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R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Wed, 06 Nov 2013 07:02:20 -0500

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/2013/Nov/06/t1383739364zraaaxouws44v0j.htm/, Retrieved Fri, 01 Nov 2024 02:20:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=222900, Retrieved Fri, 01 Nov 2024 02:20:00 +0000

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IsPrivate?

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Estimated Impact

145

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

-       [Two-Way ANOVA] [] [2013-11-06 12:02:20] [0968a8b67fc621ded3325342a6e4b095] [Current]

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Dataseries X:

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Histogram

Boxplots

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0 0 'H' 0
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0 0 'E' 1
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1 1 'F' 1
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0 0 'E' 0
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0 0 'E' 0
0 0 'F' 1
0 0 'F' 1

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=222900&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]5 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=222900&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=222900&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	5 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	0.045	-0.045	-0.045	-0.045	0.136	0.545

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.045 & -0.045 & -0.045 & -0.045 & 0.136 & 0.545 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=222900&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.045[/C][C]-0.045[/C][C]-0.045[/C][C]-0.045[/C][C]0.136[/C][C]0.545[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=222900&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=222900&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
means	0.045	-0.045	-0.045	-0.045	0.136	0.545

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	0.107	0.107	3.624	0.06
Treatment_B	1	0.009	0.005	0.155	0.856
Treatment_A:Treatment_B	1	0.475	0.237	8.047	0.001
Residuals	111	3.273	0.029

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.107 & 0.107 & 3.624 & 0.06 \tabularnewline
Treatment_B & 1 & 0.009 & 0.005 & 0.155 & 0.856 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.475 & 0.237 & 8.047 & 0.001 \tabularnewline
Residuals & 111 & 3.273 & 0.029 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=222900&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]0.107[/C][C]0.107[/C][C]3.624[/C][C]0.06[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.009[/C][C]0.005[/C][C]0.155[/C][C]0.856[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.475[/C][C]0.237[/C][C]8.047[/C][C]0.001[/C][/ROW]
[ROW][C]Residuals[/C][C]111[/C][C]3.273[/C][C]0.029[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=222900&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=222900&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
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	0.107	0.107	3.624	0.06
Treatment_B	1	0.009	0.005	0.155	0.856
Treatment_A:Treatment_B	1	0.475	0.237	8.047	0.001
Residuals	111	3.273	0.029

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
1-0	0.064	-0.003	0.131	0.06
F-E	0.014	-0.079	0.107	0.935
H-E	0.021	-0.072	0.114	0.857
H-F	0.007	-0.084	0.098	0.982
1:E-0:E	-0.045	-0.212	0.121	0.969
0:F-0:E	-0.045	-0.204	0.113	0.961
1:F-0:E	0.045	-0.105	0.196	0.951
0:H-0:E	-0.045	-0.179	0.088	0.921
1:H-0:E	0.455	0.087	0.822	0.007
0:F-1:E	0	-0.174	0.174	1
1:F-1:E	0.091	-0.076	0.258	0.613
0:H-1:E	0	-0.152	0.152	1
1:H-1:E	0.5	0.125	0.875	0.002
1:F-0:F	0.091	-0.067	0.249	0.557
0:H-0:F	0	-0.142	0.142	1
1:H-0:F	0.5	0.129	0.871	0.002
0:H-1:F	-0.091	-0.224	0.042	0.363
1:H-1:F	0.409	0.041	0.777	0.02
1:H-0:H	0.5	0.139	0.861	0.001

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 0.064 & -0.003 & 0.131 & 0.06 \tabularnewline
F-E & 0.014 & -0.079 & 0.107 & 0.935 \tabularnewline
H-E & 0.021 & -0.072 & 0.114 & 0.857 \tabularnewline
H-F & 0.007 & -0.084 & 0.098 & 0.982 \tabularnewline
1:E-0:E & -0.045 & -0.212 & 0.121 & 0.969 \tabularnewline
0:F-0:E & -0.045 & -0.204 & 0.113 & 0.961 \tabularnewline
1:F-0:E & 0.045 & -0.105 & 0.196 & 0.951 \tabularnewline
0:H-0:E & -0.045 & -0.179 & 0.088 & 0.921 \tabularnewline
1:H-0:E & 0.455 & 0.087 & 0.822 & 0.007 \tabularnewline
0:F-1:E & 0 & -0.174 & 0.174 & 1 \tabularnewline
1:F-1:E & 0.091 & -0.076 & 0.258 & 0.613 \tabularnewline
0:H-1:E & 0 & -0.152 & 0.152 & 1 \tabularnewline
1:H-1:E & 0.5 & 0.125 & 0.875 & 0.002 \tabularnewline
1:F-0:F & 0.091 & -0.067 & 0.249 & 0.557 \tabularnewline
0:H-0:F & 0 & -0.142 & 0.142 & 1 \tabularnewline
1:H-0:F & 0.5 & 0.129 & 0.871 & 0.002 \tabularnewline
0:H-1:F & -0.091 & -0.224 & 0.042 & 0.363 \tabularnewline
1:H-1:F & 0.409 & 0.041 & 0.777 & 0.02 \tabularnewline
1:H-0:H & 0.5 & 0.139 & 0.861 & 0.001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=222900&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]1-0[/C][C]0.064[/C][C]-0.003[/C][C]0.131[/C][C]0.06[/C][/ROW]
[ROW][C]F-E[/C][C]0.014[/C][C]-0.079[/C][C]0.107[/C][C]0.935[/C][/ROW]
[ROW][C]H-E[/C][C]0.021[/C][C]-0.072[/C][C]0.114[/C][C]0.857[/C][/ROW]
[ROW][C]H-F[/C][C]0.007[/C][C]-0.084[/C][C]0.098[/C][C]0.982[/C][/ROW]
[ROW][C]1:E-0:E[/C][C]-0.045[/C][C]-0.212[/C][C]0.121[/C][C]0.969[/C][/ROW]
[ROW][C]0:F-0:E[/C][C]-0.045[/C][C]-0.204[/C][C]0.113[/C][C]0.961[/C][/ROW]
[ROW][C]1:F-0:E[/C][C]0.045[/C][C]-0.105[/C][C]0.196[/C][C]0.951[/C][/ROW]
[ROW][C]0:H-0:E[/C][C]-0.045[/C][C]-0.179[/C][C]0.088[/C][C]0.921[/C][/ROW]
[ROW][C]1:H-0:E[/C][C]0.455[/C][C]0.087[/C][C]0.822[/C][C]0.007[/C][/ROW]
[ROW][C]0:F-1:E[/C][C]0[/C][C]-0.174[/C][C]0.174[/C][C]1[/C][/ROW]
[ROW][C]1:F-1:E[/C][C]0.091[/C][C]-0.076[/C][C]0.258[/C][C]0.613[/C][/ROW]
[ROW][C]0:H-1:E[/C][C]0[/C][C]-0.152[/C][C]0.152[/C][C]1[/C][/ROW]
[ROW][C]1:H-1:E[/C][C]0.5[/C][C]0.125[/C][C]0.875[/C][C]0.002[/C][/ROW]
[ROW][C]1:F-0:F[/C][C]0.091[/C][C]-0.067[/C][C]0.249[/C][C]0.557[/C][/ROW]
[ROW][C]0:H-0:F[/C][C]0[/C][C]-0.142[/C][C]0.142[/C][C]1[/C][/ROW]
[ROW][C]1:H-0:F[/C][C]0.5[/C][C]0.129[/C][C]0.871[/C][C]0.002[/C][/ROW]
[ROW][C]0:H-1:F[/C][C]-0.091[/C][C]-0.224[/C][C]0.042[/C][C]0.363[/C][/ROW]
[ROW][C]1:H-1:F[/C][C]0.409[/C][C]0.041[/C][C]0.777[/C][C]0.02[/C][/ROW]
[ROW][C]1:H-0:H[/C][C]0.5[/C][C]0.139[/C][C]0.861[/C][C]0.001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=222900&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=222900&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
	diff	lwr	upr	p adj
1-0	0.064	-0.003	0.131	0.06
F-E	0.014	-0.079	0.107	0.935
H-E	0.021	-0.072	0.114	0.857
H-F	0.007	-0.084	0.098	0.982
1:E-0:E	-0.045	-0.212	0.121	0.969
0:F-0:E	-0.045	-0.204	0.113	0.961
1:F-0:E	0.045	-0.105	0.196	0.951
0:H-0:E	-0.045	-0.179	0.088	0.921
1:H-0:E	0.455	0.087	0.822	0.007
0:F-1:E	0	-0.174	0.174	1
1:F-1:E	0.091	-0.076	0.258	0.613
0:H-1:E	0	-0.152	0.152	1
1:H-1:E	0.5	0.125	0.875	0.002
1:F-0:F	0.091	-0.067	0.249	0.557
0:H-0:F	0	-0.142	0.142	1
1:H-0:F	0.5	0.129	0.871	0.002
0:H-1:F	-0.091	-0.224	0.042	0.363
1:H-1:F	0.409	0.041	0.777	0.02
1:H-0:H	0.5	0.139	0.861	0.001

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	5	4.728	0.001
	111

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 4.728 & 0.001 \tabularnewline
  & 111 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=222900&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]5[/C][C]4.728[/C][C]0.001[/C][/ROW]
[ROW][C] [/C][C]111[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=222900&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=222900&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
	Df	F value	Pr(>F)
Group	5	4.728	0.001
	111

Figure 1

PNG link

Postscript link

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Figure 2

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Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = TRUE ;

Parameters (R input):

par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = TRUE ;

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

par4 <- 'TRUE'
par3 <- '5'
par2 <- '3'
par1 <- '4'
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code