5
9 2.1 1.5
4.5 2.1 2.25
8.5 1.65 1.5
9.5 2.7 3
8.5 2.1 3
7.5 1.95 0.75
7.5 2.25 1.5
5 2.4 1.5
7 1.95 2.25
8 2.1 2.25
5.5 2.4 1.5
8.5 2.1 2.25
9.5 2.4 2.25
7 2.4 0.75
8 2.4 2.25
8.5 2.25 3
3.5 2.4 0.75
6.5 2.1 0.75
6.5 2.1 3
10.5 1.8 3
8.5 2.7 3
8 2.1 3
10 2.1 1.5
10 2.4 3
9.5 2.55 3
9 2.55 3
10 2.1 3
7.5 2.1 1.5
4.5 2.1 2.25
4.5 2.25 0.75
0.5 2.25 0.75
6.5 2.1 2.25
4.5 2.1 3
5.5 1.95 2.25
5 2.4 3
6 2.1 2.25
4 2.4 3
8 2.4 1.5
10.5 2.4 3
6.5 1.95 0.75
8 2.1 1.5
8.5 2.1 3
5.5 2.55 3
7 2.1 3
5 2.1 2.25
3.5 2.1 2.25
5 1.95 3
9 2.25 1.5
8.5 2.4 2.25
5 1.95 2.25
9.5 2.1 2.25
3 2.1 0.75
1.5 1.95 2.25
6 2.1 1.5
0.5 2.1 2.25
6.5 1.95 1.5
7.5 2.1 0.75
4.5 1.95 1.5
8 2.4 1.5
9 2.4 2.25
7.5 2.4 1.5
8.5 1.95 1.5
7 2.7 3
9.5 2.1 2.25
6.5 1.95 1.5
9.5 2.1 0.75
6 1.95 2.25
8 2.1 3
9.5 2.25 3
8 2.7 1.5
8 2.1 1.5
9 2.4 2.25
5 1.35 0.75

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	0 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284576&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284576&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284576&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	0 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Parameters (Session):

par4 = FALSE ;

Parameters (R input):

par1 = ; par2 = ; par3 = ; par4 = FALSE ;

R code (references can be found in the software module):

par4 <- 'FALSE'
par3 <- ''
par2 <- ''
par1 <- ''
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')

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Figures (Output of Computation)

Input Parameters & R Code